Servo problem

Servo problems Consider changes in set point with no disturbance (L = 0) C = GspR. 

For illustration, we take Gm = Ga = 1 and the closed-loop transfer function for a servo problem is simply... 

The closed-loop transfer function of a servo problem with proper handling of units is Eq. (5-11) in text ... 

Servo problem The disturbance does not change [i.e., d(s) = 0] while the set point undergoes a change. The feedback controller acts in such a way as to keep y close to the changing ySP. In such a case,... 

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...

In subsequent sections we will examine only the response for the servo problem assuming that the reader has gained the facility to repeat a similar analysis for the regulator problem. 

The model-reference adaptive control was originally proposed by Whitaker et al. in 1958 and was developed for servo problems ... 

The digital control algorithms discussed in Sections 30.2 and 30.3 were designed for set point changes (servo problem). Therefore, the question arises as to how well they perform for load (disturbance) changes. It is a fortuitous coincidence that algorithms such as the deadbeat or Dahlin s perform well for both set point and load changes. 

Self-adaptive control, 436-38, 662-67 Self-regulating systems, 7, 34, 180 Self-tuning regulator, 437-38, 662-67 references, 447, 673 Serial transmission, digital signals, 561 Servo problem (see Feedback control)... 

Set-point control (see Servo problem) Set-point response with feedback controller, 260, 267, 271, 273, 276... 

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... 

In this section we repeat an analysis similar to that of the preceding section but using an integral instead of a proportional controller. Not to overwhelm the reader with the repetition of algebraic manipulations, we will limit our attention to first-order systems and for the servo problem only. ... 

For the servo problem, d(s) = 0, and the closed-loop response to set point changes is given by... 

A dynamic system is described by a set of state variables. We are interested to keep some controlled (output) variables as constant as possible (the regulator problem), or to make them follow some desired trajectory in time, (the servo problem). We achieve these goals by changing some manipulated (input) variables. The device for adjusting the manipulated inputs to keep the controlled outputs at their desired values (references or setpoints) is called controller. There are also external variables that are not manipulated, but may influence the process dynamics by their inherent variations. They are called disturbances. The main job of a control system is to rejecting disturbances. 

The disturbance does not change, it is the set point which changes [d (.s) = O]. This is called the servo problem and the process equation becomes... 

The above relation can be drawn as shown in Figure 5.57. Servo problem ... 

Next we derive the closed-loop transfer function for set-point changes. The closed-loop system behavior for set-point changes is also referred to as the servomechanism servo) problem in the control literature, because early apphcations were concerned with positioning devices called servomechanisms. We assume for this case that no disturbance change occurs and thus Z) = 0. From Fig. 11.8, it follows that... 

Thus, for the previous servo problem, we have Zf = Y p, Z = Y,Uf= KmGcGyGp, and Ilg = Gql- For the regulator problem, Zj = D,Z= Y, Ily = G, and Ilg = Gql-It is important to note that Eq. 11-31 is applicable only to portions of a block diagram that include a feedback loop with a negative sign in the comparator. 

Case b servo problem. The disturbance, Cq, does not change, whereas the set-point is modified according to a specific pattern. 

Effect of the reset time on the performance of PI controller (servo problem). 

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