Pole Placement and State Observer for Linear Time-Varying Discrete Multi-Variable Systems

The article deals with the problem of state observer design for a linear time-varying plant. To solve this problem, a number of realistic assumptions are considered, assuming that the model parameters are polynomial functions of time with unknown coefficients. The problem of observer design is solved in the class of identification approaches, which provide transformation of the original mathematical model of the plant to a static linear regression equation, in which, instead of unknown constant parameters, there are state variables of generators that model non-stationary parameters. To recover the unknown functions of the regression model, we use the recently well-established method of dynamic regressor extension and mixing (DREM), which allows to obtain monotone estimates, as well as to accelerate the convergence of estimates to the true values. Despite the fact that the article deals with the problem of state observer design, it is worth noting the possibility of using the proposed approach to solve an independent and actual estimation problem of unknown time-varying parameters.

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State Observer for Linear Time-Varying Discrete Non-Lexicographically-Fixed Systems

Visualization, Imaging and Image Processing / 783: Modelling and Simulation / 784: Wireless Communications ◽

10.2316/p.2012.783-050 ◽

2012 ◽

Cited By ~ 1

Author(s):

Yasuhiko Mutoh ◽

Tomohiro Hara

Keyword(s):

Linear Time ◽

State Observer ◽

Time Varying

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A Control Method for Non-Linear Time-Varying System Using Mixed H2/H∞ Control: Position and Force Control of 2-Link Manipulator

Volume 6A: 18th Biennial Conference on Mechanical Vibration and Noise ◽

10.1115/detc2001/vib-21326 ◽

2001 ◽

Author(s):

Itsuro Kajiwara ◽

Katsuhiro Yambe ◽

Chiaki Nishidome

Keyword(s):

Control Method ◽

Linear Time ◽

Gain Scheduling ◽

Operating Conditions ◽

Pole Placement ◽

Time Varying ◽

Linear Time Invariant ◽

Highly Nonlinear ◽

Switching Controller ◽

Time Invariant

Abstract Dynamics of multi-link manipulators are highly nonlinear and depend on the time varying configuration. This paper presents a method of gain scheduling which consists in designing a linear time invariant (LTI) controller for each operating point and in switching controller when the operating conditions change. Each LTI controller is designed based on LMI approach in which an optimization problem is defined as a mixed H2/H∞ control problem with pole placement. The performance of the force and the position controls is defined by the H2 norm, and the robust stability according to gain scheduling is evaluated with the H∞ norm and the pole placement of the closed-loop system. The effectiveness and the practicability of the proposed method are verified by both simulations and experiments with 2-link manipulator system.

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