This paper provides guidelines for the discretizing of the space variables in continuous systems governed by the second-order partial differential diffusion equation. Such lumping is necessary in all digital and many ...
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This paper provides guidelines for the discretizing of the space variables in continuous systems governed by the second-order partial differential diffusion equation. Such lumping is necessary in all digital and many analog methods. To analyze the truncation error resulting from lumped analog or digital modelling, the authors demonstrate the applicability of an upper-bound criterion combining amplitude and phase errors in the frequency domain. Dimensionless variables are used to compare lumped networks corresponding to one-dimensional continuous systems. Computer results are presented which relate truncation error to frequency for lumped models containing one to ten sections.
Finite difference methods are used to implement the solution to optimal control of distributed parameter systems. The control is assumed to be intrinsic to the partial differential equation (PDE) as well as continuous...
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Finite difference methods are used to implement the solution to optimal control of distributed parameter systems. The control is assumed to be intrinsic to the partial differential equation (PDE) as well as continuous, such that the calculus of variations is used to obtain the control law. Several important principles are developed to formulate the difference approximations to the partial differential equations which describe the system and the control law. An iterative method of solution is employed on these two equations. The convergence of the iteration is assured by stability considerations of the finite difference expressions.
A method is proposed for identifying linear distributed parameter systems from measurements on the system and inputs. Based on characteristics, the method is direct and converges rapidly for the class of problems disc...
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A method is proposed for identifying linear distributed parameter systems from measurements on the system and inputs. Based on characteristics, the method is direct and converges rapidly for the class of problems discussed.
The problem of optimum control of a distributedparameter system with boundary control is studied. The distributedparameter system considered is described by the N-dimensional wave equation. The error measure is quad...
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The optimal open loop control of systems described by a set of linear partial differential equations is investigated. The performance index is of quadratic type and the mean square error is considered as a special cas...
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The optimal open loop control of systems described by a set of linear partial differential equations is investigated. The performance index is of quadratic type and the mean square error is considered as a special case. Energy type inequality constraints are imposed on the control inputs. The problem is formulated as a minimization problem in Hilbert space. The necessary and sufficient conditions for a minimum are obtained and it is proved that these conditions yield the global minimum. It is shown how the solution to the constrained problem can be obtained from the solution of the unconstrained problem. The optimal control functions satisfy Fredholm integral equations with symmetric kernels. The paper presents an example where the solution is obtained by eigenfunction expansion.
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.
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