# Example 9.3 (Nise)

This is the 3rd post in my series on solving controller design problems from Nise [1]. This time we are going to design a pure derivative controller to meet a settling time requirement. The interesting part of this problem is how we used the settling time requirement to choose the controller zero’s location.

### Example 9.3: Designing an Ideal Derivative Controller [1]

In this problem we are given a plant and told to design a derivative controller that reduces the settling time by a factor of 3. We are also told that the plant has 16% overshoot (we will assume this is fixed throughout the problem). The solution flow is:

**(1)** Draw out the root locus.

**(2)** Calculate the damping from the overshoot specification. Use the damping coefficient to find the closed loop pole locations.

**(3)** Use the pole locations to solve for the uncompensated settling time of the system. Also calculate the desired compensated settling time (reduce by a factor of 3).

**(4)** Choose the location of the new compensated closed loop poles by calculating real and imaginary components from the settling time requirement.

**(5)** Use the sum of the phase contributions from all open loop poles and zeros to choose the position of the controller zero.

Figure 1

Figure 2

#### References:

[1] Nise, Norman S. **Control Systems Engineering, 4th Ed.** John Wiley & Sons, Inc. 2004.