FlexLab and LevLab: A Portable Lab for Dynamics and Control Teaching


 Barrie Lawson
 1 years ago
 Views:
Transcription
1 FlexLab and LevLab: A Portable Lab for Dynamics and Control Teaching Lei Zhou, Mohammad Imani Nejad, David L. Trumper Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, 39, USA Abstract This paper presents the design, modeling and control for an educational lab for control and mechatronics teaching in the department of Mechanical Engineering at MIT. The FlexLab is a system of flexible cantilever beam with permanent magnets attached to it, while the LevLab demonstrates a magnetic suspension system. Both labs are implemented on one printed circuit board, with actuators, sensors, power amplifiers arranged on it. This system works together with myrio from National Instruments. The design file for the system open source on the website of Precision Motion Control Lab at MIT. We would like to share the lab with others who might like to use it in their dynamics and control teaching. Keywords: educational lab, mechatronics, flexible beam, magnetic levitation. Introduction One major challenge in engineering course is offering student the chance of handson experiences, which is essential to obtain a fundamental understanding of phenomenas and design skills. However, in many circumstances, limited lab resources and concentrated lab time for classes may limit the depth of knowledge that student can learn. To address this, instructors for control system at MIT generated the idea of "portable educational labs". We believe that if we can make the lab portable and lend the hardware to student, the student can have chance to play with the system, discover the subtleties outside the structured lab time, and therefore achieve a better understanding of the knowledge. This will requires the educators to design a lowcost, portable, robust system that can demonstrate the intrinsic characteristics that make it applicable to a wide range of educational pursuits. Figure : Photograph of the FlexLab system. This paper introduces the design, modeling and control of the FlexLab/LevLab board, which is one of our our portable educational lab series. The design files of the lab can be downloaded at the website of Precision Motion Control Lab at MIT. The FlexLab is a system of flexible cantilever beam with permanent magnets attached to it, while the LevLab demonstrates a magnetic suspension system. Both labs are implemented on one printed circuit board, with actuators, sensors, power amplifiers arranged on it. This system works together with myrio from National Instruments [].. Hardware configuration Figure shows the hardware configuration of the FlexLab system, which is implemented as one printed circuit board (PCB). This system works together with NI myrio via the standard connector. The same system can be used for magnetic suspension experiment, known as LevLab. Figure shows the magnetic suspension with this system. In the design of the FlexLab, a inch long flexible cantilever beam made out of.5mm thick phosphore bronze sheet is anchored on the PCB. Two pair of disk shape permanent magnets are attached at the middle and at the end of cantilever beam, as shown in Figure. When the tip displacement of the can Preprint submitted to Mechatronics Figure : Photograph of the LevLab experiment November 7, 4
2 +5 V +5 V R m C m 8 V ref +  R R Coil R s +  R 4 R 3 V ref sum of sensor output(v) measured fitted V in Figure 3: Circuit diagram of the coil power amplifiers. The op amps are the power amplifiers. Here V re f is V. V re f is.5 V. Controlling signal in injected at V in. The amplifier gain is selected to be 4. Therefore R = 4R, and R 3 = R 4. R s is the sensing resistor for current measurement. R m and C m are placed for stability. In our design R m = Ω, and C m =. µf gap(mm) Figure 4: Calibration data of the hall effect sensors for position measurement. tilever is small, this system presents a linear, lightly damped massspring system. A complete electromechanical feedback system is built around this cantilever beam system, all integrated on the PCB. The controller for the system is implemented in the NI myrio. On the PCB, two spiral coils are embedded in the PCB via routing. Each coil has 3 turns, with 4 layers in total and 8 turns per layer. By driving current through the coils, a force can be generated to the cantilever beam through the interaction between the actuating current and the magnetic field from the permanent magnet. The coils are driven by linear power operational amplifiers to get rid of switching noise. In our design, TCA37 from ON semiconductor [] is selected to drive the coils. In order to make better use of the power supply from the NI myrio, single side power supply (  5V) is selected for the power operational amplifiers. The power amplifiers are differentially configured to provide the coil with both positive and negative currents. Figure 3 shows a circuit diagram of the coil power amplifier. Here the controlling signal is injected at V in, which is generated by the D/A converter of the myrio. The amplifier gain is selected to be 4. Therefore R = 4R, and R 3 = R 4. R s is the sensing resistor for current measurement. R m and C m are placed for stability. In our design R m = Ω, and C m =. µf. Two hall effect sensors are configured at both sides of every magnet on the beam to measure the position of the permanent magnet, which is also the local displacement of the cantilever beam. The signals from the two hall effect sensors around one magnet are added together and goes into the A/D converter of the myrio. The controller for the system is implemented digitally in the myrio. Figure 4 shows the calibration data of the hall sensors, with its xaxis being the vertical position of the magnet (gap between the PCB board and the magnet) while its yaxis is the sensor output. Data shows the position measurement by the hall sensors is approximately linear. The same system can be used for magnetic suspension experiment. If we take off the flexible beam, and correctly design the controller for the system, a spherical permanent magnet can be Figure 5: Principle of magnetic force generation. magnetically levitated underneath the coil in PCB. We call this system LevLab, as is shown in figure. 3. Modeling and system identification In this section the modeling and system identification for both FlexLab and LevLab systems are introduced. Here lists the assumptions that our model is based on: The motion of the permanent magnets have only one degree of freedom; Hall effect sensors and voltage control power amplifiers are linear and have no dynamics; Small deviation from the operating point is assumed; Inductance of the coil is small. 3.. Electromechanical interaction and the force generation In order to model the dynamics of the system, we first need the expression for the magnetic force that the coil applies to the magnet. This force is Lorentz force that generated by the field from magnet and the current in the coil. Figure 5 shows the principle of the magnetic force generation. In Figure 5, the permanent magnet field is modeled as a dipole pattern. When a current i is flowing in the coil, a Lorentz
