15EI303L- CONTROL SYSTEMS ENGINEERING LABORATORY

Transcription

1 15EI303L- CONTROL SYSTEMS ENGINEERING LABORATORY Department of Electronics and Instrumentation Engineering Faculty of Engineering and Technology Department of Electronics and Instrumentation Engineering SRM University, SRM Nagar Kattankulathur Kancheepuram District Tamil Nadu 1

2 CONTENTS S.No. CONTENTS Page No. 1 Mark Assessment details 3 2 General Instructions for Laboratory classes 4 3 Syllabus 5 4 Introduction to the laboratory 6 5 List of Experiments 5.1 Step, ramp and impulse response Identification of damping in second order Time domain analysis Stability analysis using routh- hurwitz method Stability analysis of linear system using various graphical methods Frequency response analysis using bode plot Frequency response analysis using polar plot Design of PID Controller for first order and second order systems Design of PID Controller for speed control of DC Motor System Design of PID Based controller for Twin Rotor Multi Input Multi Output System 45 2

3 1. MARK ASSESSMENT DETAILS ALLOTMENT OF MARKS: Internal assessment = 60 marks Practical examination = 40 marks Total = 100 marks INTERNAL ASSESSMENT (60 MARKS) Split up of internal marks Record Model exam Quiz/Viva Experiments Total 5 marks 10 marks 5 marks 40 marks 60 marks PRACTICAL EXAMINATION (40 MARKS) Split up of practical examination marks Aim and Procedure Circuit Diagram Tabulation Result Viva voce Total 25 marks 30 marks 30 marks 05 marks 10 marks 100 marks 3

4 2. GENERAL INSTRUCTIONS FOR LABORATORY CLASSES 1. Enter the Lab with CLOSED TOE SHOES. 2. Students should wear lab coat. 3. The HAIR should be protected, let it not be loose. 4. TOOLS, APPARATUS and COMPONENT sets are to be returned before leaving the lab. 5. HEADINGS and DETAILS should be neatly written i. Aim of the experiment ii. iii. Apparatus / Tools / Instruments required Theory iv. Procedure / Algorithm / Program v. Model Calculations/ Design calculations vi. vii. Block Diagram / Flow charts/ Circuit diagram Tabulations/ Waveforms/ Graph viii. Result / discussions. 6. Experiment number and date should be written in the appropriate place. 7. After completing the experiment, the answer to pre lab viva-voce questions should be neatly written in the workbook. 8. Be REGULAR, SYSTEMATIC, PATIENT, AND STEADY. 4

5 3. SYLLABUS 15EI303L Control Systems Engineering Laboratory L T P C Co-requisite: 15EI303 Prerequisite: NIL Data Book / Codes/Standards NIL Course Category P PROFESSIONAL CORE CONTROL ENGINEERING Course designed by Department of Electronics and Instrumentation Engineering Approval 32 nd Academic Council Meeting held on 23 rd July, 2016 PURPOSE To apply the concepts of control system and design and verify using software tools INSTRUCTIONAL OBJECTIVES STUDENT OUTCOMES At the end of the course, student will be able to 1. Analyze the first and second order systems using time domain analysis. a b 2. Analyze the first and second order systems using frequency domain analysis. a b 3. Design PID controller a b c e k 4. Design and Implement PID controller for any applications. a b c e k Sl. No. 1. Description of experiments a) Step, ramp and Impulse response of first order systems. b) Step, ramp and Impulse response of second order systems. Contact hours C-D- I-O IOs Reference 3 C,I Identification of damping in second order systems. 3 C,I Time domain analysis for second order systems 3 C,I Stability analysis of linear systems using Routh-Hurwitz method 3 C,I Stability analysis of linear systems using Root Locus. 3 C,I Frequency response analysis using Bode Plot. 3 C,I Frequency response analysis using Polar Plot 3 C,I Design of PID Controller for first order and second order systems. 3 C,D,I,O Design of PID Controller for speed control of DC Motor System. 3 C,D,I,O 3 2 Design of PID Based controller for Twin Rotor Multi Input 10. Multi Output System. 3 C,D,I,O 3 3 Total contact hours 30 LEARNING RESOURCES Sl. No. REFERENCES 1. LAB manual 2. Guoshinghuang, PC based PID speed control in DC Motor, IEEE, ISBN , Control of Twin Rotor MIMO System (TRMS) Using PID Controller, International Journal of Advance Engineering and Research Development, ISSN: , Course nature Assessment Method (Weightage 100%) Assessment Insemester Experiments tool Record 5 MCQ/Quiz/Viva Voce Practical Model examination Total Weightage 40% 5% 5% 10% 60% End semester examination Weightage : 40%

