matlab

Set up a closed loop system with a feedback PID controller, and a process transfer function (Gp) of 1/(s2+s+1). There will be a disturbance variable entering the system before the process (so before Gp) but after the controller. Use the add button to combine the disturbance with the controller output. If you are unsure as to what this system should look like, please contact me or a TA to be sure you have set up the Simulink model correctly.

For this homework, we will look at how the system responds to changes in the disturbance variable. Be sure to save your model as we may use this same model again on the next matlab homework.

Assume that your disturbance variable undergoes a unit step change at time=1, while the set point does not change. Use equation 8-1 to figure out what your error will be in the space below:

Make a graph in Matlab of your system’s response to the disturbance with no control.

Now, assume that you want to add proportional control. Try at least 4 different Kc values to see how different values affect the system. Make a graph in Matlab of the system response with the different Kc values, and write beneath the graph which Kc value you believe will be best and your reasoning.

Next, we’ll look at PI control. Use a Kc value of 1 (Integral Control will now take care of offset seen above), and try at least 3 τI values to see which is best. Make a graph in Matlab of the system response with the different τI values, and write beneath the graph which τI value you believe will be best and your reasoning.

Now, let’s add in D for a PID controller. Use a Kc value of 1 and τI=1, and try at least 3 τD values to see which is best. Make a graph in Matlab of the system response with the different τD values, and write beneath the graph which τD value you believe will be best and your reasoning.

Lastly, state what type of control you would choose to implement in your process: P, PI, or PID. Explain why below: