The Linear-Quadratic Control Problem: A Review of Theory and Practice

Edgar, Thomas F.; Vermeychuk, J. Gregory; Lapidus, Leon

doi:10.1080/00986447308960415

Cited by 6 publications

(7 citation statements)

References 86 publications

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“…The latter step is possible since these nonlinearities were constrained to be invertible during the identification process. To design the controller, several standard automated tuning methods such as Ziegler-Nichols PID, internal model control (IMC), linear quadratic Gaussian (LQG) and optimization based approaches were tested and the best results were obtained for the LQG design method [19]- [21]. The transfer function of the designed controller is as follows 7 …”

Section: Controller Designmentioning

confidence: 99%

A Nonlinear Dynamical Modeling and Control Method for the Vorticity Control of the Flow past a Circular Cylinder

Karaca¹,

Ozen²,

Kasnakoğlu³

2013

IJMMM

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Abstract-In this paper a systematic approach for the nonlinear modeling and feedback control of vorticity behind an immersed circular cylinder system was developed. In this technique first a number of control input points over the cylinder and some measurement points for vorticity past the cylinder are assigned. A type of nonlinear dynamic model (namely a Hammerstein-Wiener (HW) model) of the flow field is estimated via system identification techniques using measurement data obtained from a chirp input function. Once the dynamical model of the system is estimated, a controller for the linear block of the HW model is designed using internal model control method, and this controller is then mapped to the HW model by reversing the input/output nonlinearity functions. The procedure described is implemented and tested numerically in MATLAB and CFD computations performed on the closed-loop system show that the controller is capable of achieving significant reduction in the vorticity levels past the cylinder.Index Terms-Flow past a circular cylinder, nonlinear dynamical modeling and control, system identification, hammerstein-wiener method, vorticity control.

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Section: Controller Designmentioning

confidence: 99%

A Nonlinear Dynamical Modeling and Control Method for the Vorticity Control of the Flow past a Circular Cylinder

Karaca¹,

Ozen²,

Kasnakoğlu³

2013

IJMMM

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“…The general structure of the optimal controller for a nonstationary linear system with quadratic performance index is well known (see Athans and Falb, 1966;Edgar et al, 1973). The optimal control can be determined in feedback form where the n x n symmetric matrix K ( t ) is the solution of the Riccati equation…”

Section: (4)mentioning

confidence: 99%

“…It should be mentioned here that, while there are optimal design procedures which incorporate the influences of step disturbances (see Edgar et al, 1973), these were not explored because our present goal is a feedback regulator for any disturbance.…”

Section: Regulator Evaluation Proceduresmentioning

confidence: 99%

“…We had little difficulty in determining acceptable values for R by trial and error. Although more systematic procedures have been proposed (Edgar et al, 1973), they are quite involved and appear to offer minimal advantages for this example.…”

Section: Regulator Evaluation Proceduresmentioning

confidence: 99%

“…Once a suitable design has been developed, another problem which we call periodic process regulation must be resolved: What control manipulations are necessary when the operating cyclic system is disturbed by an unexpected change in its environment? This paper presents one approach to this problem for systems described by ordinary differential equations, By adopting the objective of maintaining design conditions and assuming that deviations from these conditions are sufficiently small, regulating controls can be synthesized in feedback form by solving a time-varying linearquadratic optimization problem (see Edgar et al, 1973). Employing this approach, generalized proportional (P) and proportional-integral (PI) regulators are developed.…”

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confidence: 99%

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Regulation of lumped periodic processes

Liaw

Bailey

1974

AIChE Journal

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When a periodic process is disturbed, control action may be necessary to maintain satisfactory performance. Regulating controls to achieve this objective can be synthesized by solving a linear-quadratic optimization problem with periodic coefficients. Generalized proportional and proportional-integral feedback regulators developed in this manner are tested by simulating a cyclic reactor. Very satisfactory control is achieved for 10% step disturbances in reactor feed conditions although the results are sensitive to the choice of manipulated variables. J . 4 . SCOPESignificant recent research interest has been focused on possible advantages of intentional unsteady state processing Among the potential benefits of periodic operation are increased reactor selectivity (see Bailey, 1974) and enhanced separation (see, for example, Robinson and Engel, 1967;Wilhelm et al., 1968). All previous work, however, has considered only the question of periodic process design: how should some manipulated variable be oscillated to achieve optimum performance? Once a suitable design has been developed, another problem which we call periodic process regulation must be resolved: What control manipulations are necessary when the operating cyclic system is disturbed by an unexpected change in its environment? This paper presents one approach to this problem for systems described by ordinary differential equations, By adopting the objective of maintaining design conditions and assuming that deviations from these conditions are sufficiently small, regulating controls can be synthesized in feedback form by solving a time-varying linearquadratic optimization problem (see Edgar et al., 1973). Employing this approach, generalized proportional (P) and proportional-integral (PI) regulators are developed. A continuous-flow stirred tank reactor (CSTR) in which parallel reactions occur is employed to test these regulating controls. In the absence of disturbances, periodic variations in heat flux to the reactor provide greater selectivity for the desired product than can be obtained by steady state operation.Step disturbances in feed conditions can unfavorably alter the reactor's performance. The effectiveness of flow rate or heat flux manipulation in counteracting these upsets is investigated using simulation studies. CONCLUSIONS AND SIGNIFICANCEA generalized proportional-integral control employing heat flux as the regulating variable effectively returns the cyclic reaction system to its design specifications following 10% step decreases and increases in feed concentration and temperature. This can be seen by comparing the response with this controller, denoted PI-Heat, to the periodic fluctuations of the reference design (undisturbed) process in Figures 2, 4, and 5. Proportional control using heat flux regulates the reactor almost as well but requires more extreme fluctuations in the manipulated variable as shows that flow rate is far less effective than heat flux in maintaining reference design conditions. Without a regulating control these distu...

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Advanced control practice in the chemical process industry: A view from industry

Lee

Weekman

1976

AIChE Journal

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This paper presents a commentary on the status of application of modern control theories to industrial chemical processes. The difficulties encountered in the implementation of advanced control to chemical reactors are critically examined in order to determine the reasons for its limited success to date. Chemical processes, very often poorly understood because of the physicochemical complexities, are nonlinear, highly interacting, spacially dependent, and continuously disturbed by many uncharacterized noises. It is time-consuming and expensive to develop advanced control methods for these systems because few of the available theories can be applied directly. Thus, we often find it difficult to economically justify advanced control projects.

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The Linear-Quadratic Control Problem: A Review of Theory and Practice

Cited by 6 publications

References 86 publications

A Nonlinear Dynamical Modeling and Control Method for the Vorticity Control of the Flow past a Circular Cylinder

A Nonlinear Dynamical Modeling and Control Method for the Vorticity Control of the Flow past a Circular Cylinder

Regulation of lumped periodic processes

Advanced control practice in the chemical process industry: A view from industry

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