6 INTRODUCTION TO THE LABORATORY BACKGROUND Industrial applications of intelligent methods covering a large area from paper and metallurgical industries to biotechnology and also electronics production and telecommunications. Applications consist of soft sensors, advanced control and diagnostics (lime kiln, pulp cooking, bleaching, TMP-refiner, paper machine, blast furnace, converter plant, continuous casting, solar power plant, waste water processes, bioprocesses, fluidised bed granulator), electronics production (testing, diagnostics, process analysis and simulation), rotary drying (pilot-scale process, measurements, and control test bench, distributed simulation over the web). DESCRIPTION Control Engineering Laboratory takes care of teaching at the graduate level in basics of control and instrumentation, modeling, simulation, and optimization, intelligent methods, applications in paper, metallurgical and biotechnical processes. For research students, intelligent methods (fuzzy logic, neural networks, genetic algorithms, expert systems) are the main area. CURRENT EQUIPMENT: This lab is currently equipped with 22 systems. 19 systems with HP Compaq and 2 with IBM, 1 with LENOVA with LCD display monitor, optical ps2 mouse and keyboard, CPU with Pentium processor, 2GB RAM, 150 GB hard disk, Windows XP sp2 operating system, MATLAB and other application software s. 6

7 Exercise Number: 1 Title of the Experiment: Date of the Exercise: STEP, RAMP AND IMPULSE RESPONSE OBJECTIVE (AIM) OF THE EXPERIMENT To obtain step, ramp, impulse response of first and second order system. FACILITIES REQUIRED AND PROCEDURE a) FACILITIES REQUIRED TO DO THE EXPERIMENT: S.NO APPARATUS QUANTITY 1. Matlab software 1 2. Computer 1 3. Control system tool box 1 b) THEORY: Transfer function: It is the laplace of the output divided by the laplace of the input of a system. Step-The response of a system (with all initial conditions equal to zero at t= 0-, i.e, zero state response) to the unit step input is called the unit step response. Ramp : The ramp function is a unary real function whose graph is shaped like a graph. c) PROCEDURE: Enter the program in the editor window. If the program is typed in command window, the functions should be typed without semi-colon. Enter the values in the numerator & denominator depending on order of the system. The syntax used to get transfer function is tf. The syntax used for impulse is impulse. Finally save the program and run it. 7

8 DESIGN PROCEDURE/ DESIGN CALCULATIONS: Step and Impulse Function A=input( enter numerator ); B=input( enter denominator ); h = tf(a,b); step(h); impulse(h); subplot(2,1,1),plot(step(h)); subplot(2,1,2),plot(impulse(h)); Ramp Function t = -1:0.1:1; x1= t>0; u = (t.*x1); lsim(h,u,t); STEP RESPONSE: 8

9 IMPULSE RESPONSE: RAMP RESPONSE: 9

10 FIRST ORDER STEP RESPONSE IMPULSE RESPONSE: 10

11 RAMP RESPONSE: 11

12 Pre lab questions: 1. What is meant by order of a system? The highest power of the s term in the denominator of the transfer function of the system is called the order of the system. 2. What is a transfer function? It is the laplace of the output divided by the laplace of the input of the system. Post lab questions: 1. What is step response of a system? The response of a system (with all initial conditions equal to zero at t=0- i.e zero state response) to the unit step input is called the step response. 2. What is a ramp function? The ramp function is a unary real function whose graph is shaped like a ramp. 12

