M/M
G/G = Percentage change in M
Percentage change in G ...(1.2)
where ∂ M denotes incremental change in M due to incremental change in G(∂G). One can write sensitivity-function as:
By increasing GH, the magnitude of the sensitivity-function is made arbitrarily small.
1.8 CONTROL SYSTEM ANALYSIS AND DESIGN OBJECTIVES
Control systems engineering consists of analysis and design of control systems configu-rations. 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 re-sponse should decay to a zero values as time approaches infinity, or oscillate.
System analysis means the investigation, under specified condition, of the performance of a system whose mathematical model is known. Analysis is investigation of the properties and performance of an existing control system.
By synthesis we mean using an explicit procedure to find a system that will perform in a specified way. System design refers to the process of finding a system that accomplishes a given task. 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 speci-fications.
1.9 SUMMARY
A basic control system has an input, a process, and an output. The basic objective of a control system is of regulating the value of some physical variable or causing that variable to change in a prescribed manner in time. Control systems are typically classified as open loop or closed-loop. Open-loop control systems do not monitor or correct the output for disturbances whereas closed-loop control systems do monitor the output and compare it with the input. In a closed-loop control system if an error is detected, the system corrects the output and thereby corrects the effects of disturbances. In closed-loop control systems, the system uses feedback, which is the process of measuring a control variable and returning the output to influence the value of the variable.
Block diagrams display the operational units of a control system. Each block in a compo-nent block diagram represent some major compocompo-nent of the control system, such as measure-ment, compensation, error detection, and the plant itself. It also depicts the major directions of information and energy flow from one component to another in a control system.
A block can represent the component or process to be controlled. Each block of a control system has a transfer function (represented by differential equations) and defines the block output as a function of the input.
Control system design and analysis objectives include: producing the response to a tran-sient disturbance follows a specified pattern (over-damped or under damped), minimizing the steady-state errors, and achieving the stability.
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