scholarly journals Feedback control of linear systems with optimal sensor and actuator selection

2020 ◽  
pp. 107754632093983
Author(s):  
Taranjitsingh Singh ◽  
Massimo De Mauri ◽  
Wilm Decré ◽  
Jan Swevers ◽  
Goele Pipeleers
Keyword(s):  
Feedback Control ◽  
Semidefinite Programming ◽  
Optimization Problem ◽  
Linear Time ◽  
Linear Parameter ◽  
Linear Parameter Varying ◽  
Linear Time Invariant ◽  
Combined Design ◽  
Parameter Varying ◽  
Time Invariant

This article demonstrates a combined [Formula: see text] feedback control design for linear time-invariant and linear parameter-varying systems and optimal sensors and actuator selection. The combined design problem is systematically constructed as a mixed Boolean semidefinite programming optimization problem. We impose Big-M reformulations to the non-deterministic polynomial-time-hard coupled problem to be solved as a convex optimization problem using the branch and bound algorithm. The combined design of dynamic output feedback control along with optimal actuator selection for a linear time-invariant seismic rejection controller design serves as an application for validation by simulation. In addition, active vibration control of a smart composite plate along with optimal sensor and actuator selection validates the developed approach for linear parameter-varying controller synthesis. On comparing this approach with exhaustive search, it is observed that mixed Boolean semidefinite programming approaches have faster computation time, and comparing with the iterative reweighted ℓ1 norm algorithm and mixed Boolean semidefinite programming using outer approximations, mixed Boolean semidefinite programming yields a global solution.

Determination of Different Polytopic Models of the Prototypical Aeroelastic Wing Section by TP Model Transformation

2006 ◽  
Vol 10 (4) ◽  
pp. 486-493 ◽  
Author(s):  
Péter Baranyi ◽  
◽  
Zoltán Petres ◽  
Péter L. Várkonyi ◽  
Péter Korondi ◽  
...  
Keyword(s):  
Model Transformation ◽  
Linear Time ◽  
Convex Combination ◽  
Linear Matrix ◽  
Linear Parameter Varying ◽  
Linear Time Invariant ◽  
Wing Section ◽  
Parameter Varying ◽  
Time Invariant

The Tensor Product (TP) model transformation is a recently proposed technique for transforming given Linear Parameter Varying (LPV) models into polytopic model form, namely, to parameter varying convex combination of Linear Time Invariant (LTI) models. The main advantage of the TP model transformation is that the Linear Matrix Inequality (LMI) based control design frameworks can immediately be applied to the resulting polytopic models to yield controllers with tractable and guaranteed performance. The effectiveness of the LMI design depends on the type of the convex combination in the polytopic model. Therefore, the main objective of this paper is to study how the TP model transformation is capable of determining different types of convex hulls of the LTI models. The study is conducted trough the example of the prototypical aeroelastic wing section.

Identifiability Issues for Parameter-Varying and Multidimensional Linear Systems

1997 ◽  
Author(s):  
Lawton H. Lee ◽  
Kameshwar Poolla
Keyword(s):  
Linear Time ◽  
Model Structure ◽  
Constant Matrix ◽  
Linear Parameter Varying ◽  
Linear Time Invariant ◽  
Estimation Algorithms ◽  
Finite Dimensional ◽  
Parameter Varying ◽  
Value Decomposition ◽  
Time Invariant

Abstract This paper considers the identifiability of state space models for a system that is expressed as a linear fractional transformation (LFT): a constant matrix (containing identified parameters) in feedback with a finite-dimensional, block-diagonal (“structured”) linear operator. This model structure can represent linear time-invariant, linear parameter-varying, uncertain, and multidimensional systems. Families of input-output equivalent realizations are characterized as manifolds in the parameter space whose tangent spaces — and orthogonal complements — can be obtained via singular value decomposition. As illustrated by a numerical example, restricting iterative parameter estimation algorithms (e.g., maximum-likelihood with nonlinear programming) to the orthogonal directions offers significant computational advantages.

Fixed-Order Linear Parameter-Varying Feedback Control of a Lab-Scale Overhead Crane

2016 ◽  
Vol 24 (5) ◽  
pp. 1899-1907 ◽  
Author(s):  
Gijs Hilhorst ◽  
Goele Pipeleers ◽  
Wim Michiels ◽  
Ricardo C. L. F. Oliveira ◽  
Pedro L. D. Peres ◽  
...  
Keyword(s):  
Feedback Control ◽  
Overhead Crane ◽  
Linear Parameter ◽  
Linear Parameter Varying ◽  
Order Linear ◽  
Fixed Order ◽  
Parameter Varying

scholarly journals Robust Filtering for Discrete-Time Linear Parameter-Varying Descriptor Systems

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1871 ◽  
Author(s):  
Carlos Rodriguez ◽  
Karina A. Barbosa ◽  
Daniel Coutinho
Keyword(s):  
Discrete Time ◽  
Filter Design ◽  
Linear Time ◽  
Estimation Error ◽  
Sufficient Conditions ◽  
Descriptor Systems ◽  
Linear Parameter ◽  
Linear Parameter Varying ◽  
Parameter Varying ◽  
Time Linear

This paper deals with robust state estimation for discrete-time, linear parameter varying (LPV) descriptor systems. It is assumed that all the system state-space matrices are affine functions of the uncertain parameters and both the parameters and their variations are bounded functions of time with known minimum and maximum values. First, necessary and sufficient conditions are proposed for admissibility and bounded realness for discrete linear time-varying (DLTV) descriptor systems. Next, two convex optimisation based methods are proposed for designing admissible stationary linear descriptor filters for LPV descriptor systems which ensure a prescribed upper bound on the ℓ2-induced gain from the noise signal to the estimation error regardless of model uncertainties. The proposed filter design results were based on parameter-dependent generalised Lyapunov functions, and full-order, augmented-order and reduced-order filters were considered. Numerical examples are presented to show the effectiveness of the proposed filtering scheme. In particular, the proposed approach was used to estimate the state variables of a controlled horizontal 2-DOF robotic manipulator based on noisy measurements.

scholarly journals Output feedback controller design for polynomial linear parameter varying system via parameter-dependent Lyapunov functions

2017 ◽  
Vol 9 (2) ◽  
pp. 168781401769032 ◽  
Author(s):  
Xiaobao Han ◽  
Zhenbao Liu ◽  
Huacong Li ◽  
Xianwei Liu
Keyword(s):  
Output Feedback ◽  
Optimization Problem ◽  
Controller Design ◽  
Feedback Controller ◽  
Linear Matrix ◽  
Linear Parameter ◽  
Linear Parameter Varying ◽  
Output Feedback Controller ◽  
Parameter Varying ◽  
Parameter Dependent

This article presents a new output feedback controller design method for polynomial linear parameter varying model with bounded parameter variation rate. Based on parameter-dependent Lyapunov function, the polynomial linear parameter varying system controller design is formulated into an optimization problem constrained by parameterized linear matrix inequalities. To solve this problem, first, this optimization problem is equivalently transformed into a new form with elimination of coupling relationship between parameter-dependent Lyapunov function, controller, and object coefficient matrices. Then, the control solving problem was reduced to a normal convex optimization problem with linear matrix inequalities constraint on a newly constructed convex polyhedron. Moreover, a parameter scheduling output feedback controller was achieved on the operating condition, which satisfies robust performance and dynamic performances. Finally, the feasibility and validity of the controller analysis and synthesis method are verified by the numerical simulation.

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