Input/Output Decoupling of Square Linear Systems by Dynamic Two‐Parameter Stabilizing Control

Galindo, R.

doi:10.1002/asjc.1285

Cited by 8 publications

(13 citation statements)

References 17 publications

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“…In what follows the controllable and observable subsystem is considered as a given nominal plant P(s), that is assumed to be square. A2 As in the works of Galindo (2016), Galindo and Conejo (2012) and Galindo (2009), the state dimension of P(s), denoted by n, must be even, and be double the input dimension of P(s), denoted by m. A3 The H 2 and H ∞ norms of the disturbances and uncertainties, respectively, are bounded. A4 As in the works of Galindo (2016), Galindo and Conejo (2012) and Galindo (2009), let the state space description of P(s) be,…”

Section: Problem Statementmentioning

confidence: 99%

Mixed sensitivity control: a non-iterative approach

Galindo

2020

Systems Science & Control Engineering

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Recent analytical solutions to Mixed Sensitivity Control (MSC) are developed and compared with standard MSC based on γ-iteration. The proposed MSC solution gives conditions for strong stability and overcomes the pole-zero cancellations between the plant and the controller of non-iterative solutions, keeping the low-computational effort advantage of non-iterative solutions. The proposed MSC is based on the minimization of the most common closed-loop sensitivity functions in lowfrequencies and the free-parameters of the stabilizing-controllers solve an algebraic equation of restriction that assigns the same value to the infinity-norms of the sensitivity functions at low and high-frequencies, guaranteeing robust stability and robust performance. It is assumed that the plant state dimension is double the plant input dimension and that the linear time-invariant nominal plant has a stabilizable and detectable realization and is strongly stabilizable. This MSC problem is solved in a one-parameter observer-controller configuration and reference tracking-control of positions is realized on a two-degrees of freedom feedback-configuration. An approximated optimal value of the location of the closed-loop poles is proposed based on Glover and McFarlane's optimal stability margin [(1989)] which in turn is based on Nehari's Theorem. Simulations of a mechanical system illustrate the results.

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Section: Problem Statementmentioning

confidence: 99%

Mixed sensitivity control: a non-iterative approach

Galindo

2020

Systems Science & Control Engineering

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“…min i y and max i y for 1,2,..., ip  may be specified as for example, 2%  of the appropriate set point. In case that such constraint is not able to satisfy it is naturally softened by (10) and (11) taken into consideration in (9). There are several advantages of this method.…”

Section: Adjusting Output Constraintsmentioning

confidence: 99%

“…Parameterization of block decoupling controllers along with solving an 2 H optimal problem is proposed in [9]. Reference [10] considers MIMO as proper, lumped, and linear time invariant systems and gives analytical expressions of the Input/Output (I/O) decoupling problem by the use of two-parameter stabilizing control. In [11], a robust decoupling controller for uncertain MIMO systems has been proposed, where uncertainty of model parameters and the desired performance is taken into account, and the min-max non-convex optimization problem is used in the controller design.…”

Section: Introductionmentioning

confidence: 99%

Effective Use of MPC for Dynamic Decoupling of MIMO Systems

Dworak¹,

Goyal²,

Aggarwal³

et al. 2019

ElAEE

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The article analyses possible ways of using predictive controllers to perform control tasks and dynamic decoupling for dynamic systems with Multiple Inputs and Multiple Outputs (MIMO). The results of experiments on the selected reference plant are presented, showing the effectiveness of individual decoupling methods. These are also compared to those obtained in typical control systems with Proportional-Integral-Derivative (PID) controllers. Recommendations are made on how to tune model predictive controllers (MPC) for their effective use for MIMO plants.

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“…Step 3: Compute the vectors v l ij,k , w l ij , h l ij , i = 1, · · · , p; j = 1, · · · , q i ; l = 1, · · · , p ij by (13). Then the matrices J f , V f , W f and H f are constructed by (8), (9), (11) and (12), respectively.…”

Section: Peizhao Yu and Guoshan Zhangmentioning

confidence: 99%

“…The study of polynomial matrix systems has been greatly developed with the development of polynomial matrix theory [14,29]. By using polynomial matrix theory, most fundamental problems for control systems can be solved, including impulsive modes detection [15], eigenstructure assignment, impulse elimination, stabilization and decoupling [19,25,13,5].…”

mentioning

confidence: 99%

Eigenstructure assignment for polynomial matrix systems ensuring normalization and impulse elimination

Yu¹,

Zhang²

2019

Mathematical Foundations of Computing

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In this paper, eigenstructure assignment problems for polynomial matrix systems ensuring normalization and impulse elimination are considered. By using linearization method, a polynomial matrix system is transformed into a descriptor linear system without changing the eigenstructure of original system. By analyzing the characteristic polynomial of the desired system, the normalizable condition under feedback is given, and moreover, the parametric expressions of controller gains for eigenstructure ensuring normalization are derived by singular value decomposition. Impulse elimination in polynomial matrix systems is investigated when the normalizable condition is not satisfied. The parametric expressions of controller gains for impulse elimination ensuring finite eigenstructure assignment are formulated. The solving algorithms of corresponding controller gains for eigenstructure assignment ensuring normalization and impulse elimination are also presented. Numerical examples show the effectiveness of proposed method.2010 Mathematics Subject Classification. Primary: 15A18, 93B18; Secondary: 93C05.

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Input/Output Decoupling of Square Linear Systems by Dynamic Two‐Parameter Stabilizing Control

Cited by 8 publications

References 17 publications

Mixed sensitivity control: a non-iterative approach

Mixed sensitivity control: a non-iterative approach

Effective Use of MPC for Dynamic Decoupling of MIMO Systems

Eigenstructure assignment for polynomial matrix systems ensuring normalization and impulse elimination

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