Page 144 - MATLAB an introduction with applications

Control Systems ——— 129

∂ MM Percentage change in M
/
S M = =
G ∂ GG Percentage change in G
/
where ∂M denotes incremental change in M due to incremental change in G (∂G). One can write sensitivity-
function as:
∂ MM 1
/
S G M = ∂ GG = 1 + GH
/
By increasing GH, the magnitude of the sensitivity-function is made arbitrarily small.

3.9 CONTROL SYSTEM ANALYSIS AND DESIGN OBJECTIVES

Control systems engineering consists of analysis and design of control systems configurations. Control
systems are dynamic, in that they respond to an input by first undergoing a transient response before
attaining a steady-state response which corresponds to the input. There are three main objectives of control
systems analysis and design. They are:
1. Producing the response to a transient disturbance which is acceptable
2. Minimizing the steady-state errors: Here, the concern is about the accuracy of the steady-state
response
3. Achieving stability: Control systems must be designed to be stable. Their natural response should
decay to a zero values as time approaches infinity, or oscillate.
Analysis is investigation of the properties and performance of an existing control system. Design is the
selection and arrangement of the control system components to perform a prescribed task. The design of
control systems is accomplished in two ways: design by analysis in which the characteristics of an existing
or standard system configuration are modified, and design by synthesis in which the form of the control
system is obtained directly from its specifications.

3.10 MATLAB APPLICATION

The application of MATLAB to the analysis and design of control systems, engineering mechanics (statics
and dynamics), mechanical vibration analysis, electrical circuits and numerical methods is presented in this
chapter with a number of illustrative examples. The MATLAB computational approach to the transient
response analysis, steps response, impulse response, ramp response and response to the simple inputs are
presented. Plotting root loci, Bode diagrams, polar plots, Nyquist plot, Nichols plot and state space method
are obtained using MATLAB. Extensive worked examples are included with a significant number of exercise
problems to guide the student to understand and as an aid for learning about the analysis a nd design of
control systems, engineering mechanics, vibration analysis of mechanical systems, electrical circuits and
numerical methods using MATLAB.
3.10.1 Transient Response Analysis
When the numerator and denominator of a closed-loop transfer function are known, the commands step
(num, den), step (num, den, t) in MATLAB can be used to generate plots of unit-step responses. Here, t is
the user specified time.

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