Repetitive Control Based Disturbance Cancellation Using Iterative Basis Function Feedback With Wavelet Filtering

2008 ◽  
Author(s):  
Jeng-Wen Lin ◽  
Chih-Wei Huang ◽  
Hao-Ping Wen
Keyword(s):  
Repetitive Control ◽  
Basis Functions ◽  
Projection Algorithm ◽  
Tracking Errors ◽  
Wavelet Filtering ◽  
Control Laws ◽  
Periodic Disturbance ◽  
Output Tracking ◽  
Disturbance Cancellation ◽  
Periodic Error

This paper presents repetitive control laws in real time using matched basis functions. These laws adjust the command given a feedback control system in order to eliminate tracking errors, resulting from in general a periodic disturbance and a non-periodic disturbance. The periodic error can be reduced by linear basis functions while the non-periodic error by the projection algorithm along with the wavelet filtering. The control laws do not use a system model, but instead the control action is chosen to be a linear combination of chosen input basis functions, and the corresponding output basis functions are obtained, nominally by experiment. The repetitive control laws use the projection algorithm to compute the output components on the output basis functions, and then the corresponding input components are adjusted accordingly. The output signals are reconstructed via the wavelet filtering before they are feedback to the controller. Numerical experiments show that the repetitive controllers are quite effective. In particular, the output tracking errors are further reduced because of the introduction of the wavelet filtering when compared to the previous work. In general, the repetitive control laws developed here can be used for the purpose of precision machinery control.

Tracking Control of Non-Minimum Phase Systems Using Filtered Basis Functions: A NURBS-Based Approach

2015 ◽  
Author(s):  
Molong Duan ◽  
Keval S. Ramani ◽  
Chinedum E. Okwudire
Keyword(s):  
Tracking Control ◽  
Phase Error ◽  
Approximate Model ◽  
Basis Functions ◽  
Minimum Phase ◽  
Tracking Errors ◽  
Model Inversion ◽  
B Spline ◽  
Phase Systems ◽  
Zero Phase

This paper proposes an approach for minimizing tracking errors in systems with non-minimum phase (NMP) zeros by using filtered basis functions. The output of the tracking controller is represented as a linear combination of basis functions having unknown coefficients. The basis functions are forward filtered using the dynamics of the NMP system and their coefficients selected to minimize the errors in tracking a given trajectory. The control designer is free to choose any suitable set of basis functions but, in this paper, a set of basis functions derived from the widely-used non uniform rational B-spline (NURBS) curve is employed. Analyses and illustrative examples are presented to demonstrate the effectiveness of the proposed approach in comparison to popular approximate model inversion methods like zero phase error tracking control.

Modeling and trajectory tracking control of a two-wheeled mobile robot: Gibbs–Appell and prediction-based approaches

Robotica ◽  
2018 ◽  
Vol 36 (10) ◽  
pp. 1551-1570 ◽  
Author(s):  
Hossein Mirzaeinejad ◽  
Ali Mohammad Shafei
Keyword(s):  
Trajectory Tracking ◽  
Dynamic Models ◽  
Sliding Mode ◽  
Tracking Accuracy ◽  
Wheeled Mobile Robots ◽  
Tracking Errors ◽  
Trajectory Tracking Control ◽  
Control Laws ◽  
Control Approach ◽  
Prediction Time

SUMMARYThis study deals with the problem of trajectory tracking of wheeled mobile robots (WMR's) under non-holonomic constraints and in the presence of model uncertainties. To solve this problem, the kinematic and dynamic models of a WMR are first derived by applying the recursive Gibbs–Appell method. Then, new kinematics- and dynamics-based multivariable controllers are analytically developed by using the predictive control approach. The control laws are optimally derived by minimizing a pointwise quadratic cost function for the predicted tracking errors of the WMR. The main feature of the obtained closed-form control laws is that online optimization is not needed for their implementation. The prediction time, as a free parameter in the control laws, makes it possible to achieve a compromise between tracking accuracy and implementable control inputs. Finally, the performance of the proposed controller is compared with that of a sliding mode controller, reported in the literature, through simulations of some trajectory tracking maneuvers.

Design of an Observer-Based Repetitive Control System to Reject Periodic Disturbance

2016 ◽  
Vol 25 (06) ◽  
pp. 1650061 ◽  
Author(s):  
Zhen Shao ◽  
Zhengrong Xiang
Keyword(s):  
Control System ◽  
Disturbance Rejection ◽  
Lyapunov Functional ◽  
Repetitive Control ◽  
Sufficient Condition ◽  
Two Dimensional ◽  
Periodic Disturbance ◽  
Repetitive Learning ◽  
The Stability ◽  
2D Model

This paper concerns the design of an observer-based repetitive control system (RCS) to improve the periodic disturbance rejection performance. The periodic disturbance is estimated by a repetitive learning based estimator (RLE) and rejected by incorporation of the estimation into a repetitive control (RC) input. Firstly, the configuration of the observer-based RCS with the RLE is described. Then, a continuous–discrete two-dimensional (2D) model is built to describe the RCS. By choosing an appropriate Lyapunov functional, a sufficient condition is proposed to guarantee the stability of the RCS. Finally, a numerical example is given to verify the effectiveness of the proposed method.

scholarly journals Adaptive fuzzy tracking control for a constrained flexible air-breathing hypersonic vehicle based on actuator compensation

2016 ◽  
Vol 13 (6) ◽  
pp. 172988141667111 ◽  
Author(s):  
Peng Fei Wang ◽  
Jie Wang ◽  
Xiang Wei Bu ◽  
Ying Jie Jia
Keyword(s):  
Tracking Control ◽  
Hypersonic Vehicle ◽  
Reference Trajectory ◽  
Fuzzy Logic Systems ◽  
Tracking Errors ◽  
Control Laws ◽  
Air Breathing ◽  
Adaptive Fuzzy ◽  
Adaptive Parameter ◽  
Actuator Constraints

The design of an adaptive fuzzy tracking control for a flexible air-breathing hypersonic vehicle with actuator constraints is discussed. Based on functional decomposition methodology, velocity and altitude controllers are designed. Fuzzy logic systems are applied to approximate the lumped uncertainty of each subsystem of air-breathing hypersonic vehicle model. Every controllers contain only one adaptive parameter that needs to be updated online with a minimal-learning-parameter scheme. The back-stepping design is not demanded by converting the altitude subsystem into the normal output-feedback formulