An Introduction to System Modeling and Control

15State Feedback

In Chapter 14 we discussed statespace models. We now show how these models can be used to design very effective controllers.

15.1 Two Examples

Let's do two examples to see how statespace models and state feedback are used in control systems.

Example 1 Stabilization of an Inverted Pendulum

Figure 15.1 shows the inverted pendulum on a cart. Recall the transfer function model of the inverted pendulum given by (see 13.13)

(15.1)

where

Figure 15.1. Inverted pendulum on a cart.

Let

so that a statespace representation is given by

(15.2)

Recall that the input is the force on the cart and our objective is to keep and . Let's try a state feedback controller defined ...