Modern Control Engineering

Section 1–3 / Closed-Loop Control versus Open-Loop Control 7

Using the small gain theorem, the design procedure here boils down to the deter-

mination of the controller K(s)such that the inequality

is satisfied, where G(s)is the transfer function of the model used in the design process,

K(s)is the transfer function of the controller, and W(s)is the chosen transfer function

to approximate ¢(s). In most practical cases, we must satisfy more than one such

inequality that involves G(s),K(s), and W(s)’s. For example, to guarantee robust sta-

bility and robust performance we may require two inequalities, such as

for robust stability

for robust performance

be satisfied. (These inequalities are derived in Section 10–9.) There are many different

such inequalities that need to be satisfied in many different robust control systems.

(Robust stability means that the controller K(s)guarantees internal stability of all

systems that belong to a group of systems that include the system with the actual plant.

Robust performance means the specified performance is satisfied in all systems that be-

long to the group.) In this book all the plants of control systems we discuss are assumed

to be known precisely, except the plants we discuss in Section 10–9 where an introduc-

tory aspect of robust control theory is presented.

1–3 CLOSED-LOOP CONTROL VERSUS OPEN-LOOP CONTROL

Feedback Control Systems. A system that maintains a prescribed relationship

between the output and the reference input by comparing them and using the difference

as a means of control is called a feedback control system.An example would be a room-

temperature control system. By measuring the actual room temperature and comparing

it with the reference temperature (desired temperature), the thermostat turns the heat-

ing or cooling equipment on or off in such a way as to ensure that the room tempera-

ture remains at a comfortable level regardless of outside conditions.

Feedback control systems are not limited to engineering but can be found in various

nonengineering fields as well. The human body, for instance, is a highly advanced feed-

back control system. Both body temperature and blood pressure are kept constant by

means of physiological feedback. In fact, feedback performs a vital function: It makes

the human body relatively insensitive to external disturbances, thus enabling it to func-

tion properly in a changing environment.

ß

Ws(s)

1 +K(s)G(s)

ß

q

61

ß

Wm(s)K(s)G(s)

1 +K(s)G(s)

ß

q

61

ß

W(s)

1 +K(s)G(s)

ß

q

61

Openmirrors.com