# Design of a PD controller for a double integrator system

The block diagram of a control system is given in the attachment.The inner loop is positive feedback, i.e. Ks>0, and hence the system is unstable. Adding a P-D controller on the forward channel and a unity negative feedback, one can stabilize the system.

Find:

1. The conditions of Kc and Tc to stabilize the system.

2. The value of Kc and Tc to let Mp=163% and ts=0.8, when Ks=0.8 .

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#### Solution Preview

The block diagram of a control system is given below. The inner loop is positive feedback, i.e. Ks>0，and hence the system is unstable. Adding a P-D controller on the forward channel and a unity negative feedback, one can stabilize the system. Find:

1. The conditions of Kc and Tc to stabilize the system.

2. The value of Kc and Tc to let Mp=163% and ts=0.8, when Ks=0.8 .

The actual system 1/s² is a double integrator with 2 poles at the origin. There are two loops CL1 is the inner loop while CL2 is the outer loop.

Recall that:

Mp - (peak output - steady state)/step size

tr - rise time from 10% of the step size to 90% of the step size

ts - settling time from control start to the system staying within 5% of ...

#### Solution Summary

This solution provides a step by step method for the design of a PD controller to meet some performance parameters to control a double integrator system.