EE 370L Feedback and Control Systems Lab

EE 370/L Feedback and Control Systems Lab Section 1001

Post-Lab Report

EE 370L Feedback and Control Systems LabLABORATORY 10:

LEAD-LAG COMPENSATOR

DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING UNIVERSITY OF NEVADA, LAS VEGAS

DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING

Brandon

Cross-Out

EE 370/L Feedback and Control System Lab Section 1001

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.

Class: EE370L Semester: Fall 2015

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Document Topic: Post-Lab #10

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EE 370/L Feedback and Control System Lab Section 1001

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 106:

!

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.

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EE 370/L Feedback and Control System Lab Octavio L. GonzalezSection 1001

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Theboderesponseofthepoweramplifierwithaunitygainfeedback

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Refer to code:


Thegraphoftheop-ampunityfeedback

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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.

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Refer to code:


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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


EE 370/L Feedback and Control System Lab Octavio L. GonzalezSection 1001 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

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R(s) and C(s) is the input and output respectively:

E(s) = R(s) – C(s), Where

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Taking the Laplace of the square wave with a period T = 5 for r(t) =r(t-T) then

! And C(s) is

!

!

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Task 3: Apply a sinusoidal input and record ωm,ωb,Mm.We use the same sinusoidal input but only taking the data for 1 cycle.

!

!

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Mm = Overshoot

ωm = 1.85

ωb = 2.1-1.70 = 0.4


Task 4: Repeat task 2 and task 3 for gain compensated network. For gain compensated network we want the desired K value to be 60o

By running the above code, the gain K for the compensated system is 0.1855 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.




Ts = 4.75s

Tp = 5s

Mp = 1.5

Tr = 4.2-3.05 = 1.5s

EE 370/L Feedback and Control System Lab Octavio L. GonzalezSection 1001 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:

�

�

�

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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:

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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.

!


Mm = Overshoot

ωm = 2.8

ωb = 3.1-2.6 = 0.5


!

!

!


Ts = 4.8s

Tp = 5s

Mp = 1.56

Tr = 4.2-3 = 1.5s


!

!

!



!

Ascanbeseenbelow,theLead-LagcompensatorgivesaslightlybeAerresultthanthegaincompensator.Note:TheuncompensatedcolumnsDllhasgoodresults.

Uncompensated Gain Compensated Lead Lag Compensated

Tr 0.5s 1.25s 1.2s

Tp 4.0s 5.0s 5.0s

Ts 4.8s 4.75s 4.8s

Mp 2.48 1.5 1.56

E(∞)ω 0M 0 0

ωm 3.4 2.24 2.28

ωb 15.7 12.7 13.96

Mm 1 0.2 0.2


Mm = Overshoot

ωm = 2.75

ωb = 3.1-2.55 = 0.45


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.


EE 370L Feedback and Control Systems Lab

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