scholarly journals Robust Switched Control Design for Nonlinear Systems Using Fuzzy Models

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Wallysonn Alves de Souza ◽  
Marcelo Carvalho Minhoto Teixeira ◽  
Máira Peres Alves Santim ◽  
Rodrigo Cardim ◽  
Edvaldo Assunção
Keyword(s):  
Lyapunov Function ◽  
Design Method ◽  
Time Derivative ◽  
Control Design ◽  
Linear Matrix ◽  
Control Laws ◽  
Switching Law ◽  
Fuzzy Models ◽  
Switched Control ◽  
Nonlinear Plants

The paper proposes a new switched control design method for some classes of uncertain nonlinear plants described by Takagi-Sugeno fuzzy models. This method uses a quadratic Lyapunov function to design the feedback controller gains based on linear matrix inequalities (LMIs). The controller gain is chosen by a switching law that returns the smallest value of the time derivative of the Lyapunov function. The proposed methodology eliminates the need to find the membership function expressions to implement the control laws. The control designs of a ball-and-beam system and of a magnetic levitator illustrate the procedure.

scholarly journals On Switched Control Design of Linear Time-Invariant Systems with Polytopic Uncertainties

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Wallysonn A. de Souza ◽  
Marcelo C. M. Teixeira ◽  
Máira P. A. Santim ◽  
Rodrigo Cardim ◽  
Edvaldo Assunção
Keyword(s):  
Lyapunov Function ◽  
Linear Time ◽  
Time Derivative ◽  
Control Design ◽  
Feedback Gain ◽  
Linear Time Invariant ◽  
Switched Control ◽  
Polytopic Uncertainties ◽  
Linear Time Invariant Systems ◽  
Time Invariant

This paper proposes a new switched control design method for some classes of linear time-invariant systems with polytopic uncertainties. This method uses a quadratic Lyapunov function to design the feedback controller gains based on linear matrix inequalities (LMIs). The controller gain is chosen by a switching law that returns the smallest value of the time derivative of the Lyapunov function. The proposed methodology offers less conservative alternative than the well-known controller for uncertain systems with only one state feedback gain. The control design of a magnetic levitator illustrates the procedure.

scholarly journals Design of a Takagi-Sugeno Fuzzy Regulator for a Set of Operation Points

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Máira P. A. Santim ◽  
Marcelo C. M. Teixeira ◽  
Wallysonn A. de Souza ◽  
Rodrigo Cardim ◽  
Edvaldo Assunção
Keyword(s):  
Control System ◽  
Design Method ◽  
Linear Matrix ◽  
Control System Design ◽  
Matrix Inequalities ◽  
Fuzzy Models ◽  
Single Controller ◽  
Fuzzy Regulator ◽  
Nonlinear Plants ◽  
Takagi Sugeno

The paper proposes a new design method based on linear matrix inequalities (LMIs) for tracking constant signals (regulation) considering nonlinear plants described by the Takagi-Sugeno fuzzy models. The procedure consists in designing a single controller that stabilizes the system at operation points belonging to a certain range or region, without the need of remaking the design of the controller gains at each new chosen equilibrium point. The control system design of a magnetic levitator illustrates the proposed methodology.

Iterative Learning Control for Hybrid Systems

2020 ◽  
Author(s):  
Kirti D. Mishra ◽  
K. Srinivasan
Keyword(s):  
Hybrid Systems ◽  
Iterative Learning Control ◽  
Design Method ◽  
Tracking Error ◽  
Control Design ◽  
Learning Control ◽  
Iterative Learning ◽  
Linear Matrix ◽  
Triangular Structure ◽  
Form Representation

Abstract Iterative learning control (ILC) has been growing in applicability, along with growth in theory for classes of linear and nonlinear systems, and this study extends the theory of ILC to hybrid systems. A lifted form representation of hybrid systems with input-output dependent switching rules is developed, and the proposed lifted form representation is modeled as a switched system with arbitrary/unconstrained switching rules in the trial domain for control design. The causality of hybrid systems in the time domain results in the (lower) triangular structure of switched systems in the trial domain, the triangular structure enabling systematic and efficient control design. A unique aspect of the control design method developed for ILC of hybrid systems in this study is that a solution to the required set of linear matrix inequalities (LMIs) is guaranteed to exist under mild assumptions, which is in contrast to many other studies proposing LMI based solutions in controls literature. The proposed method is validated numerically for a motion control application, and robust and monotonic convergence of the tracking error to zero is demonstrated.

