Plant equations

From the partitioned matrix in equation (9.161), the closed-loop transfer function matrix relating yi and uj is 

---

For a linear, time invariant plant, equation (9.1) beeomes... 

Hence values of K and K/ generated by the GA are inserted into equation (10.102) and the control u kT) used to drive the discrete plant equation (10.101). The fitness function J is updated at each sampling instant to give an overall value at the end of each simulation. For a population of 10 members, 10 simulations are required per generation. 

Modern control synthesis procedures are often based on the state variable representation of the plant equations. In applying them to high order systems, such as distillation columns, practical reasons of controller design require order reduction. That means one has to replace the large number of state variables obtained by physical laws, thru the introduction of a smaller set of suitably chosen state variables. 

Lewis and Stevens (This Volume and 12) have provided a useful framework for hybrid receptor modeling in which one calculates concentrations of various sulfur species relative to those of some tracer that is fairly unique to the sulfur source, e.g., Se as a tracer from coal-fired power plants. Equations are written for S02 conversion... 

This example shows that the equilibrium time in an ideal cascade with a — 1 < 1 may be relatively long, even when the stage holdup time h is very short. In a cascade that is not tapered at the product end, the equilibrium time will be even greater, because of the increased inventory of desired component in this part of the plant. Equation (12.197) may be used to estimate the equilibrium time of such a nonideal cascade Eq. (12.209) is restricted to ideal cascades. 

Note that the overall dead time of the plant (Equation 6.125) is the sum of the dead... 

Similar to batch processes, the transfer of number of stages is not always as perfect as in the case of enantiomeric separation of EMD53986. If significant deviations between the concentration profiles are observed, another component has to be taken as reference component so that the total number of stages of every component in the new plant is greater than or equal to the number of stages in the old plant (Equation 7.44). 

The chemoreflex model provides a satisfactory explanation for the chemical regulation of ventilation as well as respiratory instabihty. However, it fails to explain a fundamental aspect of ventilatory control experienced by everyone in everyday fife the increase in ventilation during muscular exercise. Typically, Vp increases in direct proportion to the metaboHc demand (17002, VO2) such that the outputs of the chemical plant. Equation 11.1 and Equation 11.2, are well regulated at constant levels from rest to exercise. As a result, homeostasis of arterial blood chemistry is closely maintained over a wide range of work rates. The dilemma is if increases in metaboHc rate are not accompanied by corresponding increases in chemical feedback, then what causes exercise hyperpnea ... 

The terms Pmax and Pmax denote the limiting capacities of the inspiratory muscles, and n is an efficiency index. The optimal Pmus(t) output is found by minimization of / subjects to the constraints set by the chemical and mechanical plants. Equation 11.1 and Equation 11.9. Because Pmusif) is generally a continuous time function with sharp phase transitions, this amounts to solving a difficult dynamic nonlinear optimal control problem with piecewise smooth trajectories. An alternative approach adopted by Poon and coworkers [1992] is to model Pmus t) as a biphasic function... 

The behavior of the plant process can be represented as states and transition among the different states. Also messages and collaboration among the different classes/objects can represent behavioral aspects of the plant. Equations controlling the transition from one state to another can be represented using object constraint language (OCL) as an associated code with the different classes and states. 

---