Controller performance criteria

Thickener control philosophies are usually based on the idea that the Iindertlow density obtained is the most important performance criterion. The o ertlow clarity is also a consideration, but this is generally not as critical. Additional factors which must be considered are optimization of tlocciilant usage and protection of the raking mechanism. 

Control philosophies for clarifiers are based on the idea that the overflow is the most important performance criterion. Underflow density or suspended sohds content is a consideration, as is optimal use of flocculation and pH control reagents. Automated controls are of three basic types (I) control loops that optimize coagulant, flocculant, and pH control reagent additions (2) those that regulate underflow removal and (3) rake drive controls. Equahzation of the feed is provided in some installations, but the clarifier feed is usually not a controlled variable with respect to the clarifier operation. 

Control of pollutants by oxidation is another exothermic process in which high conversion is the most important performance criterion. Interest in efficiency is limited to minimize byproduct formation the byproducts can be more damaging and more refractory than the original pollutants were. Commercially, most adiabatic reactors used for pollution control are of the least expensive construction. 

An alternative procedure is the dynamic programming method of Bellman (1957) which is based on the principle of optimality and the imbedding approach. The principle of optimality yields the Hamilton-Jacobi partial differential equation, whose solution results in an optimal control policy. Euler-Lagrange and Pontrya-gin s equations are applicable to systems with non-linear, time-varying state equations and non-quadratic, time varying performance criteria. The Hamilton-Jacobi equation is usually solved for the important and special case of the linear time-invariant plant with quadratic performance criterion (called the performance index), which takes the form of the matrix Riccati (1724) equation. This produces an optimal control law as a linear function of the state vector components which is always stable, providing the system is controllable. 

The steadystate error is another time-domain specification. It is not a dynamic specification, but it is an important performance criterion. In many loops (but not all) a steadystate error of zero is desired, i.e, the value of the controlled variable should eventually level out at the setpoint. 

The principal steady-state performance criterion usually is zero error at steady state. We have seen already that in most situations the proportional controller cannot achieve zero steady-state error, while a PI controller can. Also, we know that for proportional control the steady-state error (offset) tends to zero as Kc - oo. No further discussion is needed on the steady-state performance criteria. 

Compute the value of the performance criterion using a P, or PI, or PID controller with the best settings for the adjusted parameters Kc, t/, and td. 

Select that controller which gives the best value for the performance criterion. 

TABLE 9.5 Tuning Relations for PID Controller Based on ITAE Performance Criterion ... 

Sun and Yih (1996) adopted their idea to develop a neural network-based controller for manufacturing cells. In their approach, a neural network was trained to serve as decisionmaker that will select a proper dispatching rule for its associated machine to process the next job. Based on their results, the controller performs well under multiple criterion environments. In addition, when the production objectives change, the controller can respond to such change in a short time. 

Green Chemistry, defined as the design of chemical products and processes that reduce or eliminate the use and generation of hazardous substances (5), has been referred to as pollution prevention at the molecular level. This emerging area recognizes fiiat during the design phase of any chemical synthesis, product, or process, minimized hazard must be viewed as a performance criterion. Moreover, hazard must also be viewed as a physical/chemical property that is possible to manipulate and control at die molecular level. 

A majority of the modules requires certain input parameters, which have to be defined in a user-written configuration file, and is read by the main python module main.py. The configuration file specifies all class objects, modules, and submodules that are desired for optimization process. It also contains important preferences concerning the system (e.g., inpul/output paths, number of computer cores, batch system), the optimization (e.g., algorithm, step length control, stopping criterion, initial parameters, constraints), and the optimization problem (e.g., objective functions, the loss function s target values). When molecular simulations are performed, all desired properties and parameters of the thermodynamic system have to be defined (e.g., ensemble, temperatures, pressures, physical properties to be fitted, number of molecules, box size, number of MD/MC steps, time step). Hence, the file is divided into three blocks. If more than one substance is considered in the optimization, one block for each substance has to be indicated. 

The performance criterion needed to demonstrate that the above functional requirement is met is that key operation of the shield doors must be administratively controlled. Keyed locks for enabling shield door movement provide a positive feature that can be used to preclude unintentional or unauthorized door movement. 

Pandy, M. G., Gamer, B. A., and Anderson, F. C. (1995). Optimal control of non-ballistic muscular movements A constraint-based performance criterion for rising from a chair. Journal of Biomechanical Engineering, 117 15-26. 

One could be a horizontal cooperation between the operator and an expert tool whose ouq>uts are directly connected to the process. The principle is to make a dynamical repartition of the tasks using a task repartitor. The latter can be controlled either by the operator or by an optimal command algorithm, this according to a performance criterion of the man-expert tool-process system, and under the constraints imposed by the human limits. 

Determine the rate of change per unit step change in the manipulated variable, 1 gmax/ S. The recommended controller parameter settings, based on the quarter-decay performance criterion, are shown in Table 4.5. 

A simplification assumption, particularly for the formulation of the performance criterion, is that the process between the transitions is running at steady state, operating under perfect control, eliminating any disturbance and hence preventing any deviation from on-spec production. With this assumption, the production periods between the transition periods do not need to be considered in this study and the performance index accounts only for the transition periods. 

Schweickhardt and Allgower in Chapter A3 mainly concentrate on the nonlinearity assessment of processes. A comprehensive overview of general nonlinearity measures and a thorough investigation of the predictive and computational dimension of open loop measures are presented. As the main objective becomes the development of a tool to judge whether a nonlinear controller should be benefieial or needed for a particular process with specific nonlinear characteristics, the controller relevant nonlinearity is quantified. The selected measure is based on the relative differences between the output of nonlinear state feedback law and that of an equivalent linear state feedback law. The controller relevant nonlinearity measure depends not only on the plant dynamics and region of operation but also on the performance criterion used in the derivation of the controller law. 

The first two points are valid for open-loop process nonlinearity measures as well. The third point is new in control-relevant nonlinearity quantification. In a more general context, one has not only to consider the performance criterion but additionally mention the controller design method. Following the idea of Ref 24, optimal control theory with an integral performance criterion will be used here as it represents a benchmark for any achievable performance. Considering nonlinear internal model control with different filter time constants is also possible, see for example Ref 23. 

Model parameter variations and perturbations of the externally specified inputs will influence the position of the system eigenvalues through the linearised system in Eq. (6) (Ref. 36). Such a situation may lead to the appearance of dynamic modes that are responsible for the deterioration of the achievable control performance. The dynamic controllability criterion is the required tool for the investigation of the process dynamics transformation under the influence of multiple disturbances that accounts also for nonlinear interactions. Therefore, the static controllability optimisation problem in Eq. (2) is enriched as follows (Ref 37) ... 

Repeatability is, perhaps, the most important performance criterion of a process-control valve. This is especially true in applications where precise flow or pressure control is needed for optimum performance of the process system. 

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