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114 Stepsize selection in implicit Runge-Kutta methods viewed as a control problem
531
Abstracts determine the AR. The method is illustrated by examples, some of which have not been solved by conventional o~imization techniques.
107
An Efficient Computational Algorithm for Adaptive Manipulator Control H. Kawasaki, S. Mochizuki, K. Kanzaki, pp 459-462
This paper presents a new computational algorithm of adaptive manipulator control adopting the basic method proposed by Slotine and Li. The algorithm is based on the recunive NewtonEuler formulation and the minimum dynamic parameters derived by Kawasaki and Kanzaki. The number of operations required in this algorithm is about one half of those for the method presented by Niemeyer and Slotine. The paper also presents experimental results on the adaptive control of a robot manipulator with six degrees of freedom. Its control system has a 32-hit DSP for the computation of the adaptive control.
108
Relations Between Dynamic Programming and Maximum Principle for Descriptor Systems H. Xu, K. Mlzukami, pp 463-468
In this paper, the connection between dynamic programming and the maximum principle for the descriptor system is established, as in the state-space system. The maximum principle for the descriptor system is deduced with the aid of the dynamic programming method. By using this method, the assumptions of admissible initial condition, or admissible condition, can be avoided. The results obtained in this paper can extend the domain of application of the maximum principle for the descriptor system. An illustrative example without admissible initial condition assumption is given to show the application of the maximum principle.
109
A new Square-Root Balandng.Free Stochastic Truncation Model Reduction Algorithm A. Varga, K.H. Fasol, pp 469.472
The paper proposes a new computational approach with enhanced numerical robusmess for computing reduced-order models of continuous systems by using the balanced stochastic truncation model-reduction method. This circmnvents the computation of possibly ill-conditioned stochastic balancing transformations. Instead, well-conditioned projection matrices are determined for computing the state-space mlxesentations of the reduced order models directly. The projection matrices are computed in a numerically reliable way, by using exclusively the Cholesky (square-root) factors of system Gramims. The proposed algorithm can handle both minimal and non-minimal systems. II0
A Case-Study Comparison of Some Order.Reduction Approaches Based on Accuracy Enhancing Methods K.H. Fasol, A. Varga, pp 473.477
Among existing order reduction approaches, methods based on balanced realizations play an important role. Square-root balancing-free versions of some algorithms have recently been developed. These algoritlnns have better numerical performances than their original versions and are appropriate for robust software implementations. This paper presents a short survey of such methods. In a case study, each approach is applied to reduce the model of an industrial system. The results are compared. 111
Elimination of Fixed Modes in Linear Control Systems with Constrained Control Structures T. Tonino, K. Abe, M. Tanaka, pp 479-482
In this paper, the concept of degrees of fixed modes is introduced for linear time-invariant control systems with constrained control structures, typically including decentralized control systems. Moreover, the existence of minimal effective subsystems corresponding to each fixed mode is guaranteed. The minimal number of additional interconnection gains (feedback links)
necessary for eliminating the fixed mode is made clear, based on the minimal effective subsystems. A dual characterization of the degree of fixed mode, the minimal rank deficiency of feedback control structure matrices where the fixed mode is not the transmission zero of the corresponding subsystems, is also obtained. A method for eliminating phiml fixed modes is proposed.
112
Parameter Tuning of PID Control Based on Pole-Zero Area Placement Using Characteristics Graphic PaHerns O. Ono, pp 483-486
This paper considers a new type of locus analysis and a tuning method of the parameters of PID control by means of the characteristic graphic pattem of the complex plane. Following an overview of PID control, the paper presents a new method of searching for the pole-zero placement of the complex plane. It addresses a hypothetical transfer function of the PID controller. The parameter tuning produced by Ziegler and Nichols is shown to correspond to special graphic patterns of the complex plane. A new searching procedure for pole and zero location, and a parameter tuning method of PID control by means of the graphic patterns mentioned above, are demonstrated.