13 Exercise Number: 2 Title of the Experiment: IDENTIFICATION OF DAMPING IN SECOND ORDER SYSTEM. Date of the Exercise: OBJECTIVE (AIM) OF THE EXPERIMENT: To study and identify the damping in second order system using MATLAB. FACILITIES REQUIRED: MATLAB software PROCEDURE: 1. Open MATLAB software. 2. Type SIMULINK in the command window or just go to the simulink library bar. A new box will open where we can get the output of different responses using block diagrams. 3. In the New Model window, add input response, transfer function, scope and workspace. 4. Run the simulink and double click on the scope block. 5. Take the output graph. THEORY: ω n 2 The general second order transfer function is G(s) = s 2 +2ζω n s+ω 2 n Where, ζ=damping coefficient ω n =natural frequency There are 4 conditions of ζ: 1) When ζ=0, Undamped 2) When 0< ζ < 1, Underdamped 3) When ζ=1, Critically Damped 4) When ζ > 1,Over Damped As the ζ value is varied, the output graph is varied for the various inputs given be it step, ramp or impulse. For Undamped system, the graph is of continuous wave w.r.t. critical line. The amplitude differs for different ω values. If it is high, amplitude is high and vice versa. For Under Damped system, the graph is also a continuous wave but the amplitude decreases with time and it finally merges with the critical line passing through 1. 13

14 For Critically Damped system, the wave increases gradually and gets in straight line with the value of 1. This indicates the perfect damping required in a system which is controllable. For Over Damped system, the wave always remains below or critical line for anyω value. The graph always remains the same for the damping conditions. Just the nature of waves changes w.r.t. to the Critically damped system is the commonly used and effective. With varying ω values, the amplitude changes. They don t make any significant changes. The important factor is ζ. We can check the damping by using any values in the place of ω&ζ. CIRCUIT DIAGRAM / MODEL GRAPH: Undamped Condition (step) G(s)= 100 s

15 Undamped Condition (ramp) G(s)= 100 s

16 Under Damped (step) G(s)= 100 s 2 +2s+100 Under Damped (ramp) G(s)= 100 s 2 +2s

17 Critically Damped (step) G(s)= 100 s 2 +20s

18 Critically Damped (ramp) ) G(s)= 100 s 2 +20s

19 RESULT: Thus the importance of Damping Coefficient ζwas studied with its various conditions and for various ωvalues for various inputs. PRE LAB QUESTIONS: 1) What is steady state error? 2) What is target value? POST LAB QUESTIONS: 1) What do you mean by order of a system? 19

20 Exercise Number: 3 Title of the Experiment: TIME DOMAIN ANALYSIS Date of the Exercise: 28/07/2017 OBJECTIVE (AIM) OF THE EXPERIMENT To Analyze the Time Domain specifications of Under damped second order system. FACILITIES REQUIRED AND PROCEDURE: FACILITIES REQUIRED TO DO THE EXPERIMENT Matlab software A) THEORY: We can analyze the time domain of the second order under damped system. Peak value, Rise time, overshoot, settling time and steady point. The system has some in-built tolerance; therefore, the settling time is achieved when the wave signal enters this tolerance range. But in some ζ conditions, the wave isn t actually merging with reference line but is in continuous wave motion but since it has entered the tolerance range, it is considered as settled. B) PROCEDURE: Open MATLAB software. Go to New Script option which opens the editor window. Write the generic code for second order transfer function which is : Num=[25]; Den=[1,2,25]; Y=tf(num,den); Stepplot(y) By giving ζ value between 0 and 1 we can have underdamped transfer function. Changing the numerator and denominator values as per our requirement, we can generate graphs. We can measure peak value, overshoot, rise time etc in the graph itself. C) PROGRAM /COMMAND : 1. num= [10000]; 2. den =[1,20,10000]; 3. y= tf(num,den); 4. stepplot(y) 20

