作者：
GARVEY, DCDSOUZA, AFD. C. Garvey
A. F. D’Souza Dept. of Mechanical and Aerospace Engineering Illinois Institute of Technology Chicago Ill.
The partial differential equations describing distributed parameter systems may often be reduced to transcendental transfer functions with the aid of appropriate boundary conditions. In the analysis and synthesis of c...
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The partial differential equations describing distributed parameter systems may often be reduced to transcendental transfer functions with the aid of appropriate boundary conditions. In the analysis and synthesis of closed loop systems, the transcendental transfer functions have to be approximated in a suitable manner. In this paper, discrete-time model of distributed parameter systems is obtained. The model employs a sample and hold circuit in the loop. The response of the model system is compared with the response obtained by approximating the transcendental transfer function by root factor and other approximations. The stability of linear and nonlinear systems with distributedparameters is investigated by employing the Mikhailov stability criterion.
For distributed parameter systems, open-loop stability in the sense of bounded outputs for bounded inputs, and closed-loop asymptotic stability are considered. Frequency domain stability criteria for open and closed-l...
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For distributed parameter systems, open-loop stability in the sense of bounded outputs for bounded inputs, and closed-loop asymptotic stability are considered. Frequency domain stability criteria for open and closed-loop distributed parameter systems are given. The closed-loop stability criterion is similar to V. M. Popov’s stability criterion for lumped systems. The criteria are limited to those linear, time-invariant systems whose dynamics can be described by a transfer function which is the ratio of the multiple transform of the output to the multiple transform of the input. The input may or may not be distributed. An example is given to illustrate the applications of the stability criteria.
The optimal regulator of distributed parameter systems with its cost functional involving time derivatives of distributed control vectors or state spatial and time derivative terms as well as the usual terms containin...
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The optimal regulator of distributed parameter systems with its cost functional involving time derivatives of distributed control vectors or state spatial and time derivative terms as well as the usual terms containing the control and state vectors has been analyzed by introducing augmented variables. A very significant result in modern control theory is that, for a linear, finite-dimensional, dynamical systems, the state feedback law derived from a quadratic performance index function minimization problem is linear. Generalization of the above result to a infinite-dimensional, distributedparameter dynamical systems with quadratic cost functional involving derivative terms is made possible from stability considerations. The state feedback law, realized by a linear distributedparameter dynamical system, has operator representations.
For a general model of a linear distributedparameter system, the problem of minimizing the norm of the difference between desired system response and obtainable system response is considered. Here the control input i...
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For a general model of a linear distributedparameter system, the problem of minimizing the norm of the difference between desired system response and obtainable system response is considered. Here the control input is constrained to be bounded in magnitude. An optimal solution is shown to exist, and an optimal solution in a class of controls dense in the constraint set is shown to exist. This latter class is characterized by N parameters whose values are obtainable by a convex programming algorithm presented in the paper. The technique developed can also be directly applied to lumped parametersystems, lumped parameter driven distributed parameter systems and the optimum magnitude constrained input final value control problem for any of the preceding.
Direct applications of mathematical programming techniques in numerical solutions of optimal control problems are reviewed. The types of control systems discussed include linear, nonlinear, continuous- and discrete-ti...
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Direct applications of mathematical programming techniques in numerical solutions of optimal control problems are reviewed. The types of control systems discussed include linear, nonlinear, continuous- and discrete-time, deterministic, stochastic, and distributed-parametersystems. The areas of application include aerospace trajectory optimization and rendezvous problems, computer control of processes, and nuclear reactor control problems. A classified bibliography is included.
This paper presents a general discussion of the optimum control of distributed-parameter dynamical systems. The main areas of discussion are: (a) The mathematical description of distributed parameter systems, (b) the ...
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