Servo and Regulator Control

Having discussed some general points about sampled-data control techniques and algorithms, we now look specifically at how sampled-data control is applied to a distillation column. Fundamentally we are interested in achieving good control in the face of set-point changes and load disturbances—traditionally called servo and regulator control. 

GpH z) is the z-transforrh of the product of the process transfer function and zero-order hold. The output of the zero-order hold is the last value of the computer output, which is held constant until the next sample time. GlL z) is the z-transform of the product of the load transfer function and the load variable. Dl z) is determined from equation (21.3) by setting C7 (z) equal to zero. 

GlL(z) and C(z) have to be specified before Di(z) can be calculated. Therefore, some knowledge of the type of load is necessary—whether it is a step or ramp function. The time response of C(z) to the load disturbance can be specified to meet any number of criteria as long as Dl(z) is physically realizable. C(z) is in the form of a series of negative powers of z. The power of z corresponds to the number of sample points following the disturbance. The coefficient of z is the deviation from the initial value of C(z). 

The set-point compensation part of the algorithm D, z) is determined from equation (21.3) by setting GlL z) equal to zero. This says that the load variable does not change. 

The appropriate terms must be substituted into equation (21.5) to calculate D, z). Di(z) has been calculated already from equation (21.4). C (z) is the z- 

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Define in physical terms the servo and regulator control problems. 

A block diagram for internal model control, a control technique that is considered in Chapter 12, is shown in Fig. El 1.7. Transfer function Gp denotes the process model, while Gp denotes the actual process transfer function. It has been assumed that Gy = G = 1 for simplicity. Derive closed-loop transfer functions for both the servo and regulator problems. 

Homeostasis. Anyone who tries to regulate a chemical reaction system by a multitude of valves or switches (Figure 5) soon becomes frustrated with the instability of his experimental system and appreciative of automatic control devices (servo systems). For example, for the external control of preselected pH and C02 activity, an automatic titrator (pH — stat) can be used to dose continuously and automatically the quantity of C02 which is necessary to maintain constant pH. Feedback is an essential feature of such a control system there are essentially two major components, a controlling system (error detector) and a controlled system (13) (Figure Id). 

The hydrodynamic transistors shown in Table 2 can be classified in two types distinguished by the function of the gel actuator. The actuator of type B acts as servo drive actuating the valve seat. The actuator of type B is directly placed within the flow channel. Therefore, the stimulant, which is typically a component of the process medium, directly controls the sensor-actuator element. The hydrogel swells or shrinks by absorption or release of the process medium and regulates the channel cross-section. Figure 1 shows two examples of such hydrodynamic transistors. 

For every feedback control system we can distinguish two types of control problems the servo and the regulator problem. 

Brake belt combination regulating valve (refer to Figure 3.16) is a constant ratio valve which provide the regulating pressure to the front servo and control the brake belt (Bl) status change ratio of shifting quality. The ratio is 1.4 1. 

It is useful to consider the ideal situation. If we could design an ideal controller without any regard for physical realizability, what would the ideal elosed-loop regular and servo transfer functions be Clearly, we would wish a load disturbance to have no effect on the controlled variable. So the ideal closedloop regulator transfer function is zero. For setpoint changes, we would like the controlled variable to track the setpoint perfectly at all times. So the ideal servo transfer function is unity. 

Equation (15.64) gives the effects of setpoint and load changes on tbe controlled variables in the closedloop multivariable environment. The matrix (of order N X N) multiplying the vector of setpoints is the closedloop servo transfer function matrix. The matrix (N x 1) multiplying the load disturbance is the closed-loop regulator transfer function vector. 

Figure 14.3b shows the block diagram for the closed-loop system with the transfer functions for each component of the loop. The closed-loop response of the liquid level will be given by eq. (14.5), where the transfer functions Gp, Gd, Gm, Gc, and Gf are shown in Figure 14.3b. The servo problem arises when the inlet flow rate F, remains constant and we change the desired set point. In this case the controller acts in such a way as to keep the liquid level h close to the changing desired value Asp. On the other hand, for the regulator problem the set point Asp remains the...

To gain a better insight into the effect of the proportional controller, consider unit step changes in the set point (servo problem) and the load (regulator problem) and examine the resulting closed-loop responses. For the servo problem, 7sp(5) = 1/5 and d(s) = 0. Then eq. (14.19) yields... 

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