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## Compensating function Gc (s) such that one of the poles is eliminated.

Solution.pdfPart 1: Theoretical compensating function

Determine a compensating function Gc (s) such that one of the poles is eliminated. Provide all calculations in detail with explanation. [10 marks]

Part 2: Computer simulation

Using the Matlab Control System Toolbox, provide the following items, providing documentation on your methods and commenting on your results.

- Construct and document a model of the plant. [2 marks] ?
- Construct and document the functions R(s) and C(s) for a step response and an impulse ?response on the input R(s). [4 marks] ?
- Provide a Bode Plot. [5 marks] ?
- Use an appropriate Matlab tool to determine the stability of the control system. [4 marks] ?

Upload your Matlab code to blackboard in runnable form. This will be discussed in class.

Part 3: Practical implementation study

Describe in one paragraph each, two possible methods of real-time practical implementation of a control system. Choose from non-programmable control systems hardware, programmable logic controller or robotics. Cite a practical commercial example of each. [5 marks]

Your report on Parts 1, 2 and 3 should be approximately ten sides of A4 long and have a conclusion of at least 200 words, drawing out from your report the major ways in which you have met the objectives, being as specific and technical as possible. Plagiarism will be punished! Your report must be uploaded to the link in blackboard.

**Solution:**

**Part 1: Theoretical compensating function **

A plant is controlled as given,

The plant dynamics are represented by,

**Solution 1 –**

The open loop pole is

The rise time

The plant dynamics can be written as,

This is compared to,

To meet the magnitude criterion

We added,

For this part of controller to have gain 1, we need to divide by 0.10. This will not change the location of zeros.

The closed loop transfer function is,

The closed loop transfer with The Proportional Integral Derivative (PID) control –

The general transfer function of a PID controller is

The natural frequency,

The damping factor,

**Part 2: Computer simulation**

**Solution 1**

To model the plant transfer function with feedback can be calculated as

** **

To model the plant transfer function with only compensator can be calculated as

**Solution 2**

*Step response*

Input R(s) for step response is

Using above model equation we can determine the value of C(s).

*Impulse response*

Input R(s) for impulse response is

Using above model equation we can determine the value of C(s).

**Solution 3**

Bode plot can be calculated as below:

**MATLAB CODE**

clc;

clearall;

closeall;

%% Bode Plots

sys = tf([10 7 1],[1 10.7 7.01 1]);

figure;

h = bodeplot(sys);

title('Bode plot for C(s) for impulse response');

saveas(gcf,'bode_impulse.jpg','jpg')

sys1 = tf([10 7 1],[1 10.7 7.01 1 0]);

sys2 = tf(1,[1 0.7 0,01]);

figure;

h1 = bodeplot(sys1);

title('Bode plot for C(s) for step response');

saveas(gcf,'bode_unit.jpg','jpg')

figure;

h2 = bodeplot(sys2);

title('Bode plot for G(s)');

saveas(gcf,'bode_original.jpg','jpg')

**PLOTS**

**Step response**** **

**Impulse response**

For G(s)

**Solution 4**

Using below MATLAB code and corresponding analysis we can provide below stability analysis.

**Unit response**

Phase Margin and Gain Margin is greater than 0 so **system is stable** for unit step input

**Impulse Response**

Phase Margin and Gain Margin is greater than 0 so **system is stable** for impulse input

For G(s)

**Part 3: Practical implementation study **

*Robotics*

Probablereply for the issue of robot control in real time including the nonlinear model of the controller is given by utilizing a parallel handling approach. The parallelism intrinsic in the controllers which is adaptive is to acquire a proficient usage that lessens the general calculation time to inside the point of confinement adequate for constant control. The implemented distributed algorithm is executed on a system of transputers for the PUMA 560 arm.

*PLC*

A new PLC based realization in real time for control system is done by considering one application in the design of feedforward control system. The modeled approach is connected to a mechanical fuel-gas pressure framework which is utilized to provide the supply of fuel gas to attached turbines in control plants. Because of the expanding interest for quick operation point moves with elite and exactness prerequisites, the as of now connected decentralized PID controllers have all the earmarks of being not fitting any more. Consequently, by methods for framework simulations we have the new approach on a PLC. Moreover, the PLC-construct controller is tried in light of an equipment on top of it stage running with an efficient computational complexity handling system in accordance with real time application

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