Control systems multivariable

Use a decouphng control system d. Use a multivariable control scheme (e.g., model predictive control)... 

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 concepts of controllability and observability were introduced by Kalman (1960) and play an important role in the control of multivariable systems. 

This tutorial uses the MATLAB Control System Toolbox for linear quadratie regulator, linear quadratie estimator (Kalman filter) and linear quadratie Gaussian eontrol system design. The tutorial also employs the Robust Control Toolbox for multivariable robust eontrol system design. Problems in Chapter 9 are used as design examples. 

Finally, process control systems allow the unit to operate smoothly and safely. At the next level, an APC package (whether within the DCS framework or as a host-based multivariable control system) provides more precise control of operating variables against the unit s constraints. It will gain incremental throughput or cracking severity. 

Gegov, A., Distributed Fuzzy Control of Multivariable Systems, Kluwer, 1996. 

It may be useful to point out a few topics that go beyond a first course in control. With certain processes, we cannot take data continuously, but rather in certain selected slow intervals (c.f. titration in freshmen chemistry). These are called sampled-data systems. With computers, the analysis evolves into a new area of its own—discrete-time or digital control systems. Here, differential equations and Laplace transform do not work anymore. The mathematical techniques to handle discrete-time systems are difference equations and z-transform. Furthermore, there are multivariable and state space control, which we will encounter a brief introduction. Beyond the introductory level are optimal control, nonlinear control, adaptive control, stochastic control, and fuzzy logic control. Do not lose the perspective that control is an immense field. Classical control appears insignificant, but we have to start some where and onward we crawl. 

For now let us say merely that the control system shown in Fig. 1.5 is a typical conventional system It is about the minimum that would be needed to run this plant automatically without constant operator attention. Notice that even in this simple plant with a minimum of instrumentation the total number of control loops is lO. We win find that most chemical engrneering processes are multivariable. 

Unfortunately much of Ais interaction analysis work has clouded the issue of how to design an effective control system for a multivariable process. In most process control applications the problem is not setpoint responses but load responses. We want a sy stem that holds the process at the desired values in the face of load disturbances. Interaction is therefore not necessarily bad, and in fact in some systems it helps in rejecting the effects of load disturbances. Niederlinski [AIChE J 1971, Vol 17, p. 1261) showed in an early paper that the use of decouplers made the load rejection worse. 

Rosenbrock (Computer-Aided Control System Design, Academic Press, 1974) was one of the early woikers in the area of multivariable control. He proposed the use of INA plots to indicate the amount of interaction among the loops. 

As a result, there has been a lot of research activity in multivariable control, both in academia and in industry. Some practical, useful tools have been developed to design control systems for these multivariable processes. The second edition includes a fairly comprehensive discussion of what 1 feel are the useful techniques for controlling multivariable processes. 

This chapter is organized in the following way. First, the general model of the CSTR process, based on first principles, is derived. A linearized approximate model of the reactor around the equilibrium points is then obtained. The analysis of this model will provide some hints about the appropriate control structures. Decentralized control as well as multivariable (MIMO) control systems can be designed according to the requirements. 

P. Albertos and A. Safa. Multivariable Control Systems An Engineering Approach. Springer Verlag, 2004. 

Several statistics from the models can be used to monitor the performance of the controller. Square prediction error (SPE) gives an indication of the quality of the PLS model. If the correlation of all variables remains the same, the SPE value should be low, and indicate that the model is operating within the limits for which it was developed. Hotelling s 7 provides an indication of where the process is operating relative to the conditions used to develop the PLS model, while the Q statistic is a measure of the variability of a sample s response relative to the model. Thus the use of a multivariate model (PCA or PLS) within a control system can provide information on the status of the control system. 

For effective control of crystallizers, multivariable controllers are required. In order to design such controllers, a model in state space representation is required. Therefore the population balance has to be transformed into a set of ordinary differential equations. Two transformation methods were reported in the literature. However, the first method is limited to MSNPR crystallizers with simple size dependent growth rate kinetics whereas the other method results in very high orders of the state space model which causes problems in the control system design. Therefore system identification, which can also be applied directly on experimental data without the intermediate step of calculating the kinetic parameters, is proposed. 

