The Laplace transform is an extremely important tool for a control system engineer. For a given set of initial conditions, it will give the total response of the system comprising of both natural and forced responses in one operation. The idea of Laplace transform is analogous to any familiar transform. For example, Logarithms are used to change a multiplication or division problem into a simpler ......

A control system is a systematically arranged interconnection of components which together act to provide a desired response when excited by an input. Control systems are playing a vital role in the advancement of science and technology and inuence every facet of modern life. Domestically, automatic controls in heating and air conditioning regulate the temperature and humidity for comfortable livi ......

In the preceding chapter, we have learned to represent a system by a set of deferential equations by applying cause-effect equations at the various nodes of a mechanical network. In this chapter, we will explain how to use block diagrams to express a complicated system. Then, we will develop techniques to reduce an interconnected system with several blocks to a single block. Finally, we will intro ......

The response of a system as a function of time t is known as the time response of the system. The time response is the sum of transient and steady-state responses. In control systems, the transient response is defined as the part of the time response that goes to zero as t ! 1. The steady-state response is simply the part of the total response that remains after the transient has died out.

Most control systems that require the attention of control engineers are large, complex, and involve many variables. The factors are related to one another in complicated mathematical models; quantitative answers to problems are obtained by numerical solutions of model equations. Besides this approach to the analysis of control systems, engineers need a simplified qualitative investigation which w ......

The term frequency response refers to the steady-state response of a system subjected to a sinusoidal input of fixed amplitude but with frequency varied over a range. Need for frequency-domain study: The time response of a system is usually more difficult to determine analytically, especially for higher-order systems. There is no unique way of designing a control system to meet the time-domain per ......

Bode plots are subsets of complete Nyquist plots, but represented in a different form. Also, Bode plots are a good alternative to the tedious Nyquist plots. The addition of poles or zeros to an existing open-loop transfer function requires the recalculation of the frequency response, a tedious procedure. Also, the Nyquist plots do not indicate the effect of the individual poles and zeros on the fr ......

In state space analysis, we select a set of minimal variables, called the state variables, in the system. The state variables have the property that every possible signal or variable in the system at any instant t can be expressed in terms of the state variables and inputs at that instant. If we know all the state variables, then we can nd every possible signal or variable in the system at any in ......

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