Modern Control Engineering

The reason to use generalized plants, rather than individual block diagrams of con-

trol systems, is that a number of control systems with uncertain elements have been

designed using generalized plants and, consequently, established design approaches

using such plants are available.

Note that any weighting function, such as W(s), is an important parameter to in-

fluence the resulting controller K(s). In fact, the goodness of the resulting designed

system depends on the choice of the weighting function or functions used in the de-

sign process.

Note that the controller that is the solution to the Hinfinity control problem is com-

monly called the Hinfinity controller.

Solving Robust Control Problems. There are three established approaches to

solve robust control problems. They are

1. Solve robust control problems by deriving the Riccati equations and solving them.

2.Solve robust control problems by using the linear matrix inequality approach.

3.Solve robust control problems that involve structural uncertainties by using the

analysis and synthesis approach.

Solving robust control problems by use of any of the above methods requires a broad

mathematical background.

In this section we have presented only an introduction to the robust control theory.

Solving any robust control problem requires mathematical background beyond the

scope of the senior engineering student. Therefore, an interested reader may take a

graduate-level control course at an established college or university and study this sub-

ject in detail.

Example Problems and Solutions

A–10–1. Consider the system defined by

Suppose that this system is not completely state controllable. Then the rank of the controllability

matrix is less than n,or

rankCB  AB  p  An-^1 BD=q 6 n (10–136)

x

=Ax+Bu

m

m

Example Problems and Solutions 817

K

w

u

z

y

Generalized

plant

Figure 10–48
A generalized plant
diagram.