Robust Adaptive Nonlinear Controller for Robotic Systems: Linear Matrix Inequality Approach

2008 ◽  
Author(s):  
Itzhack Levy ◽  
Nadav Berman ◽  
Amit Ailon
Keyword(s):  
Linear Matrix Inequalities ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Nonlinear Controller ◽  
Closed Loop System ◽  
Storage Function ◽  
Linear Matrix Inequality Approach ◽  
Case Simulation ◽  
Robust Adaptive ◽  
Two Degree Of Freedom

In this paper the tracking problem of a robotic system with model uncertainty is considered via an application of the H∞ control theory for nonlinear systems. In particular, we develop a state feedback controller which yields a global exponential stability of the underlying system and provides the closed loop system with relatively low gains. The main ingredient which facilitates our development is the choice of a particular storage function (which serves as a Lyaponov function). This particular storage function leads to certain linear matrix inequalities, the solution of which yields the desired controller. Moreover, the resulting LMIs (Linear Matrix Inequalities) turn out to be of the same form of the LMIs achieved in the analogous linear case. Simulation results and implementation of the control algorithm in a two-degree of freedom robot illustrate the controller efficiency.

Observer-based sliding mode control for piezoelectric wing bending-torsion coupling flutter involving delayed output

2020 ◽  
pp. 107754632094912
Author(s):  
Da Li ◽  
Hui Yang ◽  
Na Qi ◽  
Jiaxin Yuan
Keyword(s):  
Time Delay ◽  
Sliding Mode Control ◽  
Linear Matrix Inequalities ◽  
Closed Loop ◽  
Sliding Mode ◽  
Loop System ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Closed Loop System ◽  
Piezoelectric Patch

An observer-based sliding mode control scheme is proposed for suppressing bending-torsion coupling flutter motions of a wing aeroelastic system with delayed output by using the piezoelectric patch actuators. The wing structure is modeled as a thin-walled beam, and the aerodynamics on the wing are computed by the strip theory. For the implementation of the control algorithm, the piezoelectric patch is bonded on the top surface of the beam to act as the actuator. Ignoring the effect of piezoelectric actuators on structural dynamics, only considering the bending moments induced by piezoelectric effects, the corresponding dynamic motion equation is established by using the Lagrange method with the assumed mode method. The flutter speed and frequency of the closed-loop system with time delay are obtained by solving a polynomial eigenvalue problem. An observer-based controller that does not dependent on time delay is developed for suppressing the flutter, and the corresponding gain matrices are obtained by solving linear matrix inequalities. The sufficient condition for the asymptotic stability of the closed-loop system is derived in terms of linear matrix inequalities. The simulation results demonstrate that the proposed control strategy based on the piezoelectric actuator is effective in wing bending-torsion coupling flutter system with a delayed output.

Exponentially Dissipative Control for Singular Impulsive Dynamical Systems

2017 ◽  
Vol 139 (4) ◽  
Author(s):  
Li Yang ◽  
Xinzhi Liu ◽  
Zhigang Zhang
Keyword(s):  
Dynamical Systems ◽  
Linear Matrix Inequalities ◽  
State Feedback ◽  
Closed Loop ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Closed Loop System ◽  
Dissipative Control ◽  
Necessary And Sufficient

This paper studies the problem of exponentially dissipative control for singular impulsive dynamical systems. Some necessary and sufficient conditions for exponential dissipativity of such systems are established in terms of linear matrix inequalities (LMIs). A state feedback controller is designed to make the closed-loop system exponentially dissipative. A numerical example is given to illustrate the feasibility of the method.

scholarly journals Robust Adaptive Fault-Tolerant Tracking Control of Three-Phase Induction Motor

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Hossein Tohidi ◽  
Koksal Erenturk
Keyword(s):  
Induction Motor ◽  
Linear Matrix Inequalities ◽  
Tracking Control ◽  
Controller Design ◽  
Fault Tolerant ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Actuator Faults ◽  
Matrix Inequalities ◽  
Robust Adaptive

This paper deals with the problem of induction motor tracking control against actuator faults and external disturbances using the linear matrix inequalities (LMIs) method and the adaptive method. A direct adaptive fault-tolerant tracking controller design method is developed based on Lyapunov stability theory and a constructive algorithm based on linear matrix inequalities for online tuning of adaptive and state feedback gains to stabilize the closed-loop system in order to reduce the fault effect with disturbance attenuation. Simulation results reveal the merits of proposed robust adaptive fault-tolerant tracking control scheme on an induction motor subjected to actuator faults.

Robust Electric Power System Controllers Synthesized on the Basis of Linear Matrix Inequalities

2018 ◽  
Vol 10 (10) ◽  
pp. 4-19
Author(s):  
Magomed G. GADZHIYEV ◽  
◽  
Misrikhan Sh. MISRIKHANOV ◽  
Vladimir N. RYABCHENKO ◽  
◽  
...  
Keyword(s):  
Power System ◽  
Electric Power ◽  
Linear Matrix Inequalities ◽  
Electric Power System ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Power System Controllers

A new control approach for a class of linear switched systems with time-varying delay

2021 ◽  
pp. 014233122199272
Author(s):  
Abbas Zabihi Zonouz ◽  
Mohammad Ali Badamchizadeh ◽  
Amir Rikhtehgar Ghiasi
Keyword(s):  
Stability Analysis ◽  
Linear Matrix Inequalities ◽  
Linear Matrix ◽  
Switching Systems ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Time Varying Delay ◽  
Linear Switching Systems ◽  
The Stability ◽  
Varying Delay

In this paper, a new method for designing controller for linear switching systems with varying delay is presented concerning the Hurwitz-Convex combination. For stability analysis the Lyapunov-Krasovskii function is used. The stability analysis results are given based on the linear matrix inequalities (LMIs), and it is possible to obtain upper delay bound that guarantees the stability of system by solving the linear matrix inequalities. Compared with the other methods, the proposed controller can be used to get a less conservative criterion and ensures the stability of linear switching systems with time-varying delay in which delay has way larger upper bound in comparison with the delay bounds that are considered in other methods. Numerical examples are given to demonstrate the effectiveness of proposed method.

scholarly journals Contractors and Linear Matrix Inequalities

2015 ◽  
Vol 1 (3) ◽  
Author(s):  
Jeremy Nicola ◽  
Luc Jaulin
Keyword(s):  
Fixed Point ◽  
Large Class ◽  
Linear Matrix Inequalities ◽  
Interior Point ◽  
Interior Point Methods ◽  
Linear Constraints ◽  
Linear Matrix ◽  
Nonlinear Constraints ◽  
Matrix Inequalities ◽  
Convex Constraints

Linear matrix inequalities (LMIs) comprise a large class of convex constraints. Boxes, ellipsoids, and linear constraints can be represented by LMIs. The intersection of LMIs are also classified as LMIs. Interior-point methods are able to minimize or maximize any linear criterion of LMIs with complexity, which is polynomial regarding to the number of variables. As a consequence, as shown in this paper, it is possible to build optimal contractors for sets represented by LMIs. When solving a set of nonlinear constraints, one may extract from all constraints that are LMIs in order to build a single optimal LMI contractor. A combination of all contractors obtained for other non-LMI constraints can thus be performed up to the fixed point. The resulting propogation is shown to be more efficient than other conventional contractor-based approaches.

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