Applied Controls-

Open Loop Response:

For this laboratory you will use the MATLAB program to simulate an open loop system. You are to determine the system response to a step and sinusoidal input. Each student will be assigned a specific system Your system transfer function is:

F(s) = d/(0.1s³ + as² + bs + c)

A = 16

B= 0.6

C = 36

D = -180

For your system plot the response and determine the following characteristics to a step input

1) Under, over, or critically damped

2) System rise time

3) Maximum overshoot

4) Maximum response rate

5) Settling time

6) Oscillation period

7) System gain

8) Delay time

For your system plot the response and determine the following characteristics to a sinusoidal input

1) Low frequency gain

2) Bandwidth

3) Natural frequency

4) Resonance peak

5) Rolloff rate

Turn in:

• Short memo with the experimental description and above parameters. This memo should include all of your results and your system transfer function.
• Plot of your systems response to a step input, with the above critical points identified.
• Bode plot of your systems response with the critical points identified.

PID Controller Tuning:

For this laboratory you will use the MATLAB program to simulate a feedback control system. Each individual has been assigned a specific system which you should use.

For your system do the following:

1. Tune a PD controller to respond as fast as possible to a step input with less than 5% overshoot and a steady state error of less than 1%.

2. Tune a PID controller to respond as fast as possible to a step input with less than 5% overshoot and a steady state error of less than 1%.

3. Tune a PID controller to respond as fast as possible to a step input with no overshoot and a steady state error of less than 0.5%.

Turn in:

• Short memo with the system description and your gains
• Plot of your systems response for each case
• Compare the results of your 'controlled' system to the open loop response of the same system to a step input.

Control Design Tools:

For this laboratory you will some of the tools from the Control Systems Toolbox in MATLAB to help visualize a systems open and/or closed loop response. Each individual has been assigned a specific system to use.

For your system do the following:

1. Make a Body plot with both the open loop response and closed loop response of your system.

2. Make a Nichols plot of your systems response.

3. Make a Zero-Pole plot of your systems response.

4. Make a Root-locus plot of your systems response. Find the critical gain and use Simulink to plot the step response of your closed lop system response to gains around the critical value.

5. Make a Nyquist plot of your systems response.  

Turn in:

• Short memo with your plots and a description of each plot and any critical points on each plot.
• When appropriate compare the results of your open loop response and /or PID controlled response to the plotted results.

Zero-Pole Placement:

For this laboratory you will use the MATLAB program to simulate a feedback control system. Each individual has previously been assigned a specific system which you should use.

For your system do the following:

1. Use the MatLab Control System Designer (controlSystemDesigner) to design a PID controller to best fit the design criteria from the PID lab.

2. Use the MatLab Control System Designer (controlSystemDesigner) to design the a lead controller to best fit the design criteria from the PID lab.

Turn in:

• Short memo with:

-The open loop plots.

-The plots of your systems response for each case (step and bode from CSD).

-Gain and phase margins for each controller.