scholarly journals RobustH∞Fuzzy Control for Nonlinear Discrete-Time Stochastic Systems with Markovian Jump and Parametric Uncertainties

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Huiying Sun ◽  
Long Yan
Keyword(s):  
Fuzzy Control ◽  
Discrete Time ◽  
Stochastic Systems ◽  
Design Method ◽  
Fuzzy Model ◽  
Control Design ◽  
Linear Matrix ◽  
Parametric Uncertainties ◽  
Markovian Jump ◽  
Parameter Uncertainties

The paper mainly investigates theH∞fuzzy control problem for a class of nonlinear discrete-time stochastic systems with Markovian jump and parametric uncertainties. The class of systems is modeled by a state space Takagi-Sugeno (T-S) fuzzy model that has linear nominal parts and norm-bounded parameter uncertainties in the state and output equations. AnH∞control design method is developed by using the Lyapunov function. The decoupling technique makes the Lyapunov matrices and the system matrices separated, which makes the control design feasible. Then, some strict linear matrix inequalities are derived on robustH∞norm conditions in which both robust stability andH∞performance are required to be achieved. Finally, a computer-simulated truck-trailer example is given to verify the feasibility and effectiveness of the proposed design method.

scholarly journals RobustH∞Control for a Class of Uncertain Switched Fuzzy Time-Delay Systems Based on T-S Models

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Yang Cui ◽  
Kaiqing Liu ◽  
Yang Zhao ◽  
Xue Wang
Keyword(s):  
Time Delay ◽  
Closed Loop ◽  
Design Method ◽  
Fuzzy Model ◽  
Delay Systems ◽  
Linear Matrix ◽  
Stable Theory ◽  
Time Delay Systems ◽  
Switching Law ◽  
Continuous State

The problem of robustH∞control for a class of uncertain switched fuzzy time-delay systems is discussed for system described by T-S fuzzy model with Lyapunov stable theory and linear matrix inequality approach. A sufficient condition in terms of the LMI is derived such that the stability of the closed-loop systems is guaranteed. The continuous state feedback controller is built to ensure the asymptotically stable closed-loop system for all allowable uncertainties, with the switching law designed to implement the global asymptotic stability of uncertain switched fuzzy time-delay systems. In this model, each and every subsystem of the switched systems is an uncertain fuzzy one to which the parallel distributed compensation (PDC) controller of each sub fuzzy system system is proposed with its main condition given in a more solvable form of convex combinations. Such a switched control system is highly robust to varying parameters. A simulation shows the feasibility and effectiveness of the design method.

Robust Control of Switched Linear Systems via Min of Quadratics

2013 ◽  
Author(s):  
Chengzhi Yuan ◽  
Fen Wu
Keyword(s):  
Lyapunov Function ◽  
Linear Systems ◽  
Output Feedback Control ◽  
Control Design ◽  
Quadratic Functions ◽  
Linear Matrix ◽  
Switched Linear Systems ◽  
Synthesis Conditions ◽  
Arbitrary Switching ◽  
Special Cases

In this paper, we will investigate the robust switching control problem for switched linear systems by using a class of composite quadratic functions, the min (of quadratics) function, to improve performance and enhance control design flexibility. The robustness is reflected in two prospectives including the ℋ ∞ performance and arbitrary switching of subsystems. A hysteresis min-switching strategy is employed to orchestrate the switching among a collection of controllers. The synthesis conditions for both state feedback and output feedback control problems are derived in terms of a set of linear matrix inequalities (LMIs) with linear search over scalar variables. The proposed min function based approach unifies the existing single Lyapunov function based method and multiple Lyapunov function based method in a general framework, and the derived LMI conditions cover the existing LMI conditions as special cases. Numerical studies are included to demonstrate the advantages of the proposed control design approach.

scholarly journals Robust Additive Manufacturing Performance through a Control Oriented Digital Twin

