# Cascade Compensation

One easy way to control the plant is to cascade a controller before the plant like in Figure 9.

We can design the controller H(s) to alter the behavior of our system.

## Proportional Integral (PI) Control

## Proportional Derivative (PD) Control

## Proportional Integral Derivative (PID) Control

A PID controller is used where we need to both eliminate steady-state error and shape the time response. We need to choose two different zero locations and set the total gain of the system.

## Lag Compensation

The purpose of a lag network is to reduce steady state error by increasing the gains at low frequency and maintaining the gain at higher frequencies. This keeps the phase margin the same. We can achieve this because of the frequency response of the lag network (shown by its bode plot in Figure 10).

We can place the pole and zero carefully to control how much the phase decreases by. The design procedure is as follows:

Set the low frequency asymptote to be 0 db and locate the lower break frequency.

Reset the system gain K to compensate for attenuation.

## Lead Controller

Its frequency response looks like in Figure 11.

Find the break frequencies.

Reset the gain.

Simulate and tweak.

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