21 D) CIRCUIT DIAGRAM / MODEL GRAPH: 1) 2) 3) 21

22 1) Here, ζ=0.1 and ω = 5 Peak amplitude = 1.53 Overshoot = 52.7 % Rise Time = seconds Settling time = 3.92 seconds 2) Here, ζ=0.05 and ω = 10 Peak amplitude = 1.85 Overshoot = % Rise Time = seconds Settling time = 7.6 seconds 3) Here, ζ=0.1 and ω = 100 Peak amplitude = 1.73 Overshoot = 72.9% Rise time = seconds Settling time = seconds INFERENCE: Through the above graphs we understand that if the ζ value is varied in between 0 and 1, the no. of waves may increase or decrease depending on ω value. If ω is taken of very high value, then rise time as well as settling time decreases. And if it is taken low then, the rise time and settling time are of mediocre range. If the ζ value is very much decreased then high overshooting takes place and it takes time to settle, i.e., high peak value is attained. In some cases we may see that settling time is achieved much before the peak value is attained. It is because that the ζ value is very close to achieve critical damping condition. RESULT: Thus the time domain of second order underdamped system is analyzed for various ζ and ω values. The graphs for the same are also plotted with step response. PRELAB QUESTIONS: 1) Define peak time and rise time? 2) What is settling time? Give example. POSTLAB QUESTIONS: 1) What is Frequency Response? 22

23 Exercise Number: 4 Title of the Experiment: STABILITY ANALYSIS USING ROUTH- HURWITZ METHOD Date of the Exercise: AIM OF THE EXPERIMENT: To determine the stability of a system using Routh Hurwitz method. FACILITIES REQUIRED: MATLAB software. Computer. THEORY: The theory of network synthesis states that any pole of the system lies on the right hand side of the origin of the s plane, it makes the system unstable. On the basis of this condition A. Hurwitz and E.J.Routh started investigating the necessary and sufficient conditions of stability of a system. We will discuss two criteria for stability of the system. A first criterion is given by A. Hurwitz and this criterion is also known as Hurwitz Criterion for stability or Routh Hurwitz Stability Criterion. With the help of characteristic equation, we will make a number of Hurwitz determinants in order to find out the stability of the system. We define characteristic equation of the system as: where n determinants for n th order characteristic equation. PROCEDURE: Enter the program in the editor window. Execute the program. Enter the coefficients of characteristic equation in the command window. Finally save the program and run it. The Routh matrix is obtained in the command window. 23

24 Program: clear clc %% firstly it is required to get first two row of routh matrix e=input('enter the coefficients of characteristic equation: '); disp(' ') l=length(e); m=mod(l,2); if m==0 a=rand(1,(l/2)); b=rand(1,(l/2)); for i=1:(l/2) a(i)=e((2*i)-1); b(i)=e(2*i); end else e1=[e 0]; a=rand(1,((l+1)/2)); b=[rand(1,((l-1)/2)),0]; for i=1:((l+1)/2) a(i)=e1((2*i)-1); b(i)=e1(2*i); end end %% now we genrate the remaining rows of routh matrix l1=length(a); c=zeros(l,l1); c(1,:)=a; c(2,:)=b; for m=3:l for n=1:l1-1 c(m,n)=-(1/c(m-1,1))*det([c((m-2),1) c((m-2),(n+1));c((m-1),1) c((m-1),(n+1))]); end end disp('the routh matrix:') disp(c) %% now we check the stablity of system if c(:,1)>0 disp('system is Stable') else disp('system is Unstable'); end 24

25 OUTPUT: enter the coefficients of characteristic equation: [ ] the routh matrix: System is Unstable PRE LAB QUESTIONS: 1. What is meant by the stabitity of a system? 2. How to determine stability of a system? POST LAB QUESTIONS: 1. Define the Routh Hurwitz rule. 25

26 Exercise Number: 5 Title of the Experiment: Date of the Exercise: STABILITY ANALYSIS OF LINEAR SYSTEM USING ROOT LOCUS OBJECTIVE (AIM) OF THE EXPERIMENT To analyze the stability of the system by using Root locus, FACILITIES REQUIRED AND PROCEDURE FACILITIES REQUIRED TO DO THE EXPERIMENT: S.NO APPARATUS 1. Personal Computer 2. Matlab Software QUANTITY 1 1 ROOT LOCUS THEORY: The root locus technique is a powerful tool for adjusting the location of closed loop poles to achieve the desired system performance by varying one or more system parameters. The path taken by the roots of the characteristics equation when open loop gain K is varied from 0 to are called root loci. PROCEDURE: 1. Enter the command window of the MATLAB. 2. Create a new M file by selecting File New M File. 3. Type and save the program. 4. Execute the program by either pressing F5 or Debug Run. 5. View the results. 6. Analyze the stability of the system for various values of gain. DESIGN PROCEDURE/ DESIGN CALCULATIONS: Problem: The open loop transfer function of a unity feedback system G(s)=K/s (s 2 +8s+17) Draw the root locus using MATLAB Software. (Assume K=1). 26

