Adaptive Control for Uncertain Hysteretic Systems

2013 ◽  
Vol 136 (1) ◽  
Author(s):  
Xiaotian Zou ◽  
Jie Luo ◽  
Chengyu Cao
Keyword(s):  
Adaptive Control ◽  
Linear Time ◽  
Adaptive Controller ◽  
Time Varying ◽  
Performance Bounds ◽  
L1 Adaptive Control ◽  
Hysteretic Systems ◽  
Time Varying Parameters ◽  
L1 Adaptive Controller ◽  
Uniformly Bounded

This paper presents an approach to use the L1 adaptive controller for a class of uncertain systems in the presence of unknown Preisach-type hysteresis in input, unknown time-varying parameters, and unknown time-varying disturbances. The hysteresis operator can be transformed into an equivalent linear time-varying (LTV) system with uncertainties, which means that the effect of the hysteresis can be considered as general uncertainties to the system. Without constructing the inverse hysteresis function, the L1 adaptive control is used to handle the uncertainties introduced by the hysteresis, as well as system dynamics. The adaptive controller presented in this paper ensures uniformly bounded transient and tracking performance for uncertain hysteretic systems. The performance bounds can be systematically improved by increasing the adaptation rate. Simulation results with Preisach-type hysteresis are provided to verify the theoretical findings.

L1 Adaptive Controller for a Class of Nonlinear Systems

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
Jie Luo ◽  
Chengyu Cao
Keyword(s):  
Nonlinear Systems ◽  
Reference System ◽  
Adaptive Controller ◽  
Time Varying ◽  
Robot Arm ◽  
Performance Bounds ◽  
Estimation Errors ◽  
State Dependent ◽  
Low Pass ◽  
L1 Adaptive Controller

This paper presents an extension of the L1 adaptive controller to a class of nonlinear systems where the control effectiveness is time-varying and unknown, but with a known sign. Moreover, this class of nonlinear systems contains time-varying and unknown state-dependent nonlinearities. The proposed L1 adaptive controller consists of three components, a state predictor used to estimate real states, an adaptive law used to update the adaptive parameters in the state predictor, and a low-pass filtered control law. First, the stable closed-loop reference system is constructed. Then, the estimation errors between estimated states and real states are proved to be arbitrarily small by increasing the adaptation rate. After that, we further prove that the adaptive controller ensures uniformly bounded transient and asymptotical tracking of the reference system. The performance bounds can be systematically improved by increasing the adaptation rate. Simulation results on a single-link nonlinear robot arm verify the theoretical findings.

Adaptive Control of Mechanical Systems With Time-Varying Parameters and Disturbances

2004 ◽  
Vol 126 (3) ◽  
pp. 520-530 ◽  
Author(s):  
Prabhakar R. Pagilla ◽  
Yongliang Zhu
Keyword(s):  
Adaptive Control ◽  
Finite Length ◽  
Mechanical Systems ◽  
Adaptive Controller ◽  
Projection Algorithm ◽  
Time Interval ◽  
Time Varying ◽  
Varying Parameters ◽  
Time Varying Parameter ◽  
Time Varying Parameters

A new adaptive control algorithm for mechanical systems with time-varying parameters and/or time-varying disturbances is proposed and investigated. The proposed method does not assume any structure to the time-varying parameter or disturbance. The method is based on the expansion of the time-varying parameter/disturbance using Taylor’s formula. This facilitates expanding a time-varying function as a finite length polynomial and a bounded residue. The coefficients of the finite-length polynomial are estimated in a small time interval so that they can be assumed to be constant within that interval. A gradient projection algorithm is used to estimate the parameters within each time interval. Stability of the proposed adaptive controller is shown and discussed. A novel experiment is designed using a two-link planar mechanical manipulator to investigate the proposed algorithm experimentally. Results of the proposed adaptive controller are compared with an ideal nonadaptive controller that assumes complete knowledge of the parameters and disturbances. A representative sample of the experimental results is shown and discussed.

scholarly journals Design of L1 Adaptive Controller for Position Control of Permanent Magnet Linear Synchronous Motor (PMLSM)

2018 ◽  
pp. 39-52
Keyword(s):  
Adaptive Control ◽  
Permanent Magnet ◽  
Position Control ◽  
Adaptive Controller ◽  
Servo Motor ◽  
Model Reference ◽  
L1 Adaptive Control ◽  
Asymptotic Tracking ◽  
L1 Adaptive Controller ◽  
Model Reference Adaptive

In the present work, the design of an L1 adaptive controller for position control of a linear servo motor for X-Y table application has been developed. The AC Permanent Magnet Linear Synchronous Servo Motor (PMLSM) is considered. A comparative study between L1 adaptive control and Model Reference Adaptive Control (MRAC) has been made. The effectiveness of the L1 adaptive controller against uncertain parameters is analyzed based on simulated results. Robustness characteristics of both L1 adaptive controller and model reference adaptive controller to different input reference signals and different structures of uncertainty have been evaluated. The L1-adaptive controller could ensure uniformly bounded transient and asymptotic tracking for input and output signals. Simulations based on MATLAB of an x-y table based on PMLSM with time-varying friction and disturbance are presented to verify the theoretical findings. The simulation results within the environment of MATLAB/SIMULINK showed that L1-adaptive controller could give better tracking performance, dynamic and steady-state characteristics, than that obtained from MRAC for considered types of input and for various structures of uncertainties.

scholarly journals Geometric L1 Adaptive Attitude Control for a Quadrotor Unmanned Aerial Vehicle