3 force is generated to the coil. The Lorentz force can be calculated by F = J B, therefore the force in the horizontal plane is generated by the vertical component of the magnetic flux B x, while the force in the vertical direction is generated by the horizontal component of the magnetic flux. The Lorentz forces in the horizontal direction are canceled due to symmetry, as a result, the total force that the magnet applies to coil is in the vertical direction. We can get the form of the magnetic force as: f magnetic = C i. () Here the C is a constant that is determined by the strength of magnet, the number of turns of the coil and the geometry. x is the distance between the coil and the permanent magnet. We will use this expression for the magnetic force in the modeling for both FlexLab and LevLab systems. 3.. LevLab modeling and system identification In this section the modeling and identification of the LevLab system is presented. In this electromagnetic system, energy is transfered from electrical domain to mechanical domain. Figure 6 shows a diagram of the magnetic levitation system. equation, we define the following constants: K i = C [N/A] : Force constant x (5a) K s = C i [N/m] : Negative sti f f ness x (5b) 3 By substituting these constants and removing the variation sign δ we reached the dynamic equation for the magnet s movement is mẍ = K i i + K s x. (6) Notice that here the x and i represents the small variations from the operating point. For the electrical domain, the mechanical system influence the electrical domain via back emf of v em f = K i ẋ. Here the constant K i is the force constant shown in Equation (6). Since the inductance of the coil is very small, the electrical dynamics is much faster than that of mechanical domain. Therefore it is reasonable for us to ignore the dynamics of the circuit by assuming the inductance value L =. According to the Kirchhoff s circuit law, the equation for the circuit can be written as: e K i ẋ = ir. (7) Substituting Equation (7) into Equation (6), the equation for the system can be achieved: Figure 6: Diagram for DOF magnetic levitation. In the mechanical domain, the dynamics of the levitated permanent magnet is: mẍ = mg f magnetic. () Note that here positive direction of x is pointing down, which corresponds to increasing the distance between the magnet and the coil. By substituting the expression for magnetic force, we reached the dynamic equation for the magnet: mẍ = K s x + K i ( e R K i ẋ) (8) R Choosing state variables = x and = ẋ, the input signal to the power amplifier to be the control input u, and the output signal of the hall effect displacement sensors to be the system output y. We can rewrite (8) into a state space representation as: = K s m K i mr y = [ g sensor + ] g amp K i mr u (9) () Using Laplace transformation we can reach the transfer function of the system: mẍ = mg C i. (3) Linearizing this equation about operating point x and i and we reached the linear differential equation: mδx = mg C i x C x δi + C i δx. (4) x 3 The constant part of the magnetic force is balanced with the magnet s weight, which is mg = C i x. In order to simplify the 3 K i mr Y(s) U(s) = g sensorg amp s + K i mr s K s m () Here g amp [V/V] is the gain of the power amplifier, while g sensor [V/m] is the gain of the hall effect displacement sensor. The LevLab system parameters are being identified by measuring the system dynamics. Table presents the design parameters of the LevLab system. Figure 7 shows the experimentally measured and fitted Bode plot of the LevLab plant plotting together, with the signal to the power amplifier being the input,
4 Table : Design parameters of the LevLab system st mode Magnet mass m.5 [kg] Power amplifier gain g amp Hall effect displacement sensor gain g sensor.5 [V/V].8 [V/mm] i i st mode Resistance of the coil R 6 [Ω] Figure 8: FlexLab system and mode shape. Magnitude Measured Model Figure 7: Measured and modeled plant bode plot of the LevLab. b F k k m m b Figure 9: Massspring model of the FlexLab system. Based on Figure 9, the differential equations of the system dynamics can be written as: m x = F k b + k ( ) + b ( ) m x = F k ( ) b ( ) F (3a) (3b) and taking the sensor signal as the output. Notice that this Bode measurement is taken with the system under closedloop control, since the system is inherently unstable. The fitted transfer function is: Y(s) U(s) =.68 (s + 6)(s 6). () By substituting values in Table into Equation () and comparing it with (), we can calculate that K s = 5.34 [N/m], and K i =. [N/A]. Therefore we can calculate the electrical damping value as b e = K i mr =.53 [Ns/m] FlexLab modeling and system identification This section introduces the modeling and identification of the FlexLab system. The FlexLab system uses the same PCB with the LevLab. In our control teaching labs, the FlexLab system can use only one set of magnets arranged on the tip of the cantilever to demonstrate a lightly damped nd order system, and the coil in the middle can be used to add disturbance to the system. The FlexLab system can also work with two sets of magnets, which can let the students to explore the complete vibration dynamics of the system. Here we present the modeling and the identification of the complete system dynamics of the FlexLab system. Figure 8 shows a diagram of the FlexLab system. Here the two coils are driven with currents i and i respectively, and magnetic forces are generated between the coils and the magnets that introduced in Section 3.. When driving the system into resonances, the system will present different mode shapes. A fourthorder massspringdamper model is being used to model the FlexLab system. Figure 9 shows the linear system. 4 Here the forces F and F are the forces the coils acting on the magnet. The calculation of these magnetic forces is discussed in Section 3.. By linearizing these force about an operating point as discussed in Section 3., the forces can be expressed to be linear with the supplied voltage to the power amplifier, with a coefficient of K i g amp /R. Define the input voltages of the two coils to be u and u, and selecting state variables x = [ ] T, the system can be written in the state space form, as: d dt = y y k +k m b +b m k m b m k b m m k m b m m + m = g sensor g sensor K i g amp R u K i g amp R u (4) (5)
5 Magnitude Magnitude Model Measured 4 Model Measured Figure : Bode plot of the FlexLab system /u. Figure : Bode plot of the FlexLab system /u. Magnitude permanent magnets on the beam. In this mode, the system demonstrates a nd order system after linearization. A step response of the system is shown in Figure 3. It is shown that this system is very lightly damped inherently. The system demonstrated a natural frequency of 38 rad/s ( Hz) and a damping ratio of ζ = Model Measured response(v).5 Figure : Bode plot of the FlexLab system /u. Note that in Equation (4) the stiffness values are the sum of mechanical stiffness of the cantilever beam and the negative stiffness between the magnet and the coil, while the damping values are a combination of both air drag damping and electrical damping due to back emf. The identification of the parameters for the FlexLab is similar to that for the LevLab, except that this is a twoinputtwooutput system. Figure through Figure present the experimentally measured and modeled Bode plot for the FlexLab system, with different input and output selection. We can see that the system zeros are appearing in the collocated measurement, and have no zero in noncollocated measurement. By matching the pole and zero positions to the measured Bode plot, we identified the system parameters as m =.3 kg, m =.4 kg, k = 8 N/m, k = 9 N/m, b =.5 Ns/m, b =. Ns/m. The modeled Bode plot of the system with these identified values are plotted in blue in Figure through Figure. Good match between the model and the measured data confirms our modeling. The FlexLab system can also operate with only one pair of time(s) Figure 3: Step response of the FlexLab system with tip magnet only. 4. System control design When operating, the FlexLab and LevLab system need to operate under closed loop control to be stable and achieve better performance. The feedback control system design and analysis are discussed in this section. 4.. Stabilization of the LevLab In this section the control for the magnetic suspension for the LevLab system is introduced. As discussed in Section 3., there is one right plane pole in the plant transfer function of the LevLab system, which makes the system unstable in openloop. As a result, feedback control is needed to stabilize it. The controller s design for the LevLab is based on the Lev Lab plant dynamics, which is depicted in Figure 7. In our design, series compensation to stabilize this magnetic suspension