27 Matlab Program: % Root locus of the transfer function G(s)=1/(S^3+8S^2+17S) num=[1]; den=[ ]; figure(1); rlocus(num,den); Title('Root Locus for the transfer function G(s)=1/(S^3+8S^2+17S)') grid; Matlab Output: 27

28 Pre lab questions: Define stability of the system. What are the disadvantages of RH criterion? How many roots are in the left half of s plane for the equation s 3-4s 2 + s + 6? Post lab questions: Discuss the effects of adding poles and zeros in a closed loop system. The transfer function of an unity feedback system is G(s) = k/s(s+2). Find the centroid and breakaway point. 28

29 Exercise Number: 6 Title of the Experiment: Date of the Exercise: FREQUENCY RESPONSE ANALYSIS USING BODE PLOT OBJECTIVE (AIM) OF THE EXPERIMENT To analyze the stability of the given linear system using Bode plot. FACILITIES REQUIRED AND PROCEDURE FACILITIES REQUIRED TO DO THE EXPERIMENT: S.NO APPARATUS 1. Personal Computer 2. Matlab Software QUANTITY 1 1 BODE PLOT : THEORY: The bode plot is a frequency response plot of the transfer function of a system. A bode plot consists of two graphs. One is plot of the magnitude of a sinusoidal transfer function versus log ω. The other is plot of the phase angle of a sinusoidal transfer function versus logω.the main advantage of the bode plot is that multiplication of magnitude can be converted into addition. Also a simple method for sketching an approximate log magnitude curve is available. DESIGN PROCEDURE/ DESIGN CALCULATIONS: Problem: The open loop transfer function of a unity feedback system G(s)=K/s(s 2 +2s+3) Draw the Bode Plot. Find (i)gain Margin (ii)phase Margin (iii)gain cross over frequency (iv)phase cross over frequency (v) Resonant Peak (vi)resonant Frequency (vii)bandwidth and Check the same results using MATLAB Software. (Assume K=1) 29

30 Matlab Program: %Draw the Bode Plot for the given transfer functiong(s)=1/s(s2+2s+3) %Find (i)gain Margin (ii) Phase Margin (iii) Gain Cross over Frequency %(iv) Phase Cross over Frequency (v)resonant Peak (vi)resonant %Frequency (vii)bandwidth num=[1 ]; den=[ ]; w=logspace(-1,3,100); figure(1); bode(num,den,w); title('bode Plot for the given transfer function G(s)=1/s(s^2+2s+3)') grid; [Gm Pm Wcg Wcp] =margin(num,den); Gain_Margin_dB=20*log10(Gm) Phase_Margin=Pm Gaincrossover_Frequency=Wcp Phasecrossover_Frequency=Wcg [M P w]=bode(num,den); [Mp i]=max(m); Resonant_PeakdB=20*log10(Mp) Wp=w(i); Resonant_Frequency=Wp for i=1:1:length(m); if M(i)<=1/(sqrt(2)); Bandwidth=w(i) break; end; end; Matlab Output: 30

31 Gain_Margin_dB = Phase_Margin = Gaincrossover_Frequency = rad/sec Phasecrossover_Frequency= rad/sec Resonant_PeakdB = Resonant_Frequency = rad/sec Bandwidth = Pre lab questions: Define frequency response analysis. What is Gain margin and phase margin? Post lab questions: What are theadvantages and disadvantages of Bode plot? How can you analyse the stability of the system with Bode plot? 31

