2004 (Volume 14)
Second - order linear state space systems: Computing the transfer function using the DFT
|George E. Antoniou|
(State University Montclair, USA)
In this paper the discrete Fourier transform (DFT) is used for determining the transfer function coefficients for second-order linear systems:
. The proposed algorithm is theoretically attractive, practically fast and has been implemented in Matlab. Two step-by-step examples illustrating the application of the algorithm are given.
keywords: linear systems, second-order systems, Fourier transform, transfer function.
Relationship between Smith zeros and invariant zeros in linear systems
(Military University of Technology, Poland)
The question how the classical concept of the Smith zeros of a linear, time-invariant (LTI), multi-input, multi-output (MIMO) continuous-time singular system S(E,A,B,C,D) (in particular, at E=I, of a standard linear system S(A,B,C,D)) can be generalized and related to the state-space methods is discussed. Nothing is assumed about the relationship of the number of inputs to the number of outputs nor about the normal rank of the underlying system matrix. The aforementioned generalization treats zeros (called further the invariant zeros) as the triples (complex number, nonzero state-zero direction, input-zero direction). Such treatment is strictly connected with the output-zeroing problem and in that spirit the zeros can be easily interpreted even in the degenerate case (i.e., when any complex number is such zero).
keywords: linear systems, zeros, state-space methods.
Stable indirect adaptive fuzzy control for a class of SISO nonlinear systems
|Salim Labiod, Mohamed Seghir Boucherit and Omar Bouhali|
(Ecole Nationale Polytechnique, Algeria)
This paper proposes an indirect adaptive fuzzy control scheme for a class of unknown continuous-time nonlinear single-input single-output (SISO) dynamic systems. Within this scheme, the fuzzy systems are employed to approximate the unknown system dynamics. Based on these fuzzy approximations and a Lyapunov synthesis approach, suitable control laws and appropriate parameter adaptive algorithms are developed. It is shown that the proposed control scheme avoids the possible controller singularity problem, guarantees the convergence of the tracking error to zero and the global boundedness of all signals in the closed-loop system. Simulation results, performed on an inverted pendulum system, are given to point out the good performance of the developed adaptive control approach.
keywords: fuzzy control, fuzzy systems, nonlinear systems, adaptive control.
A new adaptive least-squares estimation algorithm with generalized internal feedback
|Krzysztof J. Latawiec|
(Technical University of Opole, Poland)
New concepts of `covariance matrix normalization' and the `cascade structure' of the adaptive least-squares parameter estimator are shown to generalize and extend the use of internal information feedback in various robustness/alertness-oriented modifications to the standard ALS estimation algorithm. In the cascade estimation structure it is possible to `naturally' stabilize, rather than maximize, the information matrix so that the covariance zeroing and blowup are effectively eliminated and the celebrated square root update of the covariance matrix is no longer needed. Consequently, a new, partly heuristic ALS MIMO estimation algorithm, enabling to effectively track both slow and jump parameter variations, is presented. The algorithm is coupled with a simple but robust predictive control scheme, offering a new adaptive MIMO control strategy.
keywords: adaptive systems, least-squares estimation, robust estimation, time-varying systems, identification, adaptive control, predictive control.
-Synthesis: an algebraic approach
|Marek Dlapa and Roman Prokop|
(Tomas Bata University in Zlin, Czech Republic)
In the paper the problem of the robust control of continuous-time systems via
-synthesis is investigated. The robust control design is formulated as a local minimization of the peak of the structured singular value. The control parameters are derived through polynomial Diophantine equations as a pole placement principle. The poles of the nominal feedback loop are the variables for minimization which was performed by a direct search method. The procedure provided the final controller of a simple PID structure, which was applied to a system with time delay as a perturbation and the results were compared with the D-K iteration, which gave a more complex solution.
keywords: structured singular value, algebraic synthesis, time delay, PID controllers, linear fractional transformation.
Adaptive stabilization of infinite-dimensional undamped second order systems without velocity feedback
|Toshihiro Kobayashi and Masahiro Oya|
(Kyushu Institute of Technology, Japan)
In this paper adaptive stabilization of infinite-dimensional undamped second order systems is considered in the case where the input and output operators are collocated. The systems may have an infinite number of poles and zeros on the imaginary axis. In the case where only position feedback is available, a parallel compensator is effective. The stabilizer is constructed by an adaptive P-controller for the augmented system which consists of the controlled system and a parallel compensator. The asymptotic stability of the closed-loop system is proved by LaSalle's invariance principle under compactness of the resolvent.
keywords: adaptive stabilization, undamped second order dynamical systems, parallel compensators.
A controllability problem for a class of uncertain - parameters linear dynamic systems
(University of Mining and Metallurgy, Poland)
In the paper a controllability problem for the class of time invariant linear dynamic SISO systems with uncertain parameters is discussed. The system under consideration is described by a finite dimensional state - space equation with the interval diagonal state matrix, the known control and output matrices and the two - dimensional uncertain parameters space. For the considered system a simple geometric interpretation of the system spectrum can be given. The geometric interpretation of the system spectrum is the basis to formulating the controllability conditions for the discussed system. The examples are given.
keywords: linear uncertain parameters dynamic systems, controllability.