Parameter-Dependent Feedback Compensator Design for a Time-Fractional Reaction-Diffusion Equation

2021 ◽  
Author(s):  
Jun-Wei Wang ◽  
Hua-Cheng Zhou
Keyword(s):  
Linear Time ◽  
Design Method ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Linear Matrix ◽  
Parametric Form ◽  
Coupled Equations ◽  
Reaction Coefficient ◽  
Standard Linear ◽  
Parameter Dependent

Abstract This paper presents a parameter-dependent design of feedback compensator with space-varying gains for Mittag-Leffler stabilization of linear time fractional parabolic MIMO partial differential equations subject to space-varying diffusion and reaction coefficients. In the proposed design method, under a boundedness assumption, the reaction coefficient is written in a parametric form. By using the parametric form for the reaction coefficient and multiple non-collocated observation outputs, an observer-based state feedback compensator with space-varying gains is then constructed such that the resulting closed-loop coupled equations are Mittag-Leffler stable. By applying the Lyapunov technique with Caputo fractional derivative and variants of Poincaré–Wirtinger’s inequality, a sufficient condition for the existence of such feedback compensator is presented in terms of standard linear matrix inequalities. Finally, simulation results are presented to support the proposed design method.

Multi-Model Adaptive Regulation for Aircraft Dynamics With Different Zero Structures

2014 ◽  
Author(s):  
Eric D. Peterson ◽  
Harry G. Kwatny
Keyword(s):  
State Feedback ◽  
Design Method ◽  
Linear Matrix ◽  
Model Design ◽  
Multiple Model ◽  
Matrix Inequalities ◽  
Adaptive Regulation ◽  
Aircraft Dynamics ◽  
Adaptive Regulator ◽  
Parameter Dependent

An adaptive regulator is designed for parameter dependent families of systems subject to changes in the zero structure. Since continuous adaptive regulation is limited by relative degree and right half plane zeros, a multiple model adaptive regulator is implemented. The two multiple model design subproblems, covering and switching, are addressed with LQR state feedback and Lyapunov function switch logic respectively. These two subproblems are combined into a set of Linear Matrix Inequalities (LMI) and concurrently solved. The multiple model design method is applied to longitudinal aircraft dynamics.

Semi-Active Vibration Isolation Control for Multi-Degree-of-Freedom Structures

2002 ◽  
Author(s):  
Hidekazu Nishimura ◽  
Yasuhiko Okumura ◽  
Seiji Shimodaira
Keyword(s):  
Vibration Isolation ◽  
Linear Time ◽  
Design Method ◽  
Linear Matrix ◽  
Orifice Area ◽  
Convex Interpolation ◽  
Active Vibration ◽  
Active Damper ◽  
Gain Scheduled ◽  
Active Vibration Isolation

In this paper, we propose a design method of a controller for semi-active vibration isolation. We introduce a mechanism of a semi-active damper, which can change the damping in the ratio of the orifice area, in order to obtain the parameter-varying system model. Consideration of the semi-active damper mechanism is appropriate for the design of the gain-scheduled (GS) controller based on linear matrix inequalities (LMIs). The GS controller consists of four-vertex linear time-invaxiant controllers are obtained by the convex interpolation of these controllers. The designed controller switches at zero velocity of the damper and varies according to both the orifice area and the relative velocity of the isolation layer. By carrying out simulations, it is shown that our proposed method is effective for the suppression of seismic response.

scholarly journals ℋ∞Control for Two-Dimensional Markovian Jump Systems with State-Delays and Defective Mode Information

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Yanling Wei ◽  
Mao Wang ◽  
Hamid Reza Karimi ◽  
Jianbin Qiu
Keyword(s):  
State Feedback ◽  
Transition Probabilities ◽  
Linear Time ◽  
Design Method ◽  
Transition Probability ◽  
State Feedback Control ◽  
Delay Systems ◽  
Linear Matrix ◽  
Two Dimensional ◽  
Markovian Jump

This paper investigates the problem ofℋ∞state-feedback control for a class of two-dimensional (2D) discrete-time Markovian jump linear time-delay systems with defective mode information. The mathematical model of the 2D system is established based on the well-known Fornasini-Marchesini local state-space model, and the defective mode information simultaneously consists of the exactly known, partially unknown, and uncertain transition probabilities. By carefully analyzing the features of the transition probability matrices, together with the convexification of uncertain domains, a newℋ∞performance analysis criterion for the underlying system is firstly derived, and then theℋ∞state-feedback controller synthesis is developed via a linearisation technique. It is shown that the controller gains can be constructed by solving a set of linear matrix inequalities. Finally, an illustrative example is provided to verify the effectiveness of the proposed design method.

A QFT Framework for Antiwindup Control Systems Design

2010 ◽  
Vol 132 (2) ◽  
Author(s):  
J. C. Moreno ◽  
A. Baños ◽  
M. Berenguel
Keyword(s):  
Control Systems ◽  
Robust Stability ◽  
Stability Problem ◽  
Degrees Of Freedom ◽  
Actuator Saturation ◽  
Linear Time ◽  
Design Method ◽  
Systems Design ◽  
Linear Matrix ◽  
Single Input Single Output

The paper is devoted to the robust stability problem of linear time invariant feedback control systems with actuator saturation, especially in those cases with potentially large parametric uncertainty. The main motivation of the work has been twofold: First, most of the existing robust antiwindup techniques use a conservative plant uncertainty description, and second, previous quantitative feedback theory (QFT) results for control systems with actuator saturation are not suitable to achieve robust stability specifications when the control system is saturated. Traditionally, in the literature, this type of problems has been solved in terms of linear matrix inequalities (LMIs), using less structured uncertainty descriptions as given by the QFT templates. The problem is formulated for single input single output systems in an input-output (I/O) stability sense, and is approached by using a generic three degrees of freedom control structure. In this work, a QFT-based design method is proposed in order to solve the robust stability problem of antiwindup design methods. The main limitation is that the plant has poles in the closed left half plane, and at most, has one integrator. The work investigates robust adaptations of the Zames–Falb stability multipliers result, and it may be generalized to any compensation scheme that admits a decomposition as a feedback interconnection of linear and nonlinear blocks (Lur’e type system), being antiwindup systems as a particular case. In addition, an example will be shown, making explicit the advantages of the proposed method in relation to previous approaches.

