DEPARTMENT OF ELECTRONIC ENGINEERING PRACTICAL MANUAL CONTROL SYSTEMS 3 CSYS 302

Transcription

1 Name: Student number: Mark: DEPARTMENT OF ELECTRONIC ENGINEERING PRACTICAL MANUAL CONTROL SYSTEMS 3 (Process Instrumentation and Mechatronics) CSYS 30 Latest Revision: Semester

2 INTRODUCTION The practical component of this course is compulsory for all registered students. Attendance of all practical sessions is mandatory and should a student be given permission to miss a particular session (for medical reasons, for example) it is then the responsibility of the student to make up for this laboratory time. Students will not work in groups and will be expected to complete all the practical work listed. For a student to succeed in this subject he/she must: Have a good knowledge of all prerequisite subjects; Be proficient in graphical representation and analysis of numerical data; Be proficient in the use of a multimeter, oscilloscope, function generator and dual-rail psu; Be proficient in the use of hand tools; Have a good working knowledge of data logging applications; Revise and if necessary, summarize material covered during lectures. Read all material issued to them. Complete any problems set in class. Do any reading indicated to support practical work. Actively participate in practical work. RULES FOR PRACTICAL LABORATORY SESSIONS Students who do not comply with these rules will be ejected from the laboratory. No eating or drinking in the laboratories (this includes the chewing of gum). Closed shoes are to be worn at all times (slip-slops, bare feet and open shoes are not allowed). Cell phones are not to be used in the labs for making calls. No unsupervised access is allowed in any of the Instrumentation and Control laboratories. Permission must be obtained before entering a laboratory. Each student is expected to have his/her own equipment, including flat screwdriver, star screwdriver, side cutters, long nose pliers, soldering iron, multi-meter, breadboard and toolbox. Note that students will not be permitted into the laboratory without these minimum requirements. IMPORTANT DATES AND MARKING Practical sessions will commence at the start of the second week of lectures. There will be 10 weeks of practicals. The purpose of the pre-practical tutorials is to give insight into and prepare students for the practical itself. The practical manual is to be handed in at the end of each practical session and is to be collected by 1:00 on the Friday of each week. Marks are allocated for the progress throughout each practical, as indicated. All of these marks will count towards the practical mark for the subject. A minimum practical mark of 50 % (see Departmental rule EL11 (1)) is required. Some answers only count for one mark while other lengthier answers count up to four marks. The general marking rubric is as follows:

3 Work is not done or is so poorly done that it is considered totally wrong. 0 An attempt was made but very little is correct. 1 Work was done with some mistakes. Work is complete but is untidy or not properly labelled. 3 Work is complete, neat and tidy and of an acceptable standard. PRACTICAL ONE DYNAMIC RESPONSE The purpose of this practical is to revise the work done in Control Systems on Matlab as well as introduce students to the use of Simulink. Several new Matlab commands and functions are required and students are expected to research these. Consider the following position control system given in block diagram form: r(t) e(t) x x 3 c(t) x 1 PRE-PRACTICAL TUTORIAL 1.1 Choose the state variables as indicated and derive the state space representation. 3

4 PRACTICAL ( weeks) 1. For the state space model, write a Matlab script that will plot r(t), x 1 (t), x (t), x 3 (t) and e(t) due to a unit ramp input. These plots should all be on the same set of axes, with a time axis of s. Write out the script in the box provided. Make use of the lsim command. W1 1.3 Construct a Simulink model directly from the block diagram to give the same result as in 1.. Save this model to your flash drive and now write a Matlab script that calls and runs the model. Show the Matlab script here. 10 W

5 PRACTICAL TWO ANALOG VERSUS DIGITAL SIMULATION In most engineering disciplines simulation is a very important process. In this practical you are required to build an analog circuit that will simulate a transfer function, apply a 1 v step input to the circuit and record the output, then compare this output with that obtained from a pure digital simulation (done in Matlab). PRE-PRACTICAL TUTORIAL.1 The circuit diagram shows two resistors connected to form a voltage divider. What is the equation for the output voltage in terms of the input voltage? v i (t) R 1 R v o (t) 1. Now sketch a diagram to show how this same voltage divider can be implemented using only a potentiometer. Fully label your diagram and give the input/output equation..3 Revise the operational amplifier circuit configured as a summer, an integrator, an inverting amplifier and a non-inverting amplifier. Sketch the respective circuit diagrams and give the input/output equations. Summer Integrator Inverting amplifier Non-inverting amplifier 5