Metals ◽  
2021 ◽  
Vol 11 (5) ◽  
pp. 708
Author(s):  
Panagiotis Stavropoulos ◽  
Alexios Papacharalampopoulos ◽  
Christos K. Michail ◽  
George Chryssolouris
Keyword(s):  
Additive Manufacturing ◽  
Process Control ◽  
Design Method ◽  
Control Design ◽  
Open Loop ◽  
Linear Matrix ◽  
Loop Model ◽  
Digital Twin ◽  
Manufacturing Process Control ◽  
Robust Control Design

The additive manufacturing process control utilizing digital twins is an emerging issue. However, robustness in process performance is still an open aspect, due to uncertainties, e.g., in material properties. To this end, in this work, a digital twin offering uncertainty management and robust process control is designed and implemented. As a process control design method, the Linear Matrix Inequalities are adopted. Within specific uncertainty limits, the performance of the process is proven to be acceptably constant, thus achieving robust additive manufacturing. Variations of the control law are also investigated, in order for the applicability of the control to be demonstrated in different machine architectures. The comparison of proposed controllers is done against a fine-tuned conventional proportional–integral–derivative (PID) and the initial open-loop model for metals manufacturing. As expected, the robust control design achieved a 68% faster response in the settling time metric, while a well-calibrated PID only achieved 38% compared to the initial model.

scholarly journals Fuzzy Static Output Control of T-S Fuzzy Stochastic Systems via Line Integral Lyapunov Function

Processes ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 697
Author(s):  
Cheung-Chieh Ku ◽  
Yun-Chen Yeh ◽  
Yann-Hong Lin ◽  
Yu-Yen Hsieh
Keyword(s):  
Lyapunov Function ◽  
Stochastic Systems ◽  
Fuzzy Controller ◽  
Design Method ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Nonlinear Stochastic Systems ◽  
Line Integral ◽  
Output Control ◽  
Static Output

Considering some unmeasurable states, a fuzzy static output control problem of nonlinear stochastic systems is discussed in this paper. Based on a modelling approach, a Takagi–Sugeno (T–S) fuzzy system, constructed by a family of stochastic differential equations and membership functions, is applied to represent nonlinear stochastic systems. Parallel distributed compensation (PDC) technology is used to construct the static output controller. A line-integral Lyapunov function (LILF) is used to derive some sufficient conditions for guaranteeing the asymptotical stability in the mean square. From the LILF, a potential conservatism produced by the derivative of the membership function is eliminated to increase the relaxation of sufficient conditions. Furthermore, those conditions are transferred into linear matrix inequality (LMI) form via projection lemma. According to the convex optimization algorithm, the feasible solutions are directly obtained to establish the static output fuzzy controller. Finally, a numerical example is applied to demonstrate the effectiveness and usefulness of the proposed design method.

Numerical Approach to Nonlinear Control Design

1996 ◽  
Vol 118 (2) ◽  
pp. 332-337 ◽  
Author(s):  
Mile Ostojic
Keyword(s):  
Tracking Control ◽  
Recurrence Relations ◽  
Control Design ◽  
Numerical Approach ◽  
Control Algorithms ◽  
Control Laws ◽  
New Approach ◽  
Parameter Variations ◽  
Error Dynamics ◽  
Nonlinear Plants

The paper presents a new approach to designing tracking control of uncertain nonlinear plants. The approach is entirely based on numerical methods and corresponding recurrence relations. It results in recursive control laws that resolve plant nonlinearities and compensate all disturbances and parameter variations. Also, it enables a free shaping of the control error dynamics. Control algorithms based on the method of successive substitutions and the Newton’s method are studied in detail. Detailed description of an application and experimental evaluation is included.

Forwarding Control Design for Strict-Feedforward Systems

2019 ◽  
Vol 141 (8) ◽  
Author(s):  
K. D. Do
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Lyapunov Function ◽  
Control Design ◽  
Linear Partial Differential Equation ◽  
Asymptotically Stable ◽  
Bounded Control ◽  
Control Laws ◽  
Globally Asymptotically Stable ◽  
Control Designs

This paper presents a new recursive forwarding method to design control laws that globally asymptotically stabilize strict-feedforward systems, of which Jacobian linearization at the origin might not be stabilizable. At each step, a Lyapunov function is constructed based on a solution of a linear partial differential equation (PDE) or a system of globally asymptotically stable (GAS) ordinary differential equations (ODEs). Optimal and bounded control designs are also addressed. The flexibility of the proposed design is illustrated via five examples.

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