Closed-loop systems

One of the most vexing aspects of pilot-plant work can be feed and product handling as a pilot plant is neither designed nor operated as a closed-loop system like a commercial plant. Indeed, the problems involved in handling and storing feed and product materials can sometimes seem to rival the pilot-plant process problems in difficulty. 

Recycling and Reuse. (/) Install closed-loop systems. 2) Recycle on site for reuse. 3) Recycle off site for reuse. (4) Exchange wastes. 

Most controlled release dosage forms administer dmg according to thek design, whether conceptually simple, eg, a fixed release rate for a fixed amount of time, or complex, eg, several different rates for different amounts of time. Alternatively, closed-loop systems contain a sensor to monitor dmg concentration or to administer dmg according to a biological need (11). 

The oxygen sensor closed loop system automatically compensates for changes in fuel content or air density. For instance, the stoichiometric air/fuel mixture is maintained even when the vehicle climbs from sea level to high altitudes where the air density is lower. 

A closed-loop system uses the measurement of one or more process variables to move the manipulated variable to achieve control. Closed-loop systems may include reedfoi ward, feedback, or both. 

General Second-Order Element Figure 8-3 illustrates the fact that closed loop systems often exhibit oscillatory behavior. A general... 

Time-Delay Compensation Time delays are a common occurrence in the process industries because of the presence of recycle loops, fluid-flow distance lags, and dead time in composition measurements resulting from use of chromatographic analysis. The presence of a time delay in a process severely hmits the performance of a conventional PID control system, reducing the stability margin of the closed-loop control system. Consequently, the controller gain must be reduced below that which could be used for a process without delay. Thus, the response of the closed-loop system will be sluggish compared to that of the system with no time delay. 

In principle, ideal decouphng eliminates control loop interactions and allows the closed-loop system to behave as a set of independent control loops. But in practice, this ideal behavior is not attained for a variety of reasons, including imperfect process models and the presence of saturation constraints on controller outputs and manipulated variables. Furthermore, the ideal decoupler design equations in (8-52) and (8-53) may not be physically realizable andthus would have to be approximated. 

Closed loop systems inelude either a feedbaek or feedforward, eontrol loop or both to eontrol the plant. In a feedbaek eontrol loop, the eontrolled variable is eompared to a set point. The differenee between the eontrolled variable to the set point is the deviation for the eontroller to aet on to minimize the deviation. A feedforward eontrol system uses the measured load or set point to position the manipulated variable in sueh a manner to minimize any resulting deviation. 

Before starting the design for the compensation of the error amplifier, it is desirable to know what constitutes a stable closed-loop system. The rule is elementary ... 

The closed loop phase shall never exceed -330 degrees of lag whenever the gain of the closed-loop system is greater than i (or OdB). 

Phase margin. This is the value of the phase of a closed-loop system at the gain cross-over frequency (G(s) = OdB). 

Controllers for closed-loop systems 4.5.1 The generalized control problem... 

The Process Reaction Method assumes that the optimum response for the closed-loop system occurs when the ratio of successive peaks, as defined by equation (3.71), is 4 1. From equation (3.71) it can be seen that this occurs when the closed-loop damping ratio has a value of 0.21. The controller parameters, as a function of R and D, to produce this response, are given in Table 4.2. 

Fig. 4.39 Block diagrams for closed-loop systems. Amplifier...

Maximum value of the open-loop gain constant for the stability of a closed-loop system... 

Closed-loop poles (For K = 11.35) Since the closed-loop system is third-order, there are three closed-loop poles. Two of them are given in equation (5.81). The third lies on the real locus that extends from —5 to —oo. Its value is calculated using the magnitude criterion as shown in Figure 5.15. 

In practice, only the frequencies lu = 0 to+oo are of interest and since in the frequency domain. v = jtu, a simplified Nyquist stability criterion, as shown in Figure 6.18 is A closed-loop system is stable if, and only if, the locus of the G(iLu)H(iuj) function does not enclose the (—l,j0) point as lu is varied from zero to infinity. Enclosing the (—1, jO) point may be interpreted as passing to the left of the point . The G(iLu)H(iLu) locus is referred to as the Nyquist Diagram. 

The closer the open-loop frequency response locus G(ja )//(ja ) is to the (—l,j0) point, the nearer the closed-loop system is to instability. In practice, all control... 

In section 4.5, controllers, particularly PID controllers for closed-loop systems were discussed. In Chapter 5 it was demonstrated how compensators could be designed... 

Relationship between frequency response and time response for closed-loop systems... 

Since many closed-loop systems approximate to second-order systems, a few interesting observations can be made. For the case when the frequency domain specification has limited the value of Mp to 3 dB for a second-order system, then from equation (6.72)... 

In equation (8.94) the matrix (A - BK) is the closed-loop system matrix. 

The roots of equation (8.95) are the open-loop poles or eigenvalues. For the closed-loop system described by equation (8.94), the characteristic equation is... 

Robust performance then means that the closed-loop system will meet the performance specification given in equation (9.145) if and only if the nominal system is closed-loop stable (equation (9.141)) and that the sensitivity function Sm(jar) and complementary sensitivity function for the nominal system satisfy the rela-... 

The continuous and discrete closed-loop systems are shown in Figures 7.22(a) and (b). The digital compensator is given in equation (7.128). Script file examp78.m produces the step response of both systems (Figure 7.25) and prints the open and closed-loop continuous and pulse transfer functions in the command window... 

Use closed-loop systems for pickling regenerate and recover acids from spent pickling liquor using resin bed, retorting, or other regeneration methods such as vacuum crystallization of sulfuric acid baths. 

In a typical closed-loop system, liquid from the separator is cooled in a heat exchanger then recirculated. Any excess liquid added by mist and vapor flows out through a level-control valve. ... 

---