6 . Research the LM3 quad operational amplifier. Pay particular attention to the power connections for use with a dual rail supply. Draw a neat sketch indicating the pin out configuration..5 Construct a simulation diagram for a system that yields the following transfer function. Show only your final diagram. Cs 0,6s 3 Rs s s 10.6 Write a simple Matlab script to plot the step response of this transfer function over a time range of from 0 to 10 s. 6

7 .7 Save and print the figure window showing the response. Paste the response here. PRACTICAL ( weeks).8 Design an operational amplifier circuit to implement the simulation diagram. Pay careful attention to the sign of the signals throughout the circuit. Your circuit must have at least one non-inverting amplifier. Note that for a gain of less than one you may not use an amplifier but rather a voltage divider. The concept of minimum component count should be used. Show your final diagram only in the box provided on the next page..9 Your circuit and this parts list need to be checked and signed off. This will allow you to get components and build the circuit. No. Quantity Correct Part Description Supervisor Signature: Date: 7

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9 .10 Construct the circuit and do any fault finding to ensure the correct response (as found in.7). Now using the oscilloscope, save the response to a.csv file. You must show the lecturer what your response is. W.11 Now starting with the script from section.6, load the values from the.csv file and plot the two sets of values on the same figure window. Show the script here..1 Print the figure window and paste it here W

10 PRACTICAL THREE EXPERIMENTAL DETERMINATION OF A TRANSFER FUNCTION At the beginning of the Control Systems course we saw how to derive transfer functions of simple electrical and mechanical circuits. Most often it is found that this is not possible and the control system designer needs some other way of finding the transfer function. Frequency domain techniques offer a simple way of estimating a transfer function. In this practical a simple circuit is constructed and then its transfer function is to be experimentally derived. PRE-PRACTICAL TUTORIAL You are required to research a simple passive circuit for a phase lead compensator. Your research must include the circuit diagram, Bode plot, most common use of the compensator, etc. You also need to investigate the implementation of a phase lead compensator using active components and this should include the relative advantages and disadvantages of the two types of circuits. As a start to this research the following references, with page numbers, are given: [1] Ogata K, Modern Control Engineering, th Edition. Prentice Hall, New Jersey, 00 (58 to 589). [] Nise N S, Control Systems Engineering, 5 th Edition. John Wiley and Sons, Asia, 008 (581 to 588). [3] D Azzo J J and Houpis C H, Linear Control System Analysis and Design, th Ed. McGraw-Hill, New York, 1995 (6). [] Bolton W, Control Engineering. Longman Scientific and Technical, England, 199 (73 to 75). 3.1 Passive phase lead compensator circuit diagram. 3. Phase lead compensator Bode plot. 10

11 PRACTICAL ( weeks) 3.3 Using the circuit found in the pre-practical tutorial and the following values; R 1 = 5,6 k, R = 70 and C = 0,01 F, build a lead compensator on your breadboard. 3. Now connect channel one of the oscilloscope to the input and channel two to the output. Set the function generator to a sinusoidal output of about 3 v peak to peak and connect this to the input. Note that no power supply is needed. 3.5 Starting at a frequency of around 100 Hz (and going up to around 1 MHz) measure the input and output amplitudes and their phase difference. Use the oscilloscope for all these measurements. To do this you must fill in values in columns 1, 3,, 6 and 7. Twenty sets of measurements are required over this range of frequencies and be sure to space them correctly. Complete all measurements at each frequency before moving on to the next frequency. Once all your measurements are complete you must calculate the values for the remaining columns in the table Freq (Hz) Freq (rad/s) v i (v) v o (v) Lm (db) t (s) T (s) Phase (deg) W1 3.6 With the above table complete sketch the Bode magnitude and phase angle plots on semi-log graph paper. 11

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13 3.7 Using asymptotic approximations (straight lines) on the magnitude plot, estimate the transfer function. Write down only the transfer function, in the normal form. 3.8 Explain what information is obtained from the phase angle diagram. 3.9 Now derive the transfer function from first principles and write it in the normal form. 13

14 3.10 Write down the two transfer functions for comparison purposes. Experimental transfer function. First principles transfer function Give reasons for their differences. 30 W 1