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1
Content available On a linear-quadratic problem with Caputo derivative
Idczak D., Walczak S.
Opuscula Mathematica
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2016
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Vol. 36, no. 1
49--68
EN
In this paper, we study a linear-quadratic optimal control problem with a fractional control system containing a Caputo derivative of unknown function. First, we derive the formulas for the differential and gradient of the cost functional under given constraints. Next, we prove an existence result and derive a maximum principle. Finally, we describe the gradient and projection of the gradient methods for the problem under consideration.
2
Content available Infinite time horizon optimal current control of a stepper motor exploiting a finite element model
Bernat J., Stępień S., Stranz A., Szymański G., Sykulski J. K.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2014
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Vol. 62, nr 4
835--841
EN
An optimal control theory based method is presented aiming at minimizing the energy delivered from source and the power loss in a stepper motor circuit. A linear quadratic current regulator with an infinite time horizon is employed and its appropriateness for this type of a problem explained. With the purpose of improving the accuracy of the control system, the self and mutual inductances of windings are calculated using a finite element model. The numerically computed results are verified experimentally.
3
Content available Optimal boundary control problems of retarded parabolic systems
Kowalewski A., Krakowiak A.
Archives of Control Sciences
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2013
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Vol. 23, no. 3
261--279
EN
Optimal boundary control problems of retarded parabolic systems are presented. Necessary and sufficient conditions of optimality are derived for the Neumann problem. A simple example of application is also presented.
4
Content available Application of optimal current driver for the torque control of BLDC motor
Bernat J., Stępień S.
Archives of Electrical Engineering
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2011
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Vol. 60, nr 2
149-158
EN
This research presents the novel control strategy of the brushless DC motor. The optimal current driver is designed using Linear Quadratic Regulator and feedback linearization. Additionally, the current reshaping strategy is applied to control the motor torque. Thus, the torque controller is built based on the optimal current driver. The motor is simulated using the FEM analysis.
5
Content available remote Fuzzy Logic Optimal Control Of Bldc Motor Considering Lqr And Smc Methodology
Bernat J., Stępień S., Szymański G.
Foundations of Computing and Decision Sciences
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2010
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Vol. 35, No. 3
171-183
EN
This paper presents a method of the speed control of the brushless dc motor (BLDC). The proposed method is based on the linear quadratic problem and sliding mode control. In the control system, the fuzzy logic controller is applied to obtain its robustness and optimal performance. The BLDC motor model is described using finite element boundary equations, where the magnetic field equations, the stator circuit equations and the motion equations are solved simultaneously at each iteration step. The surrogate motor model is built to design the optimal controller based on the finite element analysis. Thus, the parameters identification and Kaiman filtering are employed to estimate the state of the control plant.
6
Content available remote Optimal distributed control problems of retarded parabolic systems
Kowalewski A., Krakowiak A.
Archives of Control Sciences
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2009
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Vol. 19, no. 3
279-293
EN
Optimal distributed control problems of retarded parabolic systems are presented. Necessary and sufficient conditions of optimality are derived for the Neumann problem. A simple example of application is also presented.
7
Content available remote Adaptive control for a jump linear system with quadratic cost
Czornik A.
Control and Cybernetics
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2004
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Vol. 33, no 1
51-69
EN
The adaptive control problem for a jump linear system with quadratic cost functional on infinite time interval is solved in this paper. It is assumed that the coefficients of the state equation are unknown but a compact set that contains the parameters is known. A diminishing excitation accompanies the adaptive control signal, to ensure the strong consistency of the weighted least squares algorithm.
8
Content available On descriptor systems and related linear quadratic problem
Gessing R., Czornik A.
Control and Cybernetics
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2000
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Vol. 29, no 1
79-89
EN
It is shown that a descriptor system under the condition of impulse controllability, Cobb (1984), may be converted, by means of linear transformations, to a system described in a state space and composed of state and output equations. The transfomations determine one to one correspondence between the solutions of both the systems. It is noted that the control in a feedback form may not determine a unique solution of the descriptor system what is often overlooked in many previous papers. It is also shown that the LCD problem formulated in a descriptor space for the impulse observable system, Cobb (1984); may be converted by means of linear transformations to the usual LQ problem formulated in the state space. It is stressed that the second problem may be regular even then, when the weighting matrix of the control, in the cost functional of the first problem, is singular. The proposed approach simplifies the calculations related to the LQ problem solution significantly.
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