Regulator control problem

Define in physical terms the servo and regulator control problems. 

Chapter 5 considers optimal regulator control problems. The Kalman linear quadratic regulator (LQR) problem is developed, and this optimal multivariable proportional controller is shown to be easily computable using the Riccati matrix differential equation. The regulator problem with unmeasurable... 

In most chemical processes the principal control problem is load rejection. We want a control system that can keep the controlled variables at or near their setpoints in the face of load disturbances. Thus the closedloop regulator transfer function is the most important. 

There are several control problems in chemical reactors. One of the most commonly studied is the temperature stabilization in exothermic monomolec-ular irreversible reaction A B in a cooled continuous-stirred tank reactor, CSTR. Main theoretical questions in control of chemical reactors address the design of control functions such that, for instance (i) feedback compensates the nonlinear nature of the chemical process to induce linear stable behavior (ii) stabilization is attained in spite of constrains in input control (e.g., bounded control or anti-reset windup) (iii) temperature is regulated in spite of uncertain kinetic model (parametric or kinetics type) or (iv) stabilization is achieved in presence of recycle streams. In addition, reactor stabilization should be achieved for set of physically realizable initial conditions, (i.e., global... 

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. 

Many control problems can be better solved with a diaphragm controller. The function of the diaphragm controller (see Fig. 3.27) can be easily derived from that of a diaphragm vacuum gauge the blunt end of a tube or pipe is either closed off by means of an elastic rubber diaphragm (for reference pressure > process pressure) or released (for reference pressure < process pressure) so that in the latter case, a connection is established between the process side and the vacuum pump. This elegant and more or less automatic regulation system has excellent control characteristics (see Fig. 3.28). 

Returning now to the issue of reactor temperature control, we can generally state that reactors with either substantially reversible or endothermic reactions seldom present temperature control problems. Endothermic reactions require that heat be supplied to generate products. Hence, they do not undergo the dangerous phenomenon of runaway because they are self-regulating, that is, an increase in temperature increases the reaction rate, which removes more heat and tends to decrease the temperature. 

The control structure implication is that we do not attempt to regulate the gas recycle flow and we do not worry about what we control with its manipulation. We simply maximize its flow. This removes one control degree of freedom and simplifies the control problem. 

The one by-product of pesticide use which has received the most research attention and regulative control is the residue of pesticide applied to foods. Focusing attention on food residues for so long has led some to assume it is the only problem. This assumption has made it more difficult to see the other compelling problems arising from using pesticides. 

The analytic control problem deals with the appraisal of existing control systems. What is the overall dynamic behavior of the system, and what individual contributions are made to the overall behavior by the various components in the system How may processes be characterized as to their dynamic behavior in terms useful for control system analysis What are the control characteristics of typical instruments such as the measuring devices, controllers, and regulating units ... 

For every feedback control system we can distinguish two types of control problems the servo and the regulator problem. 

A pure capacitive process will cause serious control problems, because it cannot balance itself. In the tank of Example 10.3, we can adjust manually the speed of the constant-displacement pump, so as to balance the flow coming in and thus keep the level constant. But any small change in the flow rate of the inlet stream will make the tank flood or run dry (empty). This attribute is known as non-self-regulation. 

Column upsets and operation difficulties are often initiated in an upstream unit. For instance, poor column performance may be due to an upstream column experiencing control problems, a malfunctioning pH regulation or additive injection system upstream, or a reactor performing in a different manner than design. 

The column feed was preheated by the bottoms then a steam preheater. Preheater steam was controlled by the feed temperature downstream. The feed entha fluctuated with fluctuations in column bottom flow. This interfered with the column product anal3rzer control Problem was cured by a feed enthalpy controller which regulated preheater steam flow. 

Chapter 12 considers the combination of optimal control with state and parameter estimation. The separation principle is developed, which states that the design of a control problem with measurement and model uncertainty can be treated by first performing a Kalman filter estimate of the states and then developing the optimal control law based upon the estimated states. For linear regulator problems, the problem is known as the linear quadratic Gaussian (LQG) problem. The inclusion of model parameter identification results in adaptive control algorithms. 

---