Assignment – Closed-Loop Feedback Control of Motor Position with PI...

Assignment – Closed-Loop Feedback Control of Motor Position with PID
Proportional Controller
In this section we will be looking at the impact that proportional control has on the response output. The proportional controller can be turned on by checking the “Proportional” option under the “Controller Type” tab.
1) Effect of proportion controller on system’s response
a) Set the proportional gain (Kp) to 1 and the input type to step before starting the simulation. Run the simulation for 0.9 second. Take a screenshot of the Response Output plot and include it in your final PDF.
b) Restart the simulation, set the proportional gain (Kp) to 21 and the input type to step. Run the simulation for 0.9 second. Take a screenshot of the Response Output plot and include it in your final PDF.
c) Compare the response outputs from case (a) and (b) and identify three main differences between the plots. Hint: - Compare position with respect to time and the overall profile between the two curves.
d) Restart the simulation, bring the proportional gain (Kp) back to 1. Pick five different proportional gain values between 1 and 21 and run the simulation for 0.9 secs for each of the proportional gain values. Take screenshots of the response output for different values of proportional gain and include them in the final PDF. Also, in a few sentences describe the effect the proportional controller has on the response output.
Note: - You can’t see the effect of proportional gain (Kp) if the Response output reaches the steady state value (response output stops changing with respect to time), change the “Required position” knob to see the effect of different Kp values or restart the simulation for every proportional gain (Kp) value.
2) Effect of proportional controller on the steady-state error
a) Restart the simulation by pressing the “Stop Simulation” button. Bring the proportional gain value (Kp) back to 1 and the Required position to 1 radian as well. Start the simulation and let it reach steady state (response output stops changing with respect to time). Now increase the disturbance input to 1. Attach a screen capture showing the final response and describe in a few sentences the impact of the disturbance input.
b) As the simulation from 2a is running, increase the proportional gain (Kp) to 5, 10 and 21 and take screenshots of each case, include them in your final PDF and describe in a few sentences the impact of the proportional controller on steady-state error.
3) As you were working with the proportional controller in the past two problems is there any mechanical component that behaves in a similar way as the proportional controller? If so, what is that component and what attribute of that component does increase in proportional gain affect? Hint: - As you increase the proportional gain, look at the Motor Shaft position located at the top left of the application. As mentioned in the documentation, the gauge could be thought of as a cylindrical disk attached to the motor shaft and the red indicator as a mark on the disk.

Proportional Derivative Controller
In this section we will be looking at the impact that Proportional-Derivative (PD) control has on the response output. The Proportional-Derivative (PD) controller can be turned on by checking the “Proportional” and the “Derivative” option under the “Controller Type” tab.
1) Effect of Proportional-Derivative controller on system’s response
a) Start a new instance of the simulation by setting the “Required position” to 1 radian, “Disturbance Input” to 0, proportional gain Kp to 21 and derivative gain Kd to 0.01. As the Response Output is oscillating turn up the derivative gain value to 0.29 (ensure to do this when the response output is oscillating and not during steady state to see the effect). Take a screenshot of the Response Output plot and include it in your final PDF
b) Now run the simulation for 0.5 second for three different values of derivative gain Kd 0.01, 0.08, and 0.15. Keep the values of proportional gain Kp, Required position and Disturbance Input to the ones in 1a. Take a screenshot of the response output for each value of the derivative gain and include it in the final PDF.
c) Using the plots in 1a and 1b, in a few sentences describe the effect the derivative controller has on the response output.
d) Using the plots from 1b, for each derivative gain Kd value (0.01, 0.08 and 0.15) approximately how long does the response output take to reach steady state? (As mentioned earlier steady state is when the response output doesn’t vary with time)
2) Effect of Proportional-Derivative controller on steady-state error
a) Start a new instance of the Simulation by setting the “Required position” to 1 radian, “Disturbance Input” to 0, proportional gain Kp to 21 and derivative gain Kd to 0.15. As the simulation is running increase the disturbance input to 5. Let the simulation run until 0.9 second take a screenshot and include it in your final PDF.
b) As the simulation from 2a is running, increase the derivative gain Kd. Does the derivative gain impact the steady-state error?

Proportional-Integral Controller
In this section we will be looking at the impact that Proportional-Integral (PI) control has on the response output. The Proportional-Integral (PI) controller can be turned on by checking the “Proportional” and the “Integral” option under the “Controller Type” tab.
1) Effect of Proportional-Integral controller on system’s response
a) Start a new instance of the simulation by just checking the Proportional option under the Controller Type tab i.e., start the simulation with only proportional controller. Set the proportional gain Kp to 21, Required position to 1 and Disturbance Input to 0. Let the simulation run until the response output reaches steady state value. Take a screenshot of the response output and include it in the final PDF.
b) Repeat 1a but with the integral option checked under the Controller Type tab. Take a screenshot of the response output once it reaches steady state and include it in the final PDF.
c) Using the plots from 1a and 1b, how long does the response output take to reach the steady in both cases?
d) With the PI controller enabled, run the simulation for the following values of integral gain Ki, 150, 300 and 500. For each value of the integral gain, run the simulation for 0.9 second, take screenshot of the response output and include it in the final PDF
e) Using the plots in 1d in a few sentences describe the effect the integral controller has on the response output
2) Effect of Proportional-Intergral controller on steady-state error
a) Start a new instance of the Simulation by setting the “Required position” to 1 radian, “Disturbance Input” to 0, proportional gain Kp to 21 and integral gain Kd to 0.15. Let the simulation run until response output reaches steady state. Now increase the disturbance input to 5 and the let the response output reach steady state. What happens to the steady state error?
b) Repeat the procedure in 2a for the following values of integral gain Ki, 100, 150, 200. Include response output screenshots for each Ki value and describe in few sentences the effect that integral gain Ki has on the steady state error.
Proportional-Integral-Derivative Controller
Now that we have explored different types of controllers and their effects on the response output, we will work with the PID controller in this section
1) Here you will be tuning the gains of the PID controller so that the response output closely follows the Reference input. The reference input will be a pulse signal of frequency 20Hz and 1 radian. Take a screenshot of the response output and include it in the final PDF.
2) As the simulation is running from 1) increase the disturbance input to 5