Bill Goodwine's Courses

Reading: All of chapter 9 in the course text.

Problem: Consider a mass-spring-damper system like the one illustrated in Figure 4.1 of the course text. Let m=1, b=2 and k=5.

1. Determine the transfer function relating the input force to the position of the mass.
2. Sketch the root locus plot for this system. By referring to your root locus plot, will it be possible to use proportional feedback control so that a step reference input will have a percentage overshoot less than 10% and a rise time of less than 0.6 seconds?
3. If your answer to the previous part is no, then design a lead compensator that will satisfy these two specifications.
4. For the system with lead compensation, what is the steady state error for the system with a unit step input?
5. If the steady state error is greater than 10%, then design a lag compensator so that the steady state error is less than 10%. Be sure that the transient specifications are still satisfied (the overshoot and rise time ones). Also, the system must have an error of less than 10% in less than 20 seconds.

You must do all the steps of the problem both by hand as well as using matlab. You must show the computations that were the basis for your decision for the location of the poles and zeros in the lead and lag compensators. You must also build a simulink model to verify the response of the system and submit plots of the system step response at each step in the design process.

What should the steady state response be compared to, to compute the steady state error? The uncompensated steady state response?

AlexDarr wrote:What should the steady state response be compared to, to compute the steady state error? The uncompensated steady state response?

It should be compared to 1 if the input is a unit step.