6 Magnitude Magnutude Plant Controller Loop Return Ratio 3 4 Plant Loop without notch Loop return ratio controller Figure 4: Bode plot of loop shaping control design for the LevLab system. Figure 5: Bode plot of loop shaping control design for the FlexLab system. system. This is the approach that is generally used in practice as it only assumes the measurement of the magnet s vertical position. Leadlag form of the PID controller is used for both stabilization and providing better disturbance rejection ability. The controller form is selected to be: G c (s) = K p ( + T i s )ατs + τs + (6) For the LevLab system, the lead network is chosen to have a polezero separation factor α =. The loop is designed to cross over at rad/s, thus we can calculate the lead time constant τ =.6 s to place the phase maximum at the desired crossover frequency. The integral gain for the system /T i is chosen to be 4 rad/s. Figure 4 shows a Bode plot of the loop shaping control design for the LevLab system. As a result, the system can reach a 35 Hz ( rad/s) crossover frequency with a 4 o phase margin. 4.. Position control of FlexLab In Section 3.3 we identified the system dynamics of the FlexLab, where we can see that the system has very lightly damped resonances. To better control the position of the magnet on the cantilever beam, feedback control is needed to add active damping to the system. In this experiment, the actuator at the tip of the cantilever is being used as the control input, while the actuator in the middle can be used to inject disturbance. A lead compensator is used to add damping to this position control system. In order to crossover at a higher frequency, a notch filter is used to suppress the second resonance and maintain stability. The Bode plot of the plant, controller, and the corresponding loop return ratio is shown in Figure 5. The plot shows that the notch of the controller can effectively hit down the notch in the plant. With the designed controller, a crossover frequency of 5 Hz is reached, with a phase margin of 4 degrees. Figure 6 shows a closedloop step response of the magnet position and the corresponding control effort signal of the FlexLab system. 6 Closed loop response(v) Control Effort(V) time(s) time(s) Figure 6: Bode plot of loop shaping control design for the FlexLab system Selfresonance control for FlexLab The FlexLab system can also be used to demonstrate selfresonance control, which is an important building block for a taping mode atomic force microscope probe [3]. Here let us consider the FlexLab with only the magnets on the cantilever tip, which makes the system a secondorder system after linearization. By selfresonance control we can regulate the system at its selfresonance and control its oscillation amplitude. The details of the selfresonance control is introduced in [4]. For a secondorder linear system with poles at σ ± jω n, the system will have a response as y(t) = Ae σt sin(ω n t + φ). (7) Ideally, when the real part of the system poles become, the system is marginally stable, and will demonstrate sustain oscillation. However, in practice, it is not possible to set the real part of the pols to exactly and make a perfect marginally stable system. The closedloop poles will eventually have a positive or negative real part, and the closedloop system will become either stable or unstable. To make the cantilever beam in the
7 Figure 7: Block diagram of FlexLab selfresonance amplitude control. FlexLab a pure oscillator, a closedloop amplitude controller, which measures the oscillation amplitude and adds positive or negative damping to the system to control the amplitude of the self resonance. With one pair of magnets attached to the cantilever tip, the natural frequency of the system is measured to be ω n = 38 rad/s ( Hz). It is possible to show that the oscillation amplitude envelope of the FlexLab changes as A(t) = A e ζω nt. (8) Here A is the initial amplitude of the oscillation, and ζ is the system damping ratio. Although the relationship between A and ζ is nonlinear, we can linearize it around a set point and apply linear control theory to design the controller for the oscillation amplitude control. A firstorder Taylor series linear approximation of Equation (8) about t = yields A(t) = A A ζω n t. (9) With the oscillation frequency fixed at ω n, the oscillator dynamics with the oscillation amplitude change A being the output and the damping ratio ζ being the input can be reached by applying a Laplace transform to Equation (9): Magnitude (db) Phase (deg) Frequency (rad/s) Plant Controller Loop return ratio Figure 8: Bode plot for FlexLab oscillation amplitude control design. In the control loop shown in Figure 7, the dynamics from ζ to A can be modeled as a transfer function () with a lowpass filter, where the lowpass filter represents the dynamics of the amplitude estimation functions. In our implementation the filter is designed as A(s) ζ(s) = A ω n. () s The above transfer function shows that the incremental change in the envelope of oscillation A(s) is proportional to the integral of the damping ratio ζ. We can design a controller to control the oscillation amplitude of the FlexLab system in real time based on the plant transfer function in (). Figure 7 shows a block diagram of the control system implementation. The oscillatory magnet position signal is measured by the hall effect sensors and being acquired into the embedded controller (NI myrio) via A/D conversion. A absolute value function (rectifier) and a lowpass filter is used for the measured signal to get an estimation of the envelope amplitude of the oscillation signal. The amplitude signal A is then compared with a reference amplitude A re f, and the error goes through the controller and generated the control effort signal ζ, which is the controlling damping ratio (positive or negative) added to the system. The damping signal is generated by multiplying ω n and taking derivative to the signal (added another pole for filtering), and injected to the FlexLab system. 7 LPF(s) = s/ +. () The reference amplitude of oscillation is set as A r e f = A = V. Figure 8 shows the Bode plot for the oscillation amplitude controller design. Here the plant transfer function demonstrate the dynamics from control effort ζ to amplitude estimation Â. Note that the minus sign in Equation () is reversed for design purpose. A PI controller with a form of C(s) = K p ( + /T i s) is selected for the system. By targeting at a crossover frequency at ω = rad/s and a phase margin of 4 o, the controller parameters are selected as K p =.35 and T i =.. The control loop shown in Figure?? is implemented on the FlexLab system with myrio controller. Figure 9 shows a waveform of the system output under selfresonance amplitude control under step changes of the reference amplitude A re f, and Figure and shows the corresponding envelope amplitude estimation and the control effort signal ζ. Note that the signals are asymmetric due to the nonlinearity, with the plant transfer function () depend on the current amplitude A.
