An LMI-Based Hedging Approach to Model Reference Adaptive Control With Actuator Dynamics

2015 ◽  
Author(s):  
Benjamin C. Gruenwald ◽  
Daniel Wagner ◽  
Tansel Yucelen ◽  
Jonathan A. Muse
Keyword(s):  
Dynamical System ◽  
Adaptive Control ◽  
Linear Matrix Inequalities ◽  
Model Reference Adaptive Control ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Model Reference ◽  
Actuator Dynamics ◽  
The Stability ◽  
Model Reference Adaptive

Although model reference adaptive control has been used in numerous applications to achieve system performance without excessive reliance on dynamical system models, the presence of actuator dynamics can seriously limit the stability and the achievable performance of adaptive controllers. In this paper, an linear matrix inequalities-based hedging approach is developed and evaluated for model reference adaptive control of uncertain dynamical systems in the presence of actuator dynamics. The hedging method modifies the ideal reference model dynamics in order to allow correct adaptation that does not get affected due to the presence of actuator dynamics. Specifically, we first generalize the hedging approach to cover cases in which actuator output and is known and unknown. We next show the stability of the closed-loop dynamical system using tools from Lyapunov stability and linear matrix inequalities. Finally, an illustrative numerical example is provided to demonstrate the efficacy of the proposed linear matrix-inequalities-based hedging approach to model reference adaptive control.

A Model Reference Adaptive Control Framework for Uncertain Dynamical Systems With High-Order Actuator Dynamics and Unknown Actuator Outputs

2017 ◽  
Author(s):  
Benjamin C. Gruenwald ◽  
K. Merve Dogan ◽  
Tansel Yucelen ◽  
Jonathan A. Muse
Keyword(s):  
Adaptive Control ◽  
Linear Matrix Inequalities ◽  
High Order ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Model Reference ◽  
Adaptive Controllers ◽  
Actuator Dynamics ◽  
The Stability ◽  
Model Reference Adaptive

As it is well-known, the stability properties of model reference adaptive controllers can be seriously affected by the presence of actuator dynamics. To this end, the authors recently proposed linear matrix inequalities-based hedging approaches to compute the stability limits of model reference adaptive controllers in the presence of a) scalar actuator dynamics with known outputs, b) scalar actuator dynamics with unknown outputs, and c) high-order (linear time-invariant) actuator dynamics with known outputs. The common denominator of these approaches is that they have the capability to rigorously characterize the fundamental stability interplay between the system uncertainties and the necessary bandwidth of the actuator dynamics. Building on these results, the purpose of this paper is to extend the recent work by the authors to the general case, where there exist high-order actuator dynamics with unknown outputs in the closed-loop model reference adaptive control systems. For this purpose, we propose an observer architecture to estimate the unknown output of the actuator dynamics and use the estimated actuator output to design the linear matrix inequalities-based hedging framework. Remarkably, with the proposed observer, the sufficient stability condition in this case of unknown actuator outputs is identical to the case with known actuator outputs that was established in the prior work by the authors. Therefore, a control designer can utilize the proposed framework for practical applications when the output of the actuator dynamics is not measurable, and hence, unknown (e.g., in hypersonic vehicle applications). An illustrative numerical example complements the proposed theoretical contribution.

Stability Behavior of Model Reference Adaptive Control Methods in Presence of Aircraft Structural Damage

2007 ◽  
Author(s):  
Pascal Nespeca ◽  
Nesrin Sarigul-Klijn
Keyword(s):  
Adaptive Control ◽  
Numerical Study ◽  
Function Analysis ◽  
Model Reference Adaptive Control ◽  
Approximation Technique ◽  
Control Methods ◽  
Model Reference ◽  
Stability Behavior ◽  
The Stability ◽  
Model Reference Adaptive