32 Exercise Number: 7 Title of the Experiment: Date of the Exercise: FREQUENCY RESPONSE ANALYSIS USING POLAR PLOT OBJECTIVE (AIM) OF THE EXPERIMENT To analyze the stability of the given linear system using polar plot. FACILITIES REQUIRED AND PROCEDURE FACILITIES REQUIRED TO DO THE EXPERIMENT: S.NO APPARATUS 1. Personal Computer 2. Matlab Software QUANTITY 1 1 POLAR PLOT : THEORY: The Polar plot provides a simple test for stability of a closed- loop control system by examining the open-loop system. Stability of the closed-loop control system may be determined directly by computing the poles of the closed-loop transfer function. The Polar Criteria can tell us things about the frequency characteristics of the system. A Polar plot is used in automatic control and signal processing for assessing the stability of a system with feedback. It is represented by a graph in polar coordinates in which the gain and phase of a frequency response are plotted. The plot of these phasor quantities shows the phase as the angle and the magnitude as the distance from the origin. This plot combines the two types of Bode plot magnitude and phase on a single graph with frequencry as a parameter along the curve. DESIGN PROCEDURE/ DESIGN CALCULATIONS: Problem: The open loop transfer function of a unity feedback system G(s)=K/s(s 2 +2s+3) Draw the Polar Plot. Find (i)gain Margin (ii)phase Margin (iii)gain cross over frequency (iv)phase cross over frequency and Check the same results using MATLAB Software. (Assume K=1) 32

33 Matlab Program: %Polar Plot for the Transfer Function G(s)=1/(s+1)^3 num=[1]; den=[ ]; figure(1); polar (num,den) Title('Polar Plot for the Transfer Function G(s)=1/(s+1)^3') [Gm,Pm,Wcg,Wcp] = margin(num,den) grid; [Gm,Pm,Wcg,Wcp] = margin(num,den); Gain_Margin = Gm Phase_Margin = Pm PhaseCrossover_Frequency = Wcg GainCrossover_Frequency = Wc Matlab Output: Gain_Margin = Phase_Margin =

34 PhaseCrossover_Frequency = rad/sec GainCrossover_Frequency = 0 rad/sec Pre lab questions: What is contour? Define the type number and order of the system. Post lab questions: Explain the conditions for stable system in Polar plot. State Polar stability criterion. 34

35 Exercise Number:8 Title of the Experiment: Date of the Exercise: Design of PID Controller for first order and second order systems OBJECTIVE OF THE EXPERIMENT To design a PID controller for the following first order and second order system, 1. G(s) = G(s) = (s+10) 5 s 2 +6s+5 Your design should satisfy the following specifications: i) Percentage overshoot < 15%. ii) Rise time < 100 msec. iii) Settling time < 500 msec. iv)zero steady-state error to a step. FACILITIES REQUIRED AND PROCEDURE d) FACILITIES REQUIRED TO DO THE EXPERIMENT: S.NO APPARATUS SPECIFICATION QUANTITY 1. PC MATLAB Any version Package e) THEORY: Most PID controllers are adjusted on-site and many different types of tuning rules have been proposed in different literatures. Using these tuning rules, delicate and fine tuning of PID controllers can be made on-site. Also, automatic tuning methods have been developed and some of the PID controllers may possess on-line automatic tuning capabilities. Modified forms of PID control, such as I-PD control and two-degrees-of- freedom PID control, are currently in use in industry f) PROCEDURE: Implement the understanding of effects of Proportional, Integral and Derivative Gains over the system response. g) DESIGN PROCEDURE/ DESIGN CALCULATIONS: Trial and Error basis If needed use the cascaded controllers like PID with another PID or any other combinations in series. 35

36 e) BLOCK DIAGRAM: f) DESIGN PARAMETERS OF PID CONTROLLERS: FIRST ORDER SYSTEM: Kp = Ki = Kd = SECOND ORDER SYSTEM: Kp = Ki = 36

37 Kd = g) MODEL OUTPUT RESPONSE: Figure 1: First order uncontrolled open loop response 37

38 Figure 2: First order controlled closed loop response Figure 3: Second order uncontrolled open loop response Figure 4: Second order controlled closed loop response 38

39 Pre lab questions: 2. What is conventional controller? 2. What is the effect of P, I and D on output response of a system? Post lab questions: 3. List the advantages of PID over PI controller. 4. What is the effect of addition of poles and zeros to a system? 39