8 response(v) system analysis and control at MIT. We have attempted to describe this system and its related experiments in sufficiently detail so that it can be readily duplicated by others who might like to use it in their control teaching efforts. The design file of the system is available to be download at the website of Precision Motion Control Lab at MIT. We welcome comments, questions, or suggestions for improvement of this lab design and exercise time(s) 6. Acknowledgments The authors would like to thank National Instruments for funding this project. Figure 9: Waveform of FlexLab selfresonance amplitude control. Envelope amplitude(v) References. NI myrio Hardware at a Glance. Tech. Rep.; National Instruments; 4.. On semiconductors.. A Output Current, Dual Power Operational Amplifiers. TCA37 Datasheet; Trumper DL, Hocken RJ, AminShahidi D, Ljubicic D, Overcash J. Highaccuracy atomic force microscope. In: Control Technologies for Emerging Micro and Nanoscale Systems. Springer; : Roberge JK. Operational amplifiers. Wiley; Time(s) Figure : Amplitude signal of FlexLab selfresonance amplitude control Control effort ζ Time(s) Figure : Control effort signal ( ζ) of FlexLab selfresonance amplitude control. Here ζ = ζ + ζ, where ζ is the system damping ratio, ζ is the controlling damping ratio added through control, and ζ is the total damping ratio. 5. Conclusion In this paper, a compact mechatronics system that can work as either a flexible cantilever beam or a magnetic levitation system is reported. This system will be used in teaching feedback 8
MAGNETIC LEVITATION SUSPENSION CONTROL SYSTEM FOR REACTION WHEEL
IMPACT: International Journal of Research in Engineering & Technology (IMPACT: IJRET) ISSN 23218843 Vol. 1, Issue 4, Sep 2013, 16 Impact Journals MAGNETIC LEVITATION SUSPENSION CONTROL SYSTEM FOR REACTION
More informationMechatronics. Analog and Digital Electronics: Studio Exercises 1 & 2
Mechatronics Analog and Digital Electronics: Studio Exercises 1 & 2 There is an electronics revolution taking place in the industrialized world. Electronics pervades all activities. Perhaps the most important
More informationPart 2: Second order systems: cantilever response
 cantilever response slide 1 Part 2: Second order systems: cantilever response Goals: Understand the behavior and how to characterize second order measurement systems Learn how to operate: function generator,
More informationLecture 9. Lab 16 System Identification (2 nd or 2 sessions) Lab 17 Proportional Control
246 Lecture 9 Coming week labs: Lab 16 System Identification (2 nd or 2 sessions) Lab 17 Proportional Control Today: Systems topics System identification (ala ME4232) Time domain Frequency domain Proportional
More informationMTE 360 Automatic Control Systems University of Waterloo, Department of Mechanical & Mechatronics Engineering
MTE 36 Automatic Control Systems University of Waterloo, Department of Mechanical & Mechatronics Engineering Laboratory #1: Introduction to Control Engineering In this laboratory, you will become familiar
More informationCHAPTER 6 INTRODUCTION TO SYSTEM IDENTIFICATION
CHAPTER 6 INTRODUCTION TO SYSTEM IDENTIFICATION Broadly speaking, system identification is the art and science of using measurements obtained from a system to characterize the system. The characterization
More informationLaboratory PID Tuning Based On Frequency Response Analysis. 2. be able to evaluate system performance for empirical tuning method;
Laboratory PID Tuning Based On Frequency Response Analysis Objectives: At the end, student should 1. appreciate a systematic way of tuning PID loop by the use of process frequency response analysis; 2.
More informationFree vibration of cantilever beam FREE VIBRATION OF CANTILEVER BEAM PROCEDURE
FREE VIBRATION OF CANTILEVER BEAM PROCEDURE AIM Determine the damped natural frequency, logarithmic decrement and damping ratio of a given system from the free vibration response Calculate the mass of
More informationFigure 1: Unity Feedback System. The transfer function of the PID controller looks like the following:
Islamic University of Gaza Faculty of Engineering Electrical Engineering department Control Systems Design Lab Eng. Mohammed S. Jouda Eng. Ola M. Skeik Experiment 3 PID Controller Overview This experiment
More informationRotary Motion Servo Plant: SRV02. Rotary Experiment #03: Speed Control. SRV02 Speed Control using QuaRC. Student Manual
Rotary Motion Servo Plant: SRV02 Rotary Experiment #03: Speed Control SRV02 Speed Control using QuaRC Student Manual Table of Contents 1. INTRODUCTION...1 2. PREREQUISITES...1 3. OVERVIEW OF FILES...2
More informationPoles and Zeros of H(s), Analog Computers and Active Filters
Poles and Zeros of H(s), Analog Computers and Active Filters Physics116A, Draft10/28/09 D. Pellett LRC Filter Poles and Zeros Pole structure same for all three functions (two poles) HR has two poles and
More informationHighspeed wavefront control using MEMS micromirrors T. G. Bifano and J. B. Stewart, Boston University [ ] Introduction
Highspeed wavefront control using MEMS micromirrors T. G. Bifano and J. B. Stewart, Boston University [589527] Introduction Various deformable mirrors for highspeed wavefront control have been demonstrated
More informationNew Long Stroke Vibration Shaker Design using Linear Motor Technology
New Long Stroke Vibration Shaker Design using Linear Motor Technology The Modal Shop, Inc. A PCB Group Company Patrick Timmons Calibration Systems Engineer Mark Schiefer Senior Scientist Long Stroke Shaker
More informationNonCollocation Problems in Dynamics and Control of Mechanical Systems
Cleveland State University EngagedScholarship@CSU ETD Archive 2009 NonCollocation Problems in Dynamics and Control of Mechanical Systems Timothy M. Obrzut Cleveland State University How does access to
More informationEES42042 Fundamental of Control Systems Bode Plots
EES42042 Fundamental of Control Systems Bode Plots DR. Ir. Wahidin Wahab M.Sc. Ir. Aries Subiantoro M.Sc. 2 Bode Plots Plot of db Gain and phase vs frequency It is assumed you know how to construct Bode
More informationKaradeniz Technical University Department of Electrical and Electronics Engineering Trabzon, Turkey
Karadeniz Technical University Department of Electrical and Electronics Engineering 61080 Trabzon, Turkey Chapter 32 1 Modelling and Representation of Physical Systems 3.1. Electrical Systems Bu ders
More informationA study of Vibration Analysis for Gearbox Casing Using Finite Element Analysis
A study of Vibration Analysis for Gearbox Casing Using Finite Element Analysis M. Sofian D. Hazry K. Saifullah M. Tasyrif K.Salleh I.Ishak Autonomous System and Machine Vision Laboratory, School of Mechatronic,
More informationA SIMPLE FORCE BALANCE ACCELEROMETER/SEISMOMETER BASED ON A TUNING FORK DISPLACEMENT SENSOR. D. StuartWatson and J. Tapson
A SIMPLE FORCE BALANCE ACCELEROMETER/SEISMOMETER BASED ON A TUNING FORK DISPLACEMENT SENSOR D. StuartWatson and J. Tapson Department of Electrical Engineering, University of Cape Town, Rondebosch 7701,
More informationRotary Motion Servo Plant: SRV02. Rotary Experiment #02: Position Control. SRV02 Position Control using QuaRC. Student Manual
Rotary Motion Servo Plant: SRV02 Rotary Experiment #02: Position Control SRV02 Position Control using QuaRC Student Manual Table of Contents 1. INTRODUCTION...1 2. PREREQUISITES...1 3. OVERVIEW OF FILES...2
More informationEEL2216 Control Theory CT2: Frequency Response Analysis
EEL2216 Control Theory CT2: Frequency Response Analysis 1. Objectives (i) To analyse the frequency response of a system using Bode plot. (ii) To design a suitable controller to meet frequency domain and
More informationA Machine Tool Controller using Cascaded Servo Loops and Multiple Feedback Sensors per Axis
A Machine Tool Controller using Cascaded Servo Loops and Multiple Sensors per Axis David J. Hopkins, Timm A. Wulff, George F. Weinert Lawrence Livermore National Laboratory 7000 East Ave, L792, Livermore,
More informationOther Effects in PLLs. Behzad Razavi Electrical Engineering Department University of California, Los Angeles
Other Effects in PLLs Behzad Razavi Electrical Engineering Department University of California, Los Angeles Example of Up and Down Skew and Width Mismatch Approximating the pulses on the control line by
More informationANNA UNIVERSITY :: CHENNAI MODEL QUESTION PAPER(VSEMESTER) B.E. ELECTRONICS AND COMMUNICATION ENGINEERING EC334  CONTROL SYSTEMS
ANNA UNIVERSITY :: CHENNAI  600 025 MODEL QUESTION PAPER(VSEMESTER) B.E. ELECTRONICS AND COMMUNICATION ENGINEERING EC334  CONTROL SYSTEMS Time: 3hrs Max Marks: 100 Answer all Questions PART  A (10
More informationGoals. Introduction. To understand the use of root mean square (rms) voltages and currents.
Lab 10. AC Circuits Goals To show that AC voltages cannot generally be added without accounting for their phase relationships. That is, one must account for how they vary in time with respect to one another.
More informationGoals. Introduction. To understand the use of root mean square (rms) voltages and currents.
Lab 10. AC Circuits Goals To show that AC voltages cannot generally be added without accounting for their phase relationships. That is, one must account for how they vary in time with respect to one another.
More informationMETHODS TO IMPROVE DYNAMIC RESPONSE OF POWER FACTOR PREREGULATORS: AN OVERVIEW
METHODS TO IMPROE DYNAMIC RESPONSE OF POWER FACTOR PREREGULATORS: AN OERIEW G. Spiazzi*, P. Mattavelli**, L. Rossetto** *Dept. of Electronics and Informatics, **Dept. of Electrical Engineering University
More informationDESIGN AND ANALYSIS OF FEEDBACK CONTROLLERS FOR A DC BUCKBOOST CONVERTER
DESIGN AND ANALYSIS OF FEEDBACK CONTROLLERS FOR A DC BUCKBOOST CONVERTER Murdoch University: The Murdoch School of Engineering & Information Technology Author: Jason Chan Supervisors: Martina Calais &
More informationDEEP FLAW DETECTION WITH GIANT MAGNETORESISTIVE (GMR) BASED SELFNULLING PROBE
DEEP FLAW DETECTION WITH GIANT MAGNETORESISTIVE (GMR) BASED SELFNULLING PROBE Buzz Wincheski and Min Namkung NASA Langley Research Center Hampton, VA 23681 INTRODUCTION The use of giant magnetoresistive
More informationLab 6: Building a Function Generator
ECE 212 Spring 2010 Circuit Analysis II Names: Lab 6: Building a Function Generator Objectives In this lab exercise you will build a function generator capable of generating square, triangle, and sine
More informationELECTRICAL CIRCUITS 6. OPERATIONAL AMPLIFIERS PART III DYNAMIC RESPONSE
77 ELECTRICAL CIRCUITS 6. PERATAL AMPLIIERS PART III DYNAMIC RESPNSE Introduction In the first 2 handouts on opamps the focus was on DC for the ideal and nonideal opamp. The perfect opamp assumptions
More informationDigital Signal Processing in RF Applications
Digital Signal Processing in RF Applications Part II Thomas Schilcher Outline 1. signal conditioning / down conversion 2. detection of amp./phase by digital I/Q sampling I/Q sampling non I/Q sampling digital
More informationLab 5 Second Order Transient Response of Circuits
Lab 5 Second Order Transient Response of Circuits Lab Performed on November 5, 2008 by Nicole Kato, Ryan Carmichael, and Ti Wu Report by Ryan Carmichael and Nicole Kato E11 Laboratory Report Submitted
More informationServo Tuning. Dr. Rohan Munasinghe Department. of Electronic and Telecommunication Engineering University of Moratuwa. Thanks to Dr.
