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the flow measurement of stream A (the wild stream) is used to compute the set point for the flow of stream B so that the desired ratio of components will be obtained. The Smith predictor control scheme (dead-time compensation) was developed to improve the control of a system having a large transport lag. The method is based on a model of the process that is first-order with dead time. By introducing inner loops that contain elements of the transfer function of the model, the control system is transformed ideally to one without transport lag, a system that is much easier to control. This ideal situation occurs when the process and the model are in exact agreement. In reality, the success of the Smith predictor strategy depends on the degree of agreement between process and model. Internal model control resembles the Smith predictor strategy in terms of the structure of the block diagram. To apply the IMC method, one must have an accurate model of the process, the model uncertainty, the type of disturbance (step, ramp, etc.) and the performance objective (integral of square error). The method, which is based on a rigorous mathematical foundation, leads to an IMC controller that is the best that can be designed in terms of the performance objective. The IMC structure can be reduced to a conventional control structure in which the conventional controller is related to the IMC controller and the parameters of the model. For many simple processes with simple disturbance (impulse, step, etc.), the equivalent conventional controller based on the IMC design method turns out to be the equivalent of a PID controller.
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18.1. (a) Obtain Gffor the feedforward-feedback system shown in Fig. P18.1 so that C
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does not change when a disturbance in Ci occurs. Would there be any problem in implementing this Gf (b) If Gf is to be a lead-lag transfer function
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ADVANCED
CO NT R OL
STRATEGIES
determine Tt and T2 by the Foxboro rule. How do you determine whether lead or lag is to predominate Use t,, = 1 .O in the Foxboro rule. (c) When feedforward-feedback control is present, sketch the response C(t) when Ci = l/s and when Gf from part (a) is used. (d) Repeat (c) when Gf from part (b) is used. Only a rough sketch that suggests the transient response is expected in this case. (e) Determine C(t) when Ci = l/s, and Gf = - 1, and the feedback loop is broken at AA. Obtain the numerical value of C(t) at t = 0.5,1.0, and 1.5.
CHAPTER
CONTROLLER TUNING ANDPROCESS IDENTIFICATION
The selection of a controller type (P, PI, PID) and its parameters (K,, 71, ro) is intimately related to the model of the process to be controlled. The adjustment of the controller parameters to achieve satisfactory control is called tuning. The selection of the controller parameters is essentially an optimization problem in which the designer of the control system attempts to satisfy some criterion of optimality, the result of which is often referred to as good control. The process of tuning can vary from a trial-and-error attempt to find suitable control parameters for good control to an elaborate optimization calculation based on a model of the process and a specific criterion of optimal control. In many applications, there is no model of the process and the criterion for good control is only vaguely defined. A typical criterion for good control is that the response of the system to a step change in set point or load should have minimum overshoot and one-quarter decay ratio. Other criteria may include minimum rise time and minimum settling time. In the first part of this chapter, some of the widely used tuning rules for continuous controllers will be presented. In the second part of the chapter, methods for determining the model of a process from experimental tests will be described. Determining the model of a process experimentally is referred to as process identijication. 282
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