Consider the closed-loop transfer function
T(s) = 10K/(s2 + 20s + K)
1. Obtain the family of step responses for K=10, 100, and 500. Co-plot the responses and develop a table that includes the following:
a. Percent overshoot
b. Settling time
c. Steady-state error.
A negative feedback control system is depicted in Figure 1. Suppose that your design is to find a controller, Gc(s), of minimal complexity such that your closed-loop system can track a unit step input with steady-state error of zero.
1. As a first try, consider a simple proportional controller: Gc (s) = K,
where K is a fixed gain. Let K = 2. Using MATLAB, plot the unit step response.
2. Determine the steady-state error from the plot above. Calculate the theoretical steady-state error and compare your results.
3. Now consider a more complex controller: Gc (s) = K0 + K1/s
where K0 = 2, and K1 = 20. This type of controller is known as a proportional, integral (PI) controller. Plot the unit step response using this controller.
4. Determine the steady-state error from the plot. Calculate the theoretical steady-state error and compare your results.© BrainMass Inc. brainmass.com October 25, 2018, 12:09 am ad1c9bdddf
Please see the attachment.
In problem 1, I think the problem should ask for ...
A negative feedback control system is analyzed. The design for a complex controller is given for minimal complexity such that the closed-loop system can track a unit step input with steady-state error of zero.
Determine peak time and overshoot in a control system
A system with G(s) = K/(s(s+1)(s+4)) where K = 1
Design aPI controller so that the dominant roots are at s = -0.365+j0.514 and -0.365-j0.514.
If a change of K = +50% or -50% occurs. Does the system peak time increase or decrease? Does the overshoot increase or decrease?View Full Posting Details