Servo Tuning Dr. Rohan Munasinghe Department. of Electronic and Telecommunication Engineering University of Moratuwa Thanks to Dr. Jacob Tal Overview Closed Loop Motion Control System Brain Brain Muscle
More informationBUCK Converter Control Cookbook
BUCK Converter Control Cookbook Zach Zhang, Alpha & Omega Semiconductor, Inc. A Buck converter consists of the power stage and feedback control circuit. The power stage includes power switch and output
More informationAn Introduction to Proportional IntegralDerivative (PID) Controllers
An Introduction to Proportional IntegralDerivative (PID) Controllers Stan Żak School of Electrical and Computer Engineering ECE 680 Fall 2017 1 Motivation Growing gap between real world control problems
More informationNonlinear Control Lecture
Nonlinear Control Lecture Just what constitutes nonlinear control? Control systems whose behavior cannot be analyzed by linear control theory. All systems contain some nonlinearities, most are small and
More informationDC Motor Speed Control using PID Controllers
"EE 616 Electronic System Design Course Project, EE Dept, IIT Bombay, November 2009" DC Motor Speed Control using PID Controllers Nikunj A. Bhagat (08307908) nbhagat@ee.iitb.ac.in, Mahesh Bhaganagare (CEP)
More informationAdvanced Servo Tuning
Advanced Servo Tuning Dr. Rohan Munasinghe Department of Electronic and Telecommunication Engineering University of Moratuwa Servo System Elements position encoder Motion controller (software) Desired
More informationPole, zero and Bode plot
Pole, zero and Bode plot EC04 305 Lecture notes YESAREKEY December 12, 2007 Authored by: Ramesh.K Pole, zero and Bode plot EC04 305 Lecture notes A rational transfer function H (S) can be expressed as
More informationCDS 101/110a: Lecture 81 Frequency Domain Design. Frequency Domain Performance Specifications
CDS /a: Lecture 8 Frequency Domain Design Richard M. Murray 7 November 28 Goals:! Describe canonical control design problem and standard performance measures! Show how to use loop shaping to achieve a
More informationModule 08 Controller Designs: Compensators and PIDs
Module 08 Controller Designs: Compensators and PIDs Ahmad F. Taha EE 3413: Analysis and Desgin of Control Systems Email: ahmad.taha@utsa.edu Webpage: http://engineering.utsa.edu/ taha March 31, 2016 Ahmad
More informationOperational Amplifier BME 360 Lecture Notes Ying Sun
Operational Amplifier BME 360 Lecture Notes Ying Sun Characteristics of OpAmp An operational amplifier (opamp) is an analog integrated circuit that consists of several stages of transistor amplification
More informationMaximizing LPM Accuracy AN 25
Maximizing LPM Accuracy AN 25 Application Note to the KLIPPEL R&D SYSTEM This application note provides a step by step procedure that maximizes the accuracy of the linear parameters measured with the LPM
More informationLecture 10. Lab next week: Agenda: Control design fundamentals. Proportional Control ProportionalIntegral Control
264 Lab next week: Lecture 10 Lab 17: Proportional Control Lab 18: ProportionalIntegral Control (1/2) Agenda: Control design fundamentals Objectives (Tracking, disturbance/noise rejection, robustness)
More informationECE ECE285. Electric Circuit Analysis I. Spring Nathalia Peixoto. Rev.2.0: Rev Electric Circuits I
ECE285 Electric Circuit Analysis I Spring 2014 Nathalia Peixoto Rev.2.0: 140124. Rev 2.1. 140813 1 Lab reports Background: these 9 experiments are designed as simple building blocks (like Legos) and students
More informationthe pilot valve effect of
Actiive Feedback Control and Shunt Damping Example 3.2: A servomechanism incorporating a hydraulic relay with displacement feedback throughh a dashpot and spring assembly is shown below. [Control System
More informationChapter 10 Feedback ECE 3120 Microelectronics II Dr. Suketu Naik
1 Chapter 10 Feedback Operational Amplifier Circuit Components 2 1. Ch 7: Current Mirrors and Biasing 2. Ch 9: Frequency Response 3. Ch 8: ActiveLoaded Differential Pair 4. Ch 10: Feedback 5. Ch 11: Output
More information#8A RLC Circuits: Free Oscillations
#8A RL ircuits: Free Oscillations Goals In this lab we investigate the properties of a series RL circuit. Such circuits are interesting, not only for there widespread application in electrical devices,
More informationExperiment 9. PID Controller
Experiment 9 PID Controller Objective:  To be familiar with PID controller.  Noting how changing PID controller parameter effect on system response. Theory: The basic function of a controller is to execute
More informationLab 9 AC FILTERS AND RESONANCE
151 Name Date Partners ab 9 A FITES AND ESONANE OBJETIES OEIEW To understand the design of capacitive and inductive filters To understand resonance in circuits driven by A signals In a previous lab, you
More informationSystem Inputs, Physical Modeling, and Time & Frequency Domains
System Inputs, Physical Modeling, and Time & Frequency Domains There are three topics that require more discussion at this point of our study. They are: Classification of System Inputs, Physical Modeling,
More informationA Prototype Wire Position Monitoring System
LCLSTN0527 A Prototype Wire Position Monitoring System Wei Wang and Zachary Wolf Metrology Department, SLAC 1. INTRODUCTION ¹ The Wire Position Monitoring System (WPM) will track changes in the transverse
More informationDynamic calculation of nonlinear magnetic circuit for computer aided design of a fluxgate direct current sensor
Dynamic calculation of nonlinear magnetic circuit for computer aided design of a fluxgate direct current sensor Takafumi Koseki(The Univ. of Tokyo), Hiroshi Obata(The Univ. of Tokyo), Yasuhiro Takada(The
More informationInvestigating the Electromechanical Coupling in Piezoelectric Actuator Drive Motor Under Heavy Load
Investigating the Electromechanical Coupling in Piezoelectric Actuator Drive Motor Under Heavy Load TiberiuGabriel Zsurzsan, Michael A.E. Andersen, Zhe Zhang, Nils A. Andersen DTU Electrical Engineering
More informationhigh, thinwalled buildings in glass and steel
a StaBle MiCroSCoPe image in any BUildiNG: HUMMINGBIRd 2.0 Lowfrequency building vibrations can cause unacceptable image quality loss in microsurgery microscopes. The Hummingbird platform, developed earlier
More informationExperiment 7: Frequency Modulation and Phase Locked Loops
Experiment 7: Frequency Modulation and Phase Locked Loops Frequency Modulation Background Normally, we consider a voltage wave form with a fixed frequency of the form v(t) = V sin( ct + ), (1) where c
More informationFilter Design, Active Filters & Review. EGR 220, Chapter 14.7, December 14, 2017
Filter Design, Active Filters & Review EGR 220, Chapter 14.7, 14.11 December 14, 2017 Overview ² Passive filters (no op amps) ² Design examples ² Active filters (use op amps) ² Course review 2 Example:
More informationResponse spectrum Time history Power Spectral Density, PSD
A description is given of one way to implement an earthquake test where the test severities are specified by time histories. The test is done by using a biaxial computer aided servohydraulic test rig.
More informationChapter 33. Alternating Current Circuits
Chapter 33 Alternating Current Circuits Alternating Current Circuits Electrical appliances in the house use alternating current (AC) circuits. If an AC source applies an alternating voltage to a series
More informationDC and AC Circuits. Objective. Theory. 1. Direct Current (DC) RC Circuit
[International Campus Lab] Objective Determine the behavior of resistors, capacitors, and inductors in DC and AC circuits. Theory  Reference  Young
More informationF1A Magnetic Field Transducers
DESCRIPTION: The F1A denotes a range of SENIS Magnetic Fieldto Voltage Transducers with fully integrated 1axis Hall Probe. It measures magnetic fields perpendicular to the probe plane (By). The Hall
More informationFigure 1.1: Quanser Driving Simulator
1 INTRODUCTION The Quanser HIL Driving Simulator (QDS) is a modular and expandable LabVIEW model of a car driving on a closed track. The model is intended as a platform for the development, implementation
More informationTHE integrated circuit (IC) industry, both domestic and foreign,
IEEE TRANSACTIONS ON MAGNETICS, VOL. 41, NO. 3, MARCH 2005 1149 Application of Voice Coil Motors in Active Dynamic Vibration Absorbers YiDe Chen, ChyunChau Fuh, and PiCheng Tung Abstract A dynamic vibration
More informationMultiply Resonant EOM for the LIGO 40meter Interferometer
LASER INTERFEROMETER GRAVITATIONAL WAVE OBSERVATORY  LIGO  CALIFORNIA INSTITUTE OF TECHNOLOGY MASSACHUSETTS INSTITUTE OF TECHNOLOGY LIGOXXXXXXXXXX Date: 2009/09/25 Multiply Resonant EOM for the LIGO
More informationExperiment 8 Frequency Response
Experiment 8 Frequency Response W.T. Yeung, R.A. Cortina, and R.T. Howe UC Berkeley EE 105 Spring 2005 1.0 Objective This lab will introduce the student to frequency response of circuits. The student will
More informationFinal Exam. 1. An engineer measures the (step response) rise time of an amplifier as t r = 0.1 μs. Estimate the 3 db bandwidth of the amplifier.
Final Exam Name: Score /100 Question 1 Short Takes 1 point each unless noted otherwise. 1. An engineer measures the (step response) rise time of an amplifier as t r = 0.1 μs. Estimate the 3 db bandwidth
More informationFeedback Systems. Many embedded system applications involve the concept of feedback. Sometimes feedback is designed into systems: Actuator
Feedback Systems Many embedded system applications involve the concept of feedback Sometimes feedback is designed into systems: Operator Input CPU Actuator Physical System position velocity temperature
More informationTheory: The idea of this oscillator comes from the idea of positive feedback, which is described by Figure 6.1. Figure 6.1: Positive Feedback
Name1 Name2 12/2/10 ESE 319 Lab 6: Colpitts Oscillator Introduction: This lab introduced the concept of feedback in combination with bipolar junction transistors. The goal of this lab was to first create
More informationDEPARTMENT OF ELECTRICAL AND ELECTRONIC ENGINEERING BANGLADESH UNIVERSITY OF ENGINEERING & TECHNOLOGY EEE 402 : CONTROL SYSTEMS SESSIONAL
DEPARTMENT OF ELECTRICAL AND ELECTRONIC ENGINEERING BANGLADESH UNIVERSITY OF ENGINEERING & TECHNOLOGY EEE 402 : CONTROL SYSTEMS SESSIONAL Experiment No. 1(a) : Modeling of physical systems and study of
More informationDEPARTMENT OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE MASSACHUSETTS INSTITUTE OF TECHNOLOGY CAMBRIDGE, MASSACHUSETTS 02139
DEPARTMENT OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE MASSACHUSETTS INSTITUTE OF TECHNOLOGY CAMBRIDGE, MASSACHUSETTS 019.101 Introductory Analog Electronics Laboratory Laboratory No. READING ASSIGNMENT
More informationExperiment VI: The LRC Circuit and Resonance
Experiment VI: The ircuit and esonance I. eferences Halliday, esnick and Krane, Physics, Vol., 4th Ed., hapters 38,39 Purcell, Electricity and Magnetism, hapter 7,8 II. Equipment Digital Oscilloscope Digital
More informationDualAxis, Highg, imems Accelerometers ADXL278
FEATURES Complete dualaxis acceleration measurement system on a single monolithic IC Available in ±35 g/±35 g, ±50 g/±50 g, or ±70 g/±35 g output fullscale ranges Full differential sensor and circuitry
More informationUNIT 2: DC MOTOR POSITION CONTROL
UNIT 2: DC MOTOR POSITION CONTROL 2.1 INTRODUCTION This experiment aims to show the mathematical model of a DC motor and how to determine the physical parameters of a DC motor model. Once the model is
More informationMASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8.02 Spring 2005 Experiment 10: LR and Undriven LRC Circuits
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8.0 Spring 005 Experiment 10: LR and Undriven LRC Circuits OBJECTIVES 1. To determine the inductance L and internal resistance R L of a coil,
More informationLAB 4: OPERATIONAL AMPLIFIER CIRCUITS
LAB 4: OPERATIONAL AMPLIFIER CIRCUITS ELEC 225 Introduction Operational amplifiers (OAs) are highly stable, high gain, difference amplifiers that can handle signals from zero frequency (dc signals) up
More informationand using the step routine on the closed loop system shows the step response to be less than the maximum allowed 20%.
