Posts by Farahat

In this chapter we shall look at the design of a digital controller for a control system, namely a liquid level control system. Liquid level control systems are commonly used in many process control applications to control, for example, the level of liquid in a tank. Figure 11.1 shows a typical liquid level control system. […]
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CHOICE OF SAMPLING INTERVAL Whenever a digital control system is designed, a suitable sampling interval must be chosen. Choosing a large sampling time has destabilizing effects on the system. In addition, informa- tion loss occurs when large sampling times are selected. Also, the errors that occur when a continuous system is discretized increase as the […]
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PID CONTROLLER IMPLEMENTATIONS PID controllers are very important in many process control applications. In this section we shall look at the realization of this type of controller. Equation (10.35) can easily be implemented using a direct realization. Notice that if only proportional plus integral (PI) action is required, the derivative constant Td can be set […]
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CASCADE REALIZATION The cascade realization is less sensitive to coefficient sensitivity problems. In this method the transfer function is implemented as a product of first-order and second-order transfer functions. Thus, the controller transfer function is written as
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PARALLEL REALIZATION The parallel realization also avoids the coefficient sensitivity problem. In this method the transfer function is factored and written as a sum of first-order and second-order transfer functions:
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A control algorithm which takes the form of a z-transform polynomial must be realized in the computer in the form of a program containing unit delays, constant multipliers, and adders. A given controller transfer function can be realized in many different ways. Mathematically the alternative realizations are all equivalent, differing only in the way they […]
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PID CONTROLLER The proportional–integral–derivative (PID) controller is often referred to as a ‘three-term’ controller. It is currently one of the most frequently used controllers in the process industry. In a PID controller the control variable is generated from a term proportional to the error, a term which is the integral of the error, and a […]
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The design of a digital control system begins with an accurate model of the process to be controlled. Then a control algorithm is developed that will give the required system response. The loop is closed by using a digital computer as the controller. The computer implements the control algorithm in order to achieve the required […]
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BODE DIAGRAMS The Bode diagrams used in the analysis of continuous-time systems are not very practical when used directly in the z-plane. This is because of the e j ωT term present in the sampled data system transfer functions when the frequency response is to be obtained. However, it is possible to draw the Bode […]
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NYQUIST CRITERION The Nyquist criterion is one of the widely used stability analysis techniques in the s-plane, based on the frequency response of the system. To determine the frequency response of a continuous system transfer function G(s), we replace s by j ω and use the transfer function G( j ω). In the s-plane, the […]
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