Controller tuning definitions

The tuning and/or structure of the feedback controller matrix is changed until the minimum dip in the curve is something reasonable. Doyle and Stein gave no definite recommendations, but a value of about — 12 dB seems to give good results. 

The instmment shown in Figure 2.4 is a double-axis instrument. The first axis is the adjustment of the beam conditioner, the second is the scan of the specimen through the Bragg angle. It is irrelevant to this definition that a practical diffractometer may contain a dozen or more controlled axes , for example, to tune and to align the beam conditioner, to locate the specimen in the beam, to align and to scan the specimen and to control shts. It is the differential movement of the two main axes that make the measnrement and determine the precision and accuracy of the instrument. This is the basic high resolntion diffractometer, which is now widely nsed for measniements of crystal perfection, epilayer composition and thickness. 

A few comments about the method are warranted. The controlled (dominant) variables, Ycd, should be measured such that they belong to the set Yd for rapid control. Similarly, the manipulators in the feedback control loops should belong to the set, Ud. The feedback controllers should have integral action (PI controllers). These can be tuned with minimal information (e.g., ultimate gain and frequency from a relay test). The model Ms is usually quite simple and can be developed from operating data using statistical regressions. This works because the model includes all the dominant variables of the system, Y d, as independent variables by way of their setpoints, Y. The definition of domi-... 

Controller definition information (models, tuning parameters). 

Problem Definition Selection of Controlled Variables 13.2.1 Engineering Judgment / 13.2.2 Singular Value Decomposition Selection of Manipulated Variables Elimination of Poor Pairings BET Tuning... 

The dynamic simulation results are not definitive because optimal tuning of the control loops has not been completed, nor was it the objective of the present work. The main objective is to evaluate the potential of the modular decomposition approach to synthesize an effective plantwide control structure and to demonstrate the rigor of the mAHP procedure to select an acceptable control structure from among competing alternatives in the presence of competing objectives. 

The closed-loop stability of the batch motion can be established with the application of the standard singular perturbation [25] or small gain theorems [8, 10] available in the nonlinear dynamical systems literature, in eonjunction with the definition (7) of finite-time motion stability. In a chemical process context this closed-loop stability assessments can be seen in the cascade control of a continuous reactor [22], the cascade control of a continuous distillation [21, 24], and in the calorimetric estimation [15] of a batch polymer reactor. The closed-loop motion stability is ensured if the observer gain ( o) is tuned slower than the characteristic frequency ( j) of the fastest unmodeled dynamics, and the observer ( ), secondary ( ,.), and primary ( p) gains are sufficiently separated. This is. 

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