Phase (deg); Magnitude (db) 385 Bode Diagrams 8 Gm = Inf, Pm=59.479 deg. (at 62.445 rad/sec) 6 4 22 46 81 1214 1618 11 1 1 1 1 2 1 3 and using the step routine on the closed loop system shows
More informationIntroduction to PID Control
Introduction to PID Control Introduction This introduction will show you the characteristics of the each of proportional (P), the integral (I), and the derivative (D) controls, and how to use them to obtain
More informationExperiment 8: An AC Circuit
Experiment 8: An AC Circuit PART ONE: AC Voltages. Set up this circuit. Use R = 500 Ω, L = 5.0 mh and C =.01 μf. A signal generator built into the interface provides the emf to run the circuit from Output
More informationEffect of Controller Parameters on PantographCatenary System
American International Journal of Research in Science, Technology, Engineering & Mathematics Available online at http://www.iasir.net ISSN (Print): 23283491, ISSN (Online): 2328358, ISSN (CDROM): 23283629
More informationEE2302 Passive Filters and Frequency Response
EE2302 Passive Filters and Frequency esponse Objective he student should become acquainted with simple passive filters for performing highpass, lowpass, and bandpass operations. he experimental tasks also
More informationLecture 2 Review of Signals and Systems: Part 1. EE4900/EE6720 Digital Communications
EE4900/EE6420: Digital Communications 1 Lecture 2 Review of Signals and Systems: Part 1 Block Diagrams of Communication System Digital Communication System 2 Informatio n (sound, video, text, data, ) Transducer
More informationMEMS Optical Scanner "ECO SCAN" Application Notes. Ver.0
MEMS Optical Scanner "ECO SCAN" Application Notes Ver.0 Micro Electro Mechanical Systems Promotion Dept., Visionary Business Center The Nippon Signal Co., Ltd. 1 Preface This document summarizes precautions
More informationCHAPTER 9 FEEDBACK. NTUEE Electronics L.H. Lu 91
CHAPTER 9 FEEDBACK Chapter Outline 9.1 The General Feedback Structure 9.2 Some Properties of Negative Feedback 9.3 The Four Basic Feedback Topologies 9.4 The Feedback Voltage Amplifier (SeriesShunt) 9.5
More informationCurrent Slope Measurement Strategies for Sensorless Control of a Three Phase Radial Active Magnetic Bearing
Current Slope Measurement Strategies for Sensorless Control of a Three Phase Radial Active Magnetic Bearing Matthias Hofer, Thomas Nenning, Markus Hutterer, and Manfred Schrödl Institute of Energy Systems
More information1.What is frequency response? A frequency responses the steady state response of a system when the input to the system is a sinusoidal signal.
Control Systems (EC 334) 1.What is frequency response? A frequency responses the steady state response of a system when the input to the system is a sinusoidal signal. 2.List out the different frequency
More informationCir cuit s 212 Lab. Lab #7 Filter Design. Introductions:
Cir cuit s 22 Lab Lab #7 Filter Design The purpose of this lab is multifold. This is a threeweek experiment. You are required to design a High / Low Pass filter using the LM38 OP AMP. In this lab, you
More informationUser Guide IRMCS3041 System Overview/Guide. Aengus Murray. Table of Contents. Introduction
User Guide 0607 IRMCS3041 System Overview/Guide By Aengus Murray Table of Contents Introduction... 1 IRMCF341 Application Circuit... 2 Sensorless Control Algorithm... 4 Velocity and Current Control...
More informationAdaptive Notch Filter Using RealTime Parameter Estimation
IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 19, NO. 3, MAY 2011 673 Adaptive Notch Filter Using RealTime Parameter Estimation Jason Levin, Member, IEEE, Néstor O. PérezArancibia, Member, IEEE,
More informationElectronic Measurements & Instrumentation. 1. Draw the Maxwell s Bridge Circuit and derives the expression for the unknown element at balance?
UNIT 6 1. Draw the Maxwell s Bridge Circuit and derives the expression for the unknown element at balance? Ans: Maxwell's bridge, shown in Fig. 1.1, measures an unknown inductance in of standard arm offers
More informationA Novel Control Method to Minimize Distortion in AC Inverters. Dennis Gyma
A Novel Control Method to Minimize Distortion in AC Inverters Dennis Gyma HewlettPackard Company 150 Green Pond Road Rockaway, NJ 07866 ABSTRACT In PWM AC inverters, the dutycycle modulator transfer
More informationInternational Journal of Research in Advent Technology Available Online at:
OVERVIEW OF DIFFERENT APPROACHES OF PID CONTROLLER TUNING Manju Kurien 1, Alka Prayagkar 2, Vaishali Rajeshirke 3 1 IS Department 2 IE Department 3 EV DEpartment VES Polytechnic, Chembur,Mumbai 1 manjulibu@gmail.com
More informationFundamentals of Servo Motion Control
Fundamentals of Servo Motion Control The fundamental concepts of servo motion control have not changed significantly in the last 50 years. The basic reasons for using servo systems in contrast to open
More informationLab 9 AC FILTERS AND RESONANCE
091 Name Date Partners ab 9 A FITES AND ESONANE OBJETIES OEIEW To understand the design of capacitive and inductive filters To understand resonance in circuits driven by A signals In a previous lab, you
More informationApplication Note #2442
Application Note #2442 Tuning with PL and PID Most closedloop servo systems are able to achieve satisfactory tuning with the basic Proportional, Integral, and Derivative (PID) tuning parameters. However,
More informationUsing PWM Output as a DigitaltoAnalog Converter on a TMS320C240 DSP APPLICATION REPORT: SPRA490
Using PWM Output as a DigitaltoAnalog Converter on a TMS32C2 DSP APPLICATION REPORT: SPRA9 David M. Alter Technical Staff  DSP Applications November 998 IMPORTANT NOTICE Texas Instruments (TI) reserves
More informationω d = driving frequency, F m = amplitude of driving force, b = damping constant and ω = natural frequency of undamped, undriven oscillator.
Physics 121H Fall 2015 Homework #14 16November2015 Due Date : 23November2015 Reading : Chapter 15 Note: Problems 7 & 8 are tutorials dealing with damped and driven oscillations, respectively. It may
More informationThe Feedback PI controller for BuckBoost converter combining KY and Buck converter
olume 2, Issue 2 July 2013 114 RESEARCH ARTICLE ISSN: 22785213 The Feedback PI controller for BuckBoost converter combining KY and Buck converter K. Sreedevi* and E. David Dept. of electrical and electronics
More informationMassachusetts Institute of Technology. Lab 2: Characterization of Lab System Components
OBJECTIVES Massachusetts Institute of Technology Department of Mechanical Engineering 2.004 System Dynamics and Control Fall Term 2007 Lab 2: Characterization of Lab System Components In the future lab
More informationME 365 EXPERIMENT 7 SIGNAL CONDITIONING AND LOADING
ME 365 EXPERIMENT 7 SIGNAL CONDITIONING AND LOADING Objectives: To familiarize the student with the concepts of signal conditioning. At the end of the lab, the student should be able to: Understand the
More informationElectronics Eingineering
Electronics Eingineering 1. The output of a twoinput gate is 0 if and only if its inputs are unequal. It is true for (A) XOR gate (B) NAND gate (C) NOR gate (D) XNOR gate 2. In Kmap simplification, a
More information