EE 370/L Feedback and Control Systems Lab Section Post-Lab Report. EE 370L Feedback and Control Systems Lab

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1 EE 370/L Feedback and Control Systems Lab Post-Lab Report EE 370L Feedback and Control Systems Lab LABORATORY 10: LEAD-LAG COMPENSATOR DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING UNIVERSITY OF NEVADA, LAS VEGAS

2 EE 370/L Feedback and Control System Lab Class: EE370L Semester: Fall 2015 Points: Document Author: Author s Document Topic: Post-Lab #10 Instructor s Comments: 1. Introduction / Theory of Operation The following is a brief list of the elements in this lab. Objective: To demonstrate the concept of Lead-Lag Compensation. Lab Experiments: Task 1: Construct power amplifier in a unity gain feedback. Task 2: Apply a square wave input and record Tr, Ts, Tp, Mp and ess0. Task 3: Apply sinusoidal input and record ωm, ωb and Mm. Task 4: Repeat task 2 and task 3 for gain compensated network. Task 5: Repeat task 2 and task 3 for lead-lag compensated network. Submission: Construct a table that summarizes Tr, Tp, Ts, Mp and ess0 for three feedback amplifiers examined above. Compare the performance of three feedback systems and summarize your findings. 1 of 15

3 !!! EE 370/L Feedback and Control System Lab 2. Description of Experiments The following is a description of the lab experiments, results, simulations, measurements, and screenshots for this lab. Recall: A lead-lag compensator is of the form: Since we are working with the LM12 power amplifier, its corresponding transfer function: For modeling purposes, let us scale the equation by 10 6 : Note: Since the transfer function is being scaled, the data will need to be converted back by using the same scaling factor. Task 1: Construct a power amplifier in a unity gain feedback arrangement. 2 of 15

4 EE 370/L Feedback and Control System Lab The bode response of the power amplifier with a unity gain feedback Refer to code: 3 of 15

5 EE 370/L Feedback and Control System Lab The graph of the op-amp unity feedback Refer to code: Task 2: Apply a square wave input and record Tr, Ts, Tp, Mp, esso. Using a square wave with amplitude of 1, a period of 5 seconds, taking a sample at every 0.1 second interval. 4 of 15

6 EE 370/L Feedback and Control System Lab Tp = peak time = 4s Ts = response to the input reaches approximately 5% of its final value = 4.8s Tr = response to the input rises from 10 to 90% of its final value = 0.5s 5 of 15

7 ! EE 370/L Feedback and Control System Lab Mp = resonance peak for measure of relative stability, it is defined as the max value of the magnitude of the close loop frequency response. ess0 = steady state error, for our case of an square wave input is Ess = R(s) C(s), where R(s) and C(s) is the input and output respectively: E(s) = R(s) C(s), Where Taking the Laplace of the square wave with a period T = 5 for r(t) =r(t-t) then! And C(s) is 6 of 15

8 !! EE 370/L Feedback and Control System Lab Task 3: Apply a sinusoidal input and record ω m, ω b, Mm. We use the same sinusoidal input but only taking the data for 1 cycle. Mm = Overshoot ωb = = 0.4 ωm = of 15

9 EE 370/L Feedback and Control System Lab Task 4: Repeat task 2 and task 3 for gain compensated network. For gain compensated network we want the desired K value to be 60 o By running the above code, the gain K for the compensated system is which is sufficient because K < 1, furthermore it yields a new gain compensated transfer function for a square wave input of period 5 with 2 cycle. For better simulation results, the period can be changed. Note: Changing the period does not affect the K value, it only modifies the settling time. Below are the graphs for periods of 25 and 100 respectively. It is noticed that when t approaches infinity the output settles down to the amplitude of the input. 8 of 15

10 EE 370/L Feedback and Control System Lab Mp = 1.5 Ts = 4.75s Tr = = 1.5s Tp = 5s 9 of 15

11 ! EE 370/L Feedback and Control System Lab In order to find the steady state error we employ the same method as was done for task 2. E(s) = R(s) C(s), Where Taking the Laplace of the square wave with a period T = 5 for r(t) =r(t-t) then And C(s) is: 10 of 15

12 ! EE 370/L Feedback and Control System Lab Mm = Overshoot ωb = = 0.5 ωm = 2.8 Task 5: Repeat task 2 and task 3 for lead lag compensated network Recall: The transfer function for a Lead-Lag Compensator can be expressed as: For the Lead-Lag compensator, a phase margin of > 60 degrees is required. Note: An arbitrary %OS of 0.1%, a peak time of 4.5 seconds, and K < 1 will be used. 11 of 15

13 !!! EE 370/L Feedback and Control System Lab Mp = 1.56 Ts = 4.8s Tr = = 1.5s Tp = 5s 12 of 15

14 !!! EE 370/L Feedback and Control System Lab 13 of 15

15 ! EE 370/L Feedback and Control System Lab Mm = Overshoot ωb = = 0.45 ωm = 2.75 As can be seen below, the Lead-Lag compensator gives a slightly beaer result than the gain compensator. Note: The uncompensated column sdll has good results. Uncompensated Gain Compensated Lead Lag Compensated Tr 0.5 s 1.25 s 1.2 s Tp 4.0 s 5.0 s 5.0 s Ts 4.8 s 4.75 s 4.8 s Mp E( )ω 0M 0 0 ωm ωb Mm of 15

16 EE 370/L Feedback and Control System Lab 3. Encountered Problems The following is a description of the problems encountered in this lab and how they were solved. Exchanging Signals with MATLAB During this Lab no problems were encountered. 4. Summary The following is a summary of the lab work performed. Experiments: The experiment and post-lab all consisted of modeling a lead-lag compensator. The first task was a transfer function derivation followed by a MATLAB transformation. Input parameters were given and a signal graph chart was constructed. Finally, the SIMULINK model was realized and simulated for verification. 5. Conclusions The following is the conclusion and lessons learned during this laboratory. Lessons Learned: Since the experimenter was not enrolled in a EE370 lecture, the tuning of closed loop control system parameters was something that needed to be learned outside of the classroom. Therefore, when enrolling in EE370 next semester, the experimenter will have a great preliminary understanding for what is to come. Conclusion: This lab served as a means to model and test the control system parameters for a lead-lag compensator. The experimental observations were both qualitative and quantitative in nature and allowed the user to test varying stability parameters and compare the inputs to the system response. Overall, these labs were helpful in understanding the basics associated with control system design and tuning. Furthermore, all experiments yielded expected results and provided enough balance between theory and application. 15 of 15