Servo response

From Eq. (6-20), it is immediately clear that we cannot have an ideal servo response where C/R = 1, which would require an infinite controller gain. Now Eq. (6-21) indicates that C/R cannot be some constant either. To satisfy (6-21), the closed-loop response C/R must be some function of s, meaning that the system cannot respond instantaneously and must have some finite response time. 

Setpoint changes can also be made, particularly in batch processes or in changing from one operating condition to another in a continuous process. These setpoint changes also act as disturbances to the dosedloop system. The function of the feedback controller is to drive the controlled variable to match the new setpoint. The dosedloop response to a setpoint disturbance is called the servo response (from the early applications of feedback control in mechanical servomechanism tracking systems). 

Pole and zero placement using a dynamic compensator for an SISO system can be accomplished by specifying analytically the closed loop servo response (e.g., first or second order with deadtime). Suppose that the specified response is defined by P(s) solving the closed loop equation (5) yields an analytical... 

A process that is designed with a lot of muscle (has large driving forces available for use if necessary) can quickly respond to disturbances and rapidly return the process to the desired conditions. Likewise this process can be quickly driven to new setpoints if it is desired to operate at other conditions. This is called switchability or servo-response. 

In Chapter 12, we introduced the Direct Synthesis design method, in which the closed-loop servo response is specified and the controller transfer functions are calculated algebraically. For an IMC controller (see Chapter 12), show that setting G+ = e leads to a Smith predictor controller structure when G = G for a FOPTD process. 

The final element is the compressor guide-vane mechanism. The variable clearance points are adjusted by means of a positioning cylinder that is operated by a servo valve in response to a signal from the flow controller. 

The analysis of human actions is complicated because a human is a responsive system like a servo. Such analysis does not lend itself to simple models as do inanimate components. Classifying human actions into the success or failure states used in logic models for plant equipment dix. s not account for the wide range of possible human actions. A generally applicable model of the parameters that affect human performance is not yet available. 

Cleanliness in hydraulic systems has received considerable attention recently. Some hydraulic systems, such as aerospace hydraulic systems, are extremely sensitive to contamination. Fluid cleanliness is of primary importance because contaminants can cause component malfunction, prevent proper valve seating, cause wear in components, and may increase the response time of servo valves. Fluid contaminants are discussed later in this chapter. 

This last case illustrates that the desired closedloop relationship cannot be chosen arbitrarily. You cannot moke a jumbo jet behave like a jet fighter We must select the desired response such that the controller b physically realizable. In this case all we need to do is modiiy the specified closedloop servo transfer function to include the dcadtime. 

All the Nyquist, Bode, and Nichols plots discussed in previous sections have been for openloop system transfer functions B(j ). Frequency-response plots can be made for any type of system, openloop or closedloop. The two closedloop transfer functions that we derived in Chap. 10 show how the output is affected in a closedloop system by a setpoint input and by a load. Equation (13.28) gives the closedloop servo transfer function. Equation (13.29) gives the closedloop load transfer function. 

The results for this test and for the responses to disturbances in feed compositions of B and C are summarized in Table 4. A consistent trend with the servo tests was observed, in the sense that one option provides the best common choice for the control of the system under feed disturbances on the extreme components of the mixture, but a different arrangement yields a superior dynamic performance for the control task under a feed disturbance on the intermediate component. From Table 4, the lAE values indicate that the PUL system shows the best behavior for feed disturbances in the light and heavy component. However, the PUL arrangement shows the worst response when the feed disturbance in the intermediate component was considered, in which case both the Petlyuk and the PUV systems show fairly similar rejection capabilities. 

In a setup-dominant process, it is important that the development function understand where the setup must be centered (targeted). This information is most useful when instruments can effectively and accurately measure the property of the intermediate material (e.g., powder blend) or dosage unit. This capability is reinforced whenever an instrument reading outside the given specifications causes an equipment response (e.g., activation of a servo motor on a tablet press). Caution limits within the normal product limits are established purposefully to effect this kind of control. 

Servos MR. 1999. Review of the aquatic toxicity, estrogenic responses and bioaccumulation of alkylphenols and alkylphenol polyethoxylates. Water Qual Res J Canada 34 123-177. 

Instrument used (measured response) Dia-Stron erythema meter , Minolta Chromameter , Cortex Dermaspectrometer (all measure a redness index of erythema) laser Doppler Velocimeter (blood flow) Servo-Med evaporimeter (transepidermal or skin surface water loss)... 

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. 

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... 

Consider the servo control problem of a first-order process with PI controller. It can be easily shown that the closed-loop response is given by the following equation, when Gm = G/= 1 ... 

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

Both the openloop and the closedloop frequency response curves can be easily generated on a digital computer by using the complex variables and functions in FORTRAN discussed in Chapter 10 or by using MATLAB software. The frequency response curves for the closedloop servo transfer function can also be fairly easily found graphically by using a Nichols chart. This chart was developed many years ago, before computers were available, and was widely used because it greatly facilitated the conversion of openloop frequency response to closedloop frequency response. 

In the preceding example we derived the expression for T( ) analytically for a step change in An alternative approach is to use MATLAB to calculate the step response of the closedloop servo transfer function... 

The servo feedback loop functions by reducing the amplitude of the FM superposed by the cavity response onto the MMW signal to as small a value as possible. This does not mean, however, that the MMW output becomes unmodulated. Rather, the original modulation is replaced by one at twice the modulation frequency, that goes undetected by the servo system s phase-coherent detector. It may, however, be observed and converted into DC by a second phase-coherent detector responding to twice the modulation frequency. In the system so far described, this DC voltage will correspond to the second derivative of the cavity frequency profile (Section 4.1) and will therefore take on a fixed value characteristic of the cavity-g and its coupling coefficient. 

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