40 Exercise Number: 9 Title of the Experiment: Design of PID Controller for speed control of DC Motor System. Date of the Exercise: OBJECTIVE OF THE EXPERIMENT To design a PID controller for the speed control of DC Motor Control System represented by the following transfer function, ɵ(s) = (K t /R a B) V a (s) s[(1+st a )(1+sT m ) + (K b K t /R a B)] Where kt=0.01 J=0.01 B=1 Kf=1 Kb=1 Ra=1 La=0.5 And L a = T a Electrical time constant R a J = T m Mechanical time constant B Your design should satisfy the following specifications: i) Percentage overshoot < 12%. ii) Rise time < 80 msec. iii) Settling time < 300 msec. iv)zero steady-state error to a step. FACILITIES REQUIRED AND PROCEDURE a) FACILITIES REQUIRED TO DO THE EXPERIMENT: S.NO APPARATUS SPECIFICATION QUANTITY 1. PC MATLAB Any version Package 40

41 b) THEORY: Most PID controllers are adjusted on-site and many different types of tuning rules have been proposed in different literatures. Using these tuning rules, delicate and fine tuning of PID controllers can be made on-site. Also, automatic tuning methods have been developed and some of the PID controllers may possess on-line automatic tuning capabilities. Modified forms of PID control, such as I-PD control and two-degrees-of- freedom PID control, are currently in use in industry c) PROCEDURE: Implement the understanding of effects of Proportional, Integral and Derivative Gains over the system response. d) DESIGN PROCEDURE/ DESIGN CALCULATIONS: Trial and Error basis If needed use the cascaded controllers like PID with another PID or any other combinations in series. e) BLOCK DIAGRAM: f) DESIGN PARAMETERS OF PID CONTROLLERS: Kp = Ki = Kd = 41

42 g) MODEL OUTPUT RESPONSE: Figure 1: DC Motor uncontrolled open loop response Figure 2: DC Motor controlled closed loop response 42

43 Pre lab questions: 1. What is cascaded controller? 2. What causes instability in system considering the Pole-zero form of a system? Post lab questions: 3. Discuss the effect of PD controller on system performance. 4. Summarize the P Controller and its characteristics. 43

44 Exercise Number: 10 Title of the Experiment: Design of PID Based controller for Twin Rotor Multi Input Multi Output System. Date of the Exercise: OBJECTIVE OF THE EXPERIMENT To design a PID Based controller for orientation control of Twin Rotor Multi Input Multi Output System represented by the following transfer function, G(s) = 3.6 s 3 + 6s 2 + 5s Your design should satisfy the following specifications: i) Percentage overshoot <20%. ii) Rise time <120 msec. iii) Settling time < 600 msec. iv)zero steady-state error to a step. FACILITIES REQUIRED AND PROCEDURE a) FACILITIES REQUIRED TO DO THE EXPERIMENT: S.NO APPARATUS SPECIFICATION QUANTITY 1. PC MATLAB Any version Package b) THEORY: Most PID controllers are adjusted on-site and many different types of tuning rules have been proposed in different literatures. Using these tuning rules, delicate and fine tuning of PID controllers can be made on-site. Also, automatic tuning methods have been developed and some of the PID controllers may possess on-line automatic tuning capabilities. Modified forms of PID control, such as I-PD control and two-degrees-of- freedom PID control, are currently in use in industry c) PROCEDURE: Implement the understanding of effects of Proportional, Integral and Derivative Gains over the system response. 44

45 d) DESIGN PROCEDURE/ DESIGN CALCULATIONS: Trial and Error basis If needed use the cascaded controllers like PID with another PID or any other combinations in series. e) BLOCK DIAGRAM: f) DESIGN PARAMETERS OF PID CONTROLLERS: Kp = Ki = Kd = 45

46 g) MODEL OUTPUT RESPONSE: Figure 1: TRMS uncontrolled open loop response Figure 2: TRMS controlled closed loop response 46

47 Pre-lab questions: 1. What is TRMS? 2. State the purpose of TRMS. Post lab questions: 3. Discuss the effect of PI controller on system performance. 4. Discuss the effect of adding zero to open loop transfer function of a system. 47