Chapter 8: Some Practical Aspects of Control Design, Justification and Implementation

8.1 How efficient is it to control an unknown process by a controller that consists only of a high gain of value C that in the limit becomes a relay controller?

In view of the evident efficiency of feedback controllers in controlling unknown phenomena, is it not feasible to attempt control of all processes by some very simple standard strategy?

The simplest possible controller (Figure 8.1) involves just multiplication of the error by a scalar C; the overall transfer function is CG( s)/(1 + CG( s)) and if C is very high, then the overall transfer function is approximately

Figure 8.1: The simplest possible controller - a gain C

i.e. provided that C >> 1 near-perfect control can be obtained.

What happens as C ? ?? Will this give better and better control?

Answers

As C is increased, the system may become unstable and unusable.
Assuming that the system remains stable as C ? ? (another question left for the moment is when does this arise?), then we have arrived at a switched (relay) control system (Figure 8.2). Such a system does indeed have a high performance and the low cost of a switching controller also makes such systems economically attractive. However, there are two disadvantages of (infinite gain) switching systems:

Figure 8.2: The limiting condition as c ? ? the controller becomes a relay
1. They are essentially non-linear (for instance, they respond (initially) in the same...

< Previous Excerpt Next Excerpt >

Purchase This Book

Control Theory, Second Edition

TABLE OF CONTENTS

Chapter 8: Some Practical Aspects of Control Design, Justification and Implementation

8.1 How efficient is it to control an unknown process by a controller that consists only of a high gain of value C that in the limit becomes a relay controller?

Contact Preferences

This is embarrasing...

Customize Your GlobalSpec Experience

Select Your Free Newsletters

Industry Newsletters

Select Your Free Product Alerts

This is embarrasing...