2019 ◽  
Vol 142 (3) ◽  
Author(s):  
Prasanth Kotaru ◽  
Ryan Edmonson ◽  
Koushil Sreenath
Keyword(s):  
Adaptive Control ◽  
Unmanned Aerial Vehicle ◽  
Attitude Control ◽  
Reference Model ◽  
Adaptive Controller ◽  
Control Approach ◽  
L1 Adaptive Control ◽  
Attitude Tracking ◽  
Aerial Vehicle ◽  
L1 Adaptive Controller

Abstract In this paper, we study the quadrotor unmanned aerial vehicle (UAV) attitude control on special orthogonal group (SO(3)) in the presence of unknown disturbances and model uncertainties. L1 adaptive control for UAVs using Euler angles/quaternions is shown to exhibit robustness and precise attitude tracking in the presence of disturbances and uncertainties. However, it is well known that dynamical models and controllers that use Euler angle representations are prone to singularities and typically have smaller regions of attraction while quaternion representations are subject to the unwinding phenomenon. To avoid such complexities, we present a geometric L1 adaptation control law to estimate the uncertainties. A model reference adaptive control approach is implemented, with the attitude errors between the quadrotor model and the reference model defined on the manifold. Control laws for the quadrotor and reference models are developed directly on SO(3) to track the desired trajectory while rejecting the uncertainties. Control Lyapunov function-based analysis is used to show the exponential input-to-state stability of the attitude errors. The proposed L1 adaptive controller is validated using numerical simulations. Preliminary experimental results are shown comparing a geometric proportional-derivative controller to the geometric L1 adaptive controller. Experimental validation of the proposed controller is carried out on an Autel X-star quadrotor.

A longitudinal trajectory tracking method with L1 adaptive control for hypersonic reentry vehicles

2019 ◽  
Vol 42 (3) ◽  
pp. 386-403
Author(s):  
GenSen Han ◽  
Jun Zhou ◽  
JianGuo Guo ◽  
Qing Lu
Keyword(s):  
Adaptive Control ◽  
Trajectory Tracking ◽  
Control Method ◽  
Linear Time ◽  
Adaptive Controller ◽  
Terminal State ◽  
Linear Quadratic ◽  
L1 Adaptive Control ◽  
Reentry Vehicles ◽  
Lqr Controller

This paper presents a longitudinal trajectory tracking scheme with [Formula: see text] adaptive control for hypersonic reentry vehicles (HRVs). A linear time-varying (LTV) multiple input multiple output (MIMO) model, in which influences of lateral states, earth rotation, and linearization are considered as model uncertainties, is derived based on state and input errors of longitudinal model. The normalization of error model is used to reduce differences of magnitude orders in state and input matrix elements which may affect the stability of [Formula: see text] adaptive controller. In order to achieve an accurate tracking performance, a linear quadratic regulator (LQR) controller is employed as the baseline controller, augmented with an [Formula: see text] adaptive controller to attenuate the matched and unmatched uncertainties. Based on the augmented controller, the optimization process is executed with the estimate of uncertainties at the same time. The simulation results of LQR controller, [Formula: see text] augmentation controller and robust [Formula: see text] controller show that the [Formula: see text] adaptive control method can reduce the terminal and integral of squared state errors validly. Terminal state errors in all simulation scenarios are less than 2.5m/s, 1e-3 and 10m, respectively, which reflects its effectiveness in increasing robustness of baseline controller.

L1 Adaptive Control for Aircraft Air Management System Pressure-Regulating Bleed Valve

2017 ◽  
Vol 139 (12) ◽  
Author(s):  
John Cooper ◽  
Chengyu Cao ◽  
Jiong Tang
Keyword(s):  
Management System ◽  
Control Valve ◽  
Pressure Control ◽  
Adaptive Controller ◽  
System Model ◽  
Flow Control Valve ◽  
L1 Adaptive Control ◽  
System Pressure ◽  
L1 Adaptive Controller ◽  
Linear Controllers

This paper presents an L1 adaptive controller for pressure control using an engine bleed valve in an aircraft air management system (AMS). The air management system is composed of two pressure-regulating bleed valves, a temperature control valve, a flow control valve, and a heat exchanger/precooler. Valve hysteresis due to backlash and dry friction is included in the system model. The nonlinearities involved in the system cause oscillations under linear controllers, which decrease component life. This paper is the unique in the consideration of these uncertainties for control design. This paper presents simulation results using the adaptive controller and compares them to those using a proportional–integral (PI) controller.

Output Adaptive Observers Design for Linear Non-Stationary Systems with Polynomial Parameters

2021 ◽  
Vol 22 (8) ◽  
pp. 404-410
Author(s):  
K. B. Dang ◽  
A. A. Pyrkin ◽  
A. A. Bobtsov ◽  
A. A. Vedyakov ◽  
S. I. Nizovtsev
Keyword(s):  
Linear Time ◽  
State Observer ◽  
Observer Design ◽  
Model Parameters ◽  
Time Varying ◽  
State Variables ◽  
Unknown Constant ◽  
Established Method ◽  
Time Varying Parameters ◽  
True Values

The article deals with the problem of state observer design for a linear time-varying plant. To solve this problem, a number of realistic assumptions are considered, assuming that the model parameters are polynomial functions of time with unknown coefficients. The problem of observer design is solved in the class of identification approaches, which provide transformation of the original mathematical model of the plant to a static linear regression equation, in which, instead of unknown constant parameters, there are state variables of generators that model non-stationary parameters. To recover the unknown functions of the regression model, we use the recently well-established method of dynamic regressor extension and mixing (DREM), which allows to obtain monotone estimates, as well as to accelerate the convergence of estimates to the true values. Despite the fact that the article deals with the problem of state observer design, it is worth noting the possibility of using the proposed approach to solve an independent and actual estimation problem of unknown time-varying parameters.

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