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System Control

The desire to control nature's forces has been the catalyst for progress troughout history. The goal has been to control these forces in order to perform tasks which were beyond our capabilities.

Control system engineers has been made contributions to robotics, space vehicles, aircraft autopilots and controls, control systems for ships and submarines, guidance systems for unmanned vehicles, high speed rail systems, magnetic-levitation magnetic systems. The future lies in the human ability to design control systems which can work reliably and accurately.

The control of system is an interdisciplinary subject and crosses all specialized engineering fields: electrical, mechanical, aeronautical, chemical, nuclear, economics, management, bioengineering, and other related fields. The versatility of the automatic control makes the subject one of the most promising fields, which potential grows unlimited.

Control systems performance characteristics

The performance of control systems is specified by the terms stability, sensitivity, accuracy, transient response, and residual noise. Depending on the system certain characteristics can be more important than others and are specified by the required system performance.

Stability

A fundamental requirement of a control system is that the system be stable. The control system must maintain its stability when commands are applied to the system input, power supply variations, changing in the parameters of the system due to aging or environmental conditions.

If a system has zero initial conditions and the system output is bounded for every applied bounded input then the system is referred as bounded input-bounded output (BIBO) stable system. The total response of a control system, y(t), is comprised by the natural (homogeneous) response due to initial conditions, and forced response due to the external input:

A linear time-invariant (LTI) control system is stable if the homogeneous response approaches zero, and it is unstable if the homogeneous response grows unbounded approaching infinity. If the output of a n LTI system neither grows nor decays, i.e. if an oscillation of a constant amplitude results, then such system is called marginally stable, but form practical point of view, in most of the cases it is referred as an unstable system.

Sensitivity

Sensitivity is a measure of the dependence of a control system characteristics on those of a particular element. The sensitivity, S, of a closed loop control system with transfer function H(s) with respect to the characteristics of a given parameter P(s) is defined as:

This definition is valid only for small changes.

Accuracy

Accuracy is specified in terms of the steady state response to reference inputs containing some kind of combination of position, velocity, acceleration etc. The control systems characteristics define the steady state error constants as position constant, velocity constant, acceleration constant and etc. From knowledge of these constants and the type of the reference inputs, the static accuracy of the control system can be determined. The control system designed always strives to design a control system with minimum error due to the reference inputs and disturbances.

Transient response

The control system designer is very much concerned with the control system transient response. Transient response characteristics such as rise time, time to peak, maximum percent overshoot, and settling time are defined on the basis of the response of the Second order control system to a unit step input.