Any classical control design starts by first satisfying stability and then looking towards satisfying transient requirements. Similarly, a Model Reference Adaptive Control (MRAC) Method should start with a stability analysis. Lyapunov function analysis is first used to justify the stability of the adaptive scheme. Next, a numerical study is conducted to predict the stability behavior of three different MRAC methods in the presence of large unanticipated changes in the dynamics of an aircraft. The Model reference adaptive control methods studied are: Method:1, an adaptive gain method; Method:2, a Neural Network (NN) approximation technique; and, Method:3, a linear approximation technique. For comparison purposes, the aircraft is assumed to have Linear Time Invariant, LTI dynamics. Each algorithm is given full state feedback, an inaccurate reference model and a poor Linear Quadratic Regulator, LQR design for the true plant. It is seen that when the LQR stabilizes the true plant, the three algorithms all achieve the same steady state error to a step command. Numerical results predict the different types of stability behavior that the algorithms provide. It is seen that the Methods: 2 and 3 can only provide a bounded stability, whereas Method: 1 can provide an asymptotic stability. A robust static controller can satisfy stability, but a robust static controller that accommodates variations in plant dynamics might not always be able to match transient requirements as expected. Although there may be no analytical guarantee from adaptive controllers of transient performance, one might look at anecdotal performances.

Composite Model Reference Adaptive Control for a Class of Nonlinear Fractional Order Systems

2015 ◽  
Author(s):  
Yiheng Wei ◽  
Shu Liang ◽  
Yangsheng Hu ◽  
Yong Wang
Keyword(s):  
Adaptive Control ◽  
Fractional Order ◽  
Closed Loop ◽  
Tracking Error ◽  
Model Reference Adaptive Control ◽  
Prediction Errors ◽  
Model Reference ◽  
Closed Loop Systems ◽  
The Stability ◽  
Model Reference Adaptive

This article presents a novel model reference adaptive control of fractional order nonlinear systems, which is a generalization of existing method for integer order systems. The formulating adaptive law is in terms of both tracking and prediction errors, whereas existing methods only depends on tracking error. The transient performance of the closed-loop systems with the proposed control strategy improves in the sense of generating smooth system output. The stability and tracking convergence of the resulting closed-loop system are analyzed via the indirect Lyapunov method. Meanwhile, the proposed controller is implemented by employing some fractional order tracking differentiator to generate the required fractional derivatives of a signal. Numerical examples are provided to illustrate the effectiveness of our results.

Experimental evaluation of a model reference adaptive control for a hydraulic robot: a case study

Robotica ◽  
2003 ◽  
Vol 21 (1) ◽  
pp. 71-78 ◽  
Author(s):  
Ali Kireçci ◽  
Mehmet Topalbekiroglu ◽  
İlyas Eker
Keyword(s):  
Adaptive Control ◽  
Model Reference Adaptive Control ◽  
Computational Time ◽  
Position Tracking ◽  
Control Input ◽  
Model Reference ◽  
Solution Methods ◽  
The Stability ◽  
Classical Control ◽  
Model Reference Adaptive

This paper presents the implementation of an explicit model reference adaptive control (MRAC) for position tracking of a dynamically unknown robot. An auto regressive exogenous (ARX) model is chosen to define the plant model and the control input is optimised in a H2 norm to reduce computational time and to simplify the algorithm. The theory of MRAC falls into a description of the various forms of controllers and parameter estimation techniques, therefore, applications may require very complicated solution methods depending on the selected laws. However, in this study, the proposed MRAC shows that applications may be as easy as classical control methods, such as PID, by guaranteeing the stability and achieving the convergency of the plant parameters. Despite the selected simple control model, simple optimisation method and drawbacks of the robot the experimental results show that MRAC provides an excellent position tracking compared with conventional control (PID). Many experimental implementations have been done on the robot and one of them is included in the paper.

scholarly journals On Fractional Model Reference Adaptive Control

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Bao Shi ◽  
Jian Yuan ◽  
Chao Dong
Keyword(s):  
Adaptive Control ◽  
Reference Model ◽  
Model Reference Adaptive Control ◽  
Lyapunov Theory ◽  
Model Reference ◽  
Fractional Integrator ◽  
The Stability ◽  
Adaptation Law ◽  
Integrator Model ◽  
Model Reference Adaptive

This paper extends the conventional Model Reference Adaptive Control systems to fractional ones based on the theory of fractional calculus. A control law and an incommensurate fractional adaptation law are designed for the fractional plant and the fractional reference model. The stability and tracking convergence are analyzed using the frequency distributed fractional integrator model and Lyapunov theory. Moreover, numerical simulations of both linear and nonlinear systems are performed to exhibit the viability and effectiveness of the proposed methodology.

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