Discrete control systems

As we will show quantitatively, sampling periods must be kept quite small in order to stabilize this type of system because of the inherent degradation of performance in discrete control systems. 

Generally speaking, the purpose of a control system is to supervise, control, monitor, schedule, document and record process parameters that are vital to plant operation. The control system of any plant or system is related to the process design of the plant and ultimately its operation, and must be able to cope with various uncertainties. In other words, the control system is closely tied to process operability. Process operability, in turn, involves the coordinated effort of both the operator and the automatic control system. The automatic controls system is PLC-based and includes the MCP and local control panels (LCP). PLC systems are preferred to discrete control systems because of the flexibility in establishing set-points and providing multiple functions. 

Limit Switches and Stem-Position Transmitters Travel-limit switches, position switches, and valve-position transmitters are devices that, when mounted on the valve, actuator, damper, louver, or other throtthng element, detect the component s relative position. The switches are used to operate alarms, signal hghts, relays, solenoid valves, or discrete inputs into the control system. The valve-position transmitter generates a 4-20-mA output that is proportional to the position of the valve. 

Cadzow, J.A. and Martens, H.R. (1970) Discrete-Time and Computer Control Systems, Prentice-Hall, Inc., Englewood Cliffs, N.J. 

Ogata, K. (1995) Discrete-Time Control Systems, 2nd ed., Prentice-Hall, Inc., Upper Saddle River, NJ. 

When discontinuous measurements are involved, the control system is referred to as a sampled data or discrete controller. Concentration measurements by chromatography would represent such a case. 

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. 

Process Control. The traditional process control will be expanded toward new applications such as nonlinear process control of biosystems. However, in the commodity chemicals industry there will be increased need for synthesizing plantwide control systems, as well as integrating dynamics, discrete events, and safety functions, which will be achieved through new mathematical and computer science developments in hybrid systems. 

The development of digital control computers and of chromatographic composition analyzers has resulted in a large number of control systems that have discontinuous, intermittent components. The nature of operation of both of these devices is such that their input and output signals are discrete. 

To analyze systems with discontinuous control elements we will need to learn another new language. The mathematical tool of z transformation is used to desigii control systems for discrete systems, z transforms are to sampled-data systems what Laplace transforms are to continuous systems. The mathematics in the z domain and in the Laplace domain are very similar. We have to learn how to translate our small list of words from English and Russian into the language of z transforms, which we will call German. 

There is a special type of controller, called a Smith predictor or deadtime compensator, that can be applied in either continuous or discrete form. It is basically a special type of model-based controller, in the same family as IMC. Figure 20.6a gives a sketch of a conventional feedback control system. Let s break up the total openloop process into the portion without any deadtime G j,(s) nd deadtime e... 

Summary. In this chapter the control problem of output tracking with disturbance rejection of chemical reactors operating under forced oscillations subjected to load disturbances and parameter uncertainty is addressed. An error feedback nonlinear control law which relies on the existence of an internal model of the exosystem that generates all the possible steady state inputs for all the admissible values of the system parameters is proposed, to guarantee that the output tracking error is maintained within predefined bounds and ensures at the same time the stability of the closed-loop system. Key theoretical concepts and results are first reviewed with particular emphasis on the development of continuous and discrete control structures for the proposed robust regulator. The role of disturbances and model uncertainty is also discussed. Several numerical examples are presented to illustrate the results. 

As in the case of continuous linear systems, the exponential holder will then ensure the fulfilment of the regulation conditions for a continuous linear system with a discrete controller. This result is summarized in the following theorem. 

O.M. Grasselli and S. Longhi. Robust tracking and regulation of bnear periodic discrete-time systems. Int. J. Control, 54 613-633, 1991. 

S. Monaco and D. Normand-Cyrot. Minimum phase nonlinear discrete-time systems and feedback stabilization. In IEEE Conf. Decision and Control (CDC), pages 979-986, Los Angeles, USA, 2002. 

S. Tarbouriech and G. Garcia. Stabilization of Linear Discrete-Time Systems with Saturating Controls and Norm-Bounded Time-Varying Uncertainty. Control of uncertain systems with bounded inputs Lecture Notes in Control and Information Science 221. Springer-Verlag Berlin, 1997. 

Ogata, 0. Discrete-time control systems Prentice-Hall Englewood Cliffs, New Jersey, I987. 

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. 

Lastly, non-elementary several-stage reactions are considered in Chapters 8 and 9. We start with the Lotka and Lotka-Volterra reactions as simple model systems. An existence of the undamped density oscillations is established here. The complementary reactions treated in Chapter 9 are catalytic surface oxidation of CO and NH3 formation. These reactions also reveal undamped concentration oscillations and kinetic phase transitions. Their adequate treatment need a generalization of the fluctuation-controlled theory for the discrete (lattice) systems in order to take correctly into account the geometry of both lattice and absorbed molecules. As another illustration of the formalism developed by the authors, the kinetics of reactions upon disorded surfaces is considered. 

Fig. 7.91. Closed-loop control system with discrete time controller...

Thus the discrete time form of the control system is less stable than the equivalent continuous case. 

Coughanowr, D. R. Process Systems Analysis and Control, 2nd edn. (McGraw-Hill, New York, 1991). Kuo, B. C. Discrete Data Control Systems (Prentice-Hall, Englewood Cliffs, New Jersey, 1970). Landau, Y. D. Adaptive Control—The Model Reference Approach (Marcel Dekker, New York, 1979). Popovic, D. and Bhatkar, V. P. Distributed Computer Control for Industrial Automation (Marcel Dekker, New York, 1990). 

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