In simplifying the packed bed reactor model, it is advantageous for control system design if the equations can be reduced to lit into the framework of modern multivariable control theory, which usually requires a model expressed as a set of linear first-order ordinary differential equations in the so-called state-space form ... 

Even after linearization, the state-space model often contains too many dependent variables for controller design or for implementation as part of the actual control system. Low-order models are thus required for on-line implementation of multivariable control strategies. In this section, we study the reduction in size, or order, of the linearized model. 

Second, it underlines the importance of viewing consciousness as a highly plastic, multivariate, dynamic function with an almost infinite set of possible instantiations. Third, it vindicates the comparative approach by showing that features of one canonical state (e.g., dreaming) can appear in another canonical state (e.g., waking) simply by changing one aspect of the control systems of the brain that normally maintain the discreteness of those states. 

Control system Effective multivariable process control system in place for online applications... 

Three examples of simple multivariable control systems are shown in Fig. 8-39. The in-line blending system blends pure components A and B to produce a product stream with flow rate w and mass fraction of A, x. Adjusting either inlet flow rate wA or wB affects both of the controlled variables w and x. For the pH neutralization process in Fig. 8-39b, liquid level h and exit stream pH are to be controlled by adjusting the acid and base flow rates wA and wB. Each of the manipulated variables affects both of the controlled variables. Thus, both the blending system and the pH neutralization process are said to exhibit... 

The nonlinear MFA controller is a general-purpose controller that provides a more uniform solution to nonlinear control problems. Figure 2.55 illustrates how a multivariable MFA control system works with a two-input-two-output (2 x 2) system, which consists of two controllers (Cri, C22), and... 

From a practical perspective, this is the model that should be used to design a (multivariable) controller that manipulates the inputs us to fulfill the control objectives ys. It is important to note that the availability of a low-order ODE model of the process-level dynamics affords significant flexibility in designing the supervisory control system, since any of the available inversion- or optimization-based (e.g., Kravaris and Kantor 1990, Mayne et al. 2000, Zavala... 

Rosenbrock, H. H., "Design of Multivariable Control Systems Using the Inverse Nyquist Array," Proc. IEEE, 1969, 116, 1929. 

MacFarlane, A. G. J., "Commutative Controller A New Technique for the Design of Multivariable Control Systems," Electron Letters, 1970, 6, 121. 

Typical functions of the middle layer are anti-reset windup, variable structure elements, selectors, etc. Although essential for the proper functioning of any practical control system, they have been completely neglected in research circles. We have yet to find an effective multivariable anti-reset windup scheme that works on all our test cases. Can all, or at least most, industrial control problems be solved satisfactorily with some simple loops and minimum-maximum selectors How can the appropriate logic structure be designed How should the loops be tuned to work smoothly in conjunction with the logic How can one detect deteriorating valves and sensors from on-line measurements before these control elements have failed entirely ... 

Our understanding is that MPC has found widespread use in the petroleum industry. The chemical industry, however, is still dominated by the use of distributed control systems implementing simple PID controllers. We are addressing the plantwide control problem within this context. We are not addressing the application of multivariable model-based controllers in this book. 

This configuration adds two degrees of freedom to the conventional column (the liquid flowrate to the stripper and the heat input to the stripper reboiler), so two compositions in the sidestream product from the stripper can theoretically be controlled. The control system shown in Fig. 6.23a uses stripper reboiler heat input to control the impurity of A in the sidestream product. The impurity of C in the sidestream product is controlled by manipulating the flowrate of liquid to the stripper. This system presents a highly interacting 4X4 multivariable control problem. Therefore in practice it may be more effective to control only one composition (or temperature) in the stripper and one temperature in the main column, with the flowrate of reflux and liquid to the stripper flow controlled. 

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