Control systems model parameters

If the process is not known well, we need to evaluate the objective function on-line (while the process is operating) using the values of the controlled output. Then the adaptation mechanism will change the controller parameters in such a way as to optimize (maximize or minimize) the value of the objective function (criterion). In the following two examples we examine the logic of two special self-adaptive control systems model reference adaptive control (MRAC) and self-tuning regulators (STRs). 

The next problem to consider is how chaotic attractors evolve from tire steady state or oscillatory behaviour of chemical systems. There are, effectively, an infinite number of routes to chaos [25]. However, only some of tliese have been examined carefully. In tire simplest models tliey depend on a single control or bifurcation parameter. In more complicated models or in experimental systems, variations along a suitable curve in the control parameter space allow at least a partial observation of tliese well known routes. For chemical systems we describe period doubling, mixed-mode oscillations, intennittency, and tire quasi-periodic route to chaos. 

A real-time optimization (RTO) system determines set point changes and implements them via the computer control system without intervention from unit operators. The RTO system completes all data transfer, optimization c culations, and set point implementation before unit conditions change and invahdate the computed optimum. In addition, the RTO system should perform all tasks without upsetting plant operations. Several steps are necessaiy for implementation of RTO, including determination of the plant steady state, data gathering and vahdation, updating of model parameters (if necessaiy) to match current operations, calculation of the new (optimized) set points, and the implementation of these set points. 

Computer tools can contribute significantly to the optimization of processes. Computer data acquisition allows data to be more readily collected, and easy-to-implement control systems can also be achieved. Mathematical modeling can save personnel time, laboratory time and materials, and the tools for solving differential equations, parameter estimation, and optimization problems can be easy to use and result in great productivity gains. Optimizing the control system resulted in faster startup and consequent productivity gains in the extruder laboratory. 

Cohen and Coon observed that the response of most uncontrolled (controller disconnected) processes to a step change in the manipulated variable is a sigmoidally shaped curve. This can be modelled approximately by a first-order system with time lag Tl, as given by the intersection of the tangent through the inflection point with the time axis (Fig. 2.34). The theoretical values of the controller settings obtained by the analysis of this system are summarised in Table 2.2. The model parameters for a step change A to be used with this table are calculated as follows... 

The design procedures depend heavily on the dynamic model of the process to be controlled. In more advanced model-based control systems, the action taken by the controller actually depends on the model. Under circumstances where we do not have a precise model, we perform our analysis with approximate models. This is the basis of a field called "system identification and parameter estimation." Physical insight that we may acquire in the act of model building is invaluable in problem solving. 

In the event that we are modeling a process, we would use a subscript p (x = xp, K = Kp). Similarly, the parameters would be the system time constant and system steady state gain when we analyze a control system. To avoid confusion, we may use a different subscript for a system. 

As seen previously for some specific applications such as wastewater treatment plants, software sensors can be envisaged to provide on-line estimation of non-measurable variables, model parameters or to overcome measurement delays [81-83]. Software sensors have been developed mainly for monitoring bioprocesses because the control system design of bioreactors is not straightforward due to [84] significant model uncertainty, lack of reliable on-line sensors, the non-linear and time-varying nature of the system or slow response of the process. 

In the present chapter, steady state, self-oscillating and chaotic behavior of an exothermic CSTR without control and with PI control is considered. The mathematical models have been explained in part one, so it is possible to use a simplified model and a more complex model taking into account the presence of inert. When the reactor works without any control system, and with a simple first order irreversible reaction, it will be shown that there are intervals of the inlet flow temperature and concentration from which a small region or lobe can appears. This lobe is not a basin of attraction or a strange attractor. It represents a zone in the parameters-plane inlet stream flow temperature-concentration where the reactor has self-oscillating behavior, without any periodic external disturbance. 

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. 

Dignum et al. [8, 10] followed this process in detail on a production site in Bali to measure the various parameters of the processing in order to mimic these in a laboratory model curing system. The parameters are summarised in Table 9.1. On the basis of the observations, a model curing system was set up to study different parameters under controlled conditions and the effect on some enzymes and the vanillin production. 

Since the orthogonal collocation or OCFE procedure reduces the original model to a first-order nonlinear ordinary differential equation system, linearization techniques can then be applied to obtain the linear form (72). Once the dynamic equations have been transformed to the standard state-space form and the model parameters estimated, various procedures can be used to design one or more multivariable control schemes. 

Thermal as well as oxidative dimers have also been isolated and characterized from pure fatty acid and TGs oxidized under simulated deep fat frying conditions. These model systems have been employed in order to simplify and control the various parameters affecting the thermal-oxidative reactions and to facilitate the structure elucidation of the decomposition products. 

We will formulate the problem simply but generally. Consider a system of structureless, classical particles, characterized macroscopically by a set of thermodynamic coordinates (such as the temperature T) and microscopically by a set of model parameters that prescribe their interactions. The two sets of parameters play a strategically similar role it is therefore convenient to denote them, collectively, by a single label, c (for conditions or constraints or control parameters in thermodynamic-and-model space). 

In the design of a static-control system, parameters such as capacitance of the personnel, maximum anticipated potential static buildup, and the time to discharge the personnel to safe levels should be known for the model. This is also true when designing static discharge systems for containers entering static protected environments. Such containers should be discharged to safe levels prior to entering the protected space. 

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