Variable structure control of linear time invariant fractional order systems using a finite number of state feedback law

2011 ◽  
Vol 16 (3) ◽  
pp. 1433-1442 ◽  
Author(s):  
Saeed Balochian ◽  
Ali Khaki Sedigh ◽  
Asef Zare
Keyword(s):  
Finite Number ◽  
Fractional Order ◽  
State Feedback ◽  
Linear Time ◽  
Variable Structure Control ◽  
Variable Structure ◽  
Fractional Order Systems ◽  
Structure Control ◽  
Linear Time Invariant ◽  
Time Invariant

Adaptive Variable Structure Control for Uncertain Linear Time-Invariant Delay Singular Systems

2012 ◽  
Vol 433-440 ◽  
pp. 3734-3740
Author(s):  
Bo Meng ◽  
Cun Chen Gao ◽  
Shu Hong Tang
Keyword(s):  
Control Strategy ◽  
Sliding Mode ◽  
Linear Time ◽  
Singular Systems ◽  
Variable Structure Control ◽  
Variable Structure ◽  
Delay Systems ◽  
Structure Control ◽  
Linear Time Invariant ◽  
Time Invariant

This paper discusses the control problems of singular linear time-invariant delay systems with uncertainties. A new adaptive variable structure control strategy is given by Lyapunov stability theory. The invariance of sliding mode is proved in the circumstances of the external disturbance and parameter perturbation with matching conditions. Through memory and memoryless of the linear state feedback, the control strategy ensure that system reaches sliding mode in finite time and the closed-loop system is global asymptotic stable. Simulation results further show that the strategy is feasible and effective.

Variable Structure Control Based Wavelet Transforms for Linear Time-Invariant Distributed Parameter Systems

2012 ◽  
Vol 482-484 ◽  
pp. 1809-1815
Author(s):  
Gui Ge Gao ◽  
Xian Wen Zeng
Keyword(s):  
Control Problem ◽  
Linear Time ◽  
Variable Structure Control ◽  
Variable Structure ◽  
Distributed Parameter Systems ◽  
Distributed Parameter ◽  
Structure Control ◽  
Linear Time Invariant ◽  
Lumped Parameter ◽  
Time Invariant

The distributed parameter systems(DPS) are usually described by the partial differential equations(PDEs). Compared the variable structure control problem of DPS with that of the lumped parameter systems(LPS) , it is more complicated because the problem of variable structure control for DPS is often closely related to the theory of the differential operator or integral operator. Based on Haar wavelets transform, the operational matrixes and their characteristics, this paper attempts to propose a new approach for the variable structure control problem of a class linear time-invariant DPS by converting it into that of lumped parameter systems(LPS) and then makes use of the mature research methods of LPS to design the variable structure control problem so as to solve the variable structure control problem of DPS. The proposed method in this paper has the advantages of the simpler algorithm, less computation and better control effect. The simulation results also prove that it is an efficient algorithm for DPS.

scholarly journals Optimal Control Problem Investigation for Linear Time-Invariant Systems of Fractional Order with Lumped Parameters Described by Equations with Riemann-Liouville Derivative

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
V. A. Kubyshkin ◽  
S. S. Postnov
Keyword(s):  
Fractional Order ◽  
Caputo Derivative ◽  
Linear Time ◽  
Fractional Order Systems ◽  
Linear Time Invariant ◽  
Liouville Derivative ◽  
Lumped Parameters ◽  
Linear Time Invariant Systems ◽  
Time Invariant ◽  
Problem Setting

This paper studies two optimal control problems for linear time-invariant systems of fractional order with lumped parameters whose dynamics is described by equations which contain Riemann-Liouville derivative. The first problem is to find control with minimal norm and the second one is to find control with minimal control time at given restriction for control norm. The problem setting with nonlocal initial conditions is considered which differs from other known settings for integer-order systems and fractional-order systems described in terms of equations with Caputo derivative. Admissible controls are allowed to belong to the class of functions which arep-integrable on half segment. The basic investigation approach is the moment method. The correctness and solvability of moment problem are validated for considered problem setting for the system of arbitrary dimension. It is shown that corresponding conditions are analogous to those derived for systems which are described in terms of equations with Caputo derivative. For several particular cases of one- and two-dimensional systems the posed problems are solved explicitly. The dependencies of basic values from derivative index and control time are analyzed. The comparison is performed of obtained results with known results for analogous integer-order systems and fractional-order systems which are described by equations with Caputo derivative.

scholarly journals Extending the Root-Locus Method to Fractional-Order Systems

2008 ◽  
Vol 2008 ◽  
pp. 1-13 ◽  
Author(s):  
Farshad Merrikh-Bayat ◽  
Mahdi Afshar
Keyword(s):  
Fractional Order ◽  
Transfer Functions ◽  
Linear Time ◽  
Rational Functions ◽  
Fractional Order Systems ◽  
Root Locus ◽  
Linear Time Invariant ◽  
Locus Method ◽  
Linear Time Invariant Systems ◽  
Time Invariant

The well-known root-locus method is developed for special subset of linear time-invariant systems known as fractional-order systems. Transfer functions of these systems are rational functions with polynomials of rational powers of the Laplace variables. Such systems are defined on a Riemann surface because of their multivalued nature. A set of rules for plotting the root loci on the first Riemann sheet is presented. The important features of the classical root-locus method such as asymptotes, roots condition on the real axis, and breakaway points are extended to fractional case. It is also shown that the proposed method can assess the closed-loop stability of fractional-order systems in the presence of a varying gain in the loop. Three illustrative examples are presented to confirm the effectiveness of the proposed algorithm.

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