113
The Construction and Properties of the Set of Noninferior Solutions of MultiobJective Convex Programming Lequn Hu, Cangpu Wu, pp 487-494
The convexity assumption is usually used in the theory of multiobjective optimization and its algorithms. In this paper, the set of nonlnferior solutions is constmcted and its geometric propeRies are studied under the convexity assumption. It is shown that in m-dimensional value space, the set of noninferior solutions turns out to be a strictly decreasing, strictly concave and nonchinky block (or piece) of the (hyper-)surface (or curve).
114
Stepsize Selection in Implicit Runge-Kutta Methods Viewed as a Control Problem K. Gustafsson, pp 495-498
The choice of stepsize in a numerical integration method is an important issue that affects both accuracy and efficiency. This paper analyzes the algorithms in use today from a feedback control point of view. The analysis points out deficienciesin the standard algorithm, and a new, improved controlleris derived. The new controllerprovides superior performance at littleextra expense.
115
Optimum FWL Design of Sampled Data Controllers A. Madievski, pp 499-502
The problem of optimal finite word length state-space digital controllerdesign is investigated. The closed loop to be considered consists of a continuous-time plant, a discrete-time controller,a sampler, a zero-order hold and an anti-aliasingfilter. An effective algorithm to design the sampled data controller minimizing a measure of sensitivityof the closcd-lcop performance with respect to finiteword length representationis proposed.
116
Compensator Realizations that Minimize the Closed Loop Pole Sensitivity Gang LI, M. Gever~ pp 503-506
This paper investigates optimal realizations of systems and compensators in terms of minimizing a weighted pole sensitivity measure. The main new result is to derive expressions for the pole sensitivity functions of a closed-loop system with respect to the parameters of the compensator realization, and to give the necessary and sufficient condition that must be satisfied by all compensator realizations that minimize a weighted pole sensitivity measure of the dosed-loop system. An algorithm is given to solve this problem. The new weighted pole sensitivity minimisation scheme is a contribution to Stability Robustness theory; the
Abstracts determine the AR. The method is illustrated by examples, some of which have not been solved by conventional o~imization techniques.
107
An Efficient Computational Algorithm for Adaptive Manipulator Control H. Kawasaki, S. Mochizuki, K. Kanzaki, pp 459-462
This paper presents a new computational algorithm of adaptive manipulator control adopting the basic method proposed by Slotine and Li. The algorithm is based on the recunive NewtonEuler formulation and the minimum dynamic parameters derived by Kawasaki and Kanzaki. The number of operations required in this algorithm is about one half of those for the method presented by Niemeyer and Slotine. The paper also presents experimental results on the adaptive control of a robot manipulator with six degrees of freedom. Its control system has a 32-hit DSP for the computation of the adaptive control.
108
Relations Between Dynamic Programming and Maximum Principle for Descriptor Systems H. Xu, K. Mlzukami, pp 463-468
In this paper, the connection between dynamic programming and the maximum principle for the descriptor system is established, as in the state-space system. The maximum principle for the descriptor system is deduced with the aid of the dynamic programming method. By using this method, the assumptions of admissible initial condition, or admissible condition, can be avoided. The results obtained in this paper can extend the domain of application of the maximum principle for the descriptor system. An illustrative example without admissible initial condition assumption is given to show the application of the maximum principle.
109
A new Square-Root Balandng.Free Stochastic Truncation Model Reduction Algorithm A. Varga, K.H. Fasol, pp 469.472
The paper proposes a new computational approach with enhanced numerical robusmess for computing reduced-order models of continuous systems by using the balanced stochastic truncation model-reduction method. This circmnvents the computation of possibly ill-conditioned stochastic balancing transformations. Instead, well-conditioned projection matrices are determined for computing the state-space mlxesentations of the reduced order models directly. The projection matrices are computed in a numerically reliable way, by using exclusively the Cholesky (square-root) factors of system Gramims. The proposed algorithm can handle both minimal and non-minimal systems. II0
A Case-Study Comparison of Some Order.Reduction Approaches Based on Accuracy Enhancing Methods K.H. Fasol, A. Varga, pp 473.477
Among existing order reduction approaches, methods based on balanced realizations play an important role. Square-root balancing-free versions of some algorithms have recently been developed. These algoritlnns have better numerical performances than their original versions and are appropriate for robust software implementations. This paper presents a short survey of such methods. In a case study, each approach is applied to reduce the model of an industrial system. The results are compared. 111
Elimination of Fixed Modes in Linear Control Systems with Constrained Control Structures T. Tonino, K. Abe, M. Tanaka, pp 479-482
In this paper, the concept of degrees of fixed modes is introduced for linear time-invariant control systems with constrained control structures, typically including decentralized control systems. Moreover, the existence of minimal effective subsystems corresponding to each fixed mode is guaranteed. The minimal number of additional interconnection gains (feedback links)
necessary for eliminating the fixed mode is made clear, based on the minimal effective subsystems. A dual characterization of the degree of fixed mode, the minimal rank deficiency of feedback control structure matrices where the fixed mode is not the transmission zero of the corresponding subsystems, is also obtained. A method for eliminating phiml fixed modes is proposed.
112
Parameter Tuning of PID Control Based on Pole-Zero Area Placement Using Characteristics Graphic PaHerns O. Ono, pp 483-486
This paper considers a new type of locus analysis and a tuning method of the parameters of PID control by means of the characteristic graphic pattem of the complex plane. Following an overview of PID control, the paper presents a new method of searching for the pole-zero placement of the complex plane. It addresses a hypothetical transfer function of the PID controller. The parameter tuning produced by Ziegler and Nichols is shown to correspond to special graphic patterns of the complex plane. A new searching procedure for pole and zero location, and a parameter tuning method of PID control by means of the graphic patterns mentioned above, are demonstrated.
113
The Construction and Properties of the Set of Noninferior Solutions of MultiobJective Convex Programming Lequn Hu, Cangpu Wu, pp 487-494
The convexity assumption is usually used in the theory of multiobjective optimization and its algorithms. In this paper, the set of nonlnferior solutions is constmcted and its geometric propeRies are studied under the convexity assumption. It is shown that in m-dimensional value space, the set of noninferior solutions turns out to be a strictly decreasing, strictly concave and nonchinky block (or piece) of the (hyper-)surface (or curve).
114
Stepsize Selection in Implicit Runge-Kutta Methods Viewed as a Control Problem K. Gustafsson, pp 495-498
The choice of stepsize in a numerical integration method is an important issue that affects both accuracy and efficiency. This paper analyzes the algorithms in use today from a feedback control point of view. The analysis points out deficienciesin the standard algorithm, and a new, improved controlleris derived. The new controllerprovides superior performance at littleextra expense.
115
Optimum FWL Design of Sampled Data Controllers A. Madievski, pp 499-502
The problem of optimal finite word length state-space digital controllerdesign is investigated. The closed loop to be considered consists of a continuous-time plant, a discrete-time controller,a sampler, a zero-order hold and an anti-aliasingfilter. An effective algorithm to design the sampled data controller minimizing a measure of sensitivityof the closcd-lcop performance with respect to finiteword length representationis proposed.
116
Compensator Realizations that Minimize the Closed Loop Pole Sensitivity Gang LI, M. Gever~ pp 503-506
This paper investigates optimal realizations of systems and compensators in terms of minimizing a weighted pole sensitivity measure. The main new result is to derive expressions for the pole sensitivity functions of a closed-loop system with respect to the parameters of the compensator realization, and to give the necessary and sufficient condition that must be satisfied by all compensator realizations that minimize a weighted pole sensitivity measure of the dosed-loop system. An algorithm is given to solve this problem. The new weighted pole sensitivity minimisation scheme is a contribution to Stability Robustness theory; the