Parameter-Dependent ℋ∞ Filtering for Linear Time-Varying Systems

2012 ◽  
Vol 135 (2) ◽  
Author(s):  
Hui Zhang ◽  
Yang Shi
Keyword(s):  
Filter Design ◽  
Linear Time ◽  
Linear Matrix ◽  
Simulation Studies ◽  
Continuous Time Systems ◽  
Parameter Variations ◽  
Time Varying Systems ◽  
Norm Bound ◽  
Parameter Dependent ◽  
Time Systems

In this paper, we investigate the filter design problem for linear continuous-time systems with parameter variations in system matrices. The parameter variations are assumed to belong to a polytope with finite and known vertices. The designed filter parameters and the constructed Lyapunov function are both dependent on the online measured variations. A new sufficient condition for the existence of parameter-dependent filters is established and it can guarantee that the filtering error dynamic system is asymptotically stable and can satisfy the prescribed ℋ∞ norm bound. Then, the design of the filter is proposed by solving a set of linear matrix inequalities (LMIs). Simulation studies and comparison examples are provided to illustrate the effectiveness of the proposed method.

Exponential passive filter design for switched neural networks with time-delay and reaction-diffusion terms

2021 ◽  
pp. 2150434
Author(s):  
Weipeng Tai ◽  
Dong Xu ◽  
Tong Guo ◽  
Jianping Zhou
Keyword(s):  
Neural Networks ◽  
Time Delay ◽  
Filter Design ◽  
Design Method ◽  
Reaction Diffusion ◽  
Linear Matrix ◽  
External Interference ◽  
Passive Filter ◽  
Switched Neural Networks ◽  
Complex Valued

This paper investigates the problem of exponential passive filter design for switched neural networks with time-delay and reaction-diffusion terms. With the aid of a suitable Lyapunov–Krasovskii functional and some inequalities, a linear matrix inequality-based design method is developed that not only makes the filtering error system exponentially stable but also forces it to be passive from external interference to output error. Then, the filter design is extended to the complex-valued case via separating the system into real-valued and complex-valued parts. Finally, a numerical example is utilized to illustrate the effectiveness of the filter design methods for the real-valued and complex-valued cases, respectively.

scholarly journals Design of LPV-Based Sliding Mode Controller with Finite Time Convergence for a Morphing Aircraft

2017 ◽  
Vol 2017 ◽  
pp. 1-20 ◽  
Author(s):  
Nuan Wen ◽  
Zhenghua Liu ◽  
Yang Sun ◽  
Lingpu Zhu
Keyword(s):  
Finite Time ◽  
Sliding Mode ◽  
Linear Time ◽  
Stability Control ◽  
Linear Matrix ◽  
Parameter Uncertainties ◽  
Morphing Aircraft ◽  
Finite Time Convergence ◽  
Lpv System ◽  
Parameter Dependent

This paper proposes a finite time convergence sliding mode control (FSMC) strategy based on linear parameter-varying (LPV) methodology for the stability control of a morphing aircraft subject to parameter uncertainties and external disturbances. Based on the Kane method, a longitudinal dynamic model of the morphing aircraft is built. Furthermore, the linearized LPV model of the aircraft in the wing transition process is obtained, whose scheduling parameters are wing sweep angle and wingspan. The FSMC scheme is developed into LPV systems by applying the previous results for linear time-invariant (LTI) systems. The sufficient condition in form of linear matrix inequality (LMI) constraints is derived for the existence of a reduced-order sliding mode, in which the dynamics can be ensured to keep robust stability and L2 gain performance. The tensor-product (TP) model transformation approach can be directly applied to solve infinite LMIs belonging to the polynomial parameter-dependent LPV system. Then, by the parameter-dependent Lyapunov function stability analysis, the synthesized FSMC is proved to drive the LPV system trajectories toward the predefined switching surface with a finite time arrival. Comparative simulation results in the nonlinear model demonstrate the robustness and effectiveness of this approach.

Design of H∞ Loop-Shaping Controller for LTI System With Input Saturation: Polytopic Gain Scheduled Approach

2010 ◽  
Vol 133 (1) ◽  
Author(s):  
S. Patra ◽  
S. Sen ◽  
G. Ray
Keyword(s):  
Linear Time ◽  
Design Method ◽  
Input Saturation ◽  
Robust Stabilization ◽  
Linear Matrix ◽  
Linear Time Invariant ◽  
Loop Shaping ◽  
Lti System ◽  
Interpolation Procedure ◽  
The Stability

This paper demonstrates the design of H∞ loop-shaping controller for a linear time invariant (LTI) system with input saturation constraint. The design problem has been formulated in the four-block H∞ synthesis framework, which is equivalent to normalized coprime factor robust stabilization problem. The shaped plant is represented as a polytopic linear parameter varying (LPV) system while saturation nonlinearity is considered. For a polytopic model, the LTI H∞ loop-shaping controllers have been designed at each vertex of the polytope using linear matrix inequalities, and subsequently controllers are scheduled by adopting a certain interpolation procedure. The proposed controller ensures the stability and robust L2-performance of the closed-loop system due to vertex property of the polytopic LPV shaped plant. The effectiveness of the design method has been illustrated through a numerical example.

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