# 3

# MODERN CONTROL-SYSTEM DESIGN USING STATE-SPACE, POLE PLACEMENT, ACKERMANN'S FORMULA, ESTIMATION, ROBUST CONTROL, AND *H*^{∞} TECHNIQUES

## 3.1. INTRODUCTION

State-space analysis was introduced in Chapter 1, and has been used in parallel with the classical frequency-domain analyses techniques presented in Chapter 2. The state-space approach is applicable to a wider class of problems such as multiple-input/multiple-output (MIMO) control systems. Chapter 2 applied the frequency-domain approaches such as the Bode diagram, and the root locus to linear control-system design.

In the design of a control system, the question arises as to where to place the closed-loop roots. In Section 2.9 which presented the root-locus method, we could specify where to place the dominant-pair of complex-conjugate roots in order to obtain a desired transient response. However, we could not do so with great certainty because we were never sure what effect the higher-order poles would have on the second-order approximation.

The control-system design engineer desires to have design methods available which would enable the design to proceed by specifying all of the closed-loop poles of higher-order control systems. Unfortunately, the frequency-domain design methods presented in Chapter 2 do not permit the control-system engineer to specify all poles in control systems which are higher than two because they do not provide a sufficient number of unknowns for solving uniquely for the specified closed-loop poles. This ...