Closed-control loop

In order to cope with the frequent existence of process disturbances, closed-loop strategies can be implemented. If some of the state variables and/or end-use properties are monitored in real time, then the simplest closed-loop strategies can be implemented in the form  

In the illustrative example of Section 8.5.2.1, implementation of a closed-loop strategy requires that the instantaneous copolymer composition be evaluated with the help of some of the techniques described in Section 8.3. For instance, combination of calorimetric and spectroscopic techniques can allow for monitoring of monomer concentrations and reaction rates in real time. If copolymer compositions can be inferred in-line, then these values can be compared to the desired setpoint values for formulation of a closed-loop strategy. 

Depending on how u (t) is updated, different control strategies can be formulated. For instance, when standard PI controllers are used to control the process performance [15], Equation 8.35 can be written as 

If a reliable process model is available and can provide solutions in real time, the model can be used to provide the corrected setpoint trajectories for u without decouphng or empirical tuning of controller gains. If a process performance index is defined, then the controller action can be computed directly by inverting the process model. For instance, if it is assumed that the current process states [x(f),y(f)] are known and that it is desired to reach the optimum reference trajectory after tf time units, then Equations 8.18b and 8.35 can be written as 

Equation 8.37a can be inverted to provide the corrected trajectory u . This can be performed with the help of standard Newton-Raphson routines or of RSA techniques. In the illustrative example, assuming that the initial states are known (evaluated through combination of spectroscopic and calorimetric techniques, for instance), then one may compute the feed flow rate value that allows for attainment of the desired composition after some time, with the help of the process model. In order to do that, as an explicit solution is not available, it would be necessary to calculate the model responses for different flow rate values and select the best result. 

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Considerable work has been done on mathematic models of the extmsion process, with particular emphasis on screw design. Good results are claimed for extmsion of styrene-based resins using these mathematical methods (229,232). With the advent of low cost computers, closed-loop control of... 

AH closed loop control systems must measure the amount of air needed under all conditions of engine demand. Air measurement is most often done using a hot wire anemometer, usually referred to as a mass air meter (99,100). 

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. 

Dynamics of Process Measurements Especially where the measurement device is incorporated into a closed loop control configuration, dynamics are important. The dynamic characteristics depend on the nature of the measurement device, and also on the nature of components associated with the measurement device (for example, thermowells and sample conditioning equipment). The term mea-.sui ement system designates the measurement device and its associated components. 

The primary impact of unfavorable measurement dynamics is on the performance of closed loop control systems. This explains why most control engineers are very concerned with measurement dynamics. The goal to improve the dynamic characteristics of measurement devices is made difficult because the discussion regarding measurement dynamics is often subjective. 

Peiformance. Depending on the application, accuracy, repeatability, or perhaps some other measure of performance is appropriate. Where closed loop control is contemplated, speed of response must be included. 

Figure 6.6 Typical block diagram of a W/control scheme with open- or closed-loop control scheme...

For field-oriented controls, a mathematical model of the machine is developed in terms of rotating field to represent its operating parameters such as /V 4, 7, and 0 and all parameters that can inlluence the performance of the machine. The actual operating quantities arc then computed in terms of rotating field and corrected to the required level through open- or closed-loop control schemes to achieve very precise speed control. To make the model similar to that lor a d.c. machine, equation (6.2) is further resolved into two components, one direct axis and the other quadrature axis, as di.sciis.sed later. Now it is possible to monitor and vary these components individually, as with a d.c. machine. With this phasor control we can now achieve a high dynamic performance and accuracy of speed control in an a.c. machine, similar to a separately excited d.c. machine. A d.c. machine provides extremely accurate speed control due to the independent controls of its field and armature currents. 

This is an alternative to FOC and can provide a very fast response. The choice of a static drive, whether through a simple V7/control, field-oriented phasor control or direct torque control with open or closed-loop control and feedback schemes, would depend upon the size of the machine, the range of speed control (whether required to operate at very low speeds, 5% and below), the accuracy of speed control and the speed of correction (response time). The manufacturers of such drives will be the best guide for the most appropriate and economical drive for a particular application or process line. 

Up to + 0.01% in open-loop and 0.001% in closed-loop control systems... 

Blascke, F., The principle of the field oriented iransvertor as applied to the new closed loop control. system for rotating field machines, Siemens Review 34. 217-220 (1972). 

In most cases, closed-loop control can be improved by moving the surge control line to a more conservative position in response to disturbances. When the flow measurement is sufficiently stable (good signal-to-noise ratio), the controller can calculate the time derivative of the compressor map. 

A similar type of open-loop control response is combined with closed-loop control in a patented method of surge protection. In this control method an open-loop control response is added before surge occurs. 

To get good control of the entire PRT, not only should the expander be controlled, but a completely integrated control system for this application should be designed. Most conventional control systems consist of individual control loops that only consider their specific tasks. The PRT—from a control perspective—is a multivariable system that requires integration between the different control loops. Further, some of the disturbances on the PRT are so fast that closed-loop control is too slow to keep the train under control. 

The elements of a closed-loop control system are represented in block diagram form using the transfer function approach. The general form of such a system is shown in Figure 4.1. 

Fig. 4.1 Block diagram of a closed-loop control system. R s) = Laplace transform of reference input r(t) C(s) = Laplace transform of controlled output c(t) B s) = Primary feedback signal, of value H(s)C(s) E s) = Actuating or error signal, of value R s) - B s), G s) = Product of all transfer functions along the forward path H s) = Product of all transfer functions along the feedback path G s)H s) = Open-loop transfer function = summing point symbol, used to denote algebraic summation = Signal take-off point Direction of information flow.

A generalized closed-loop control system is shown in Figure 4.22. The control problem can be stated as The control action u t) will be such that the controlled output c t) will be equal to the reference input r t) for all values of time, irrespective of the value of the disturbance input riit) . 

A frequency domain stability criterion developed by Nyquist (1932) is based upon Cauchy s theorem. If the function F(s) is in fact the characteristic equation of a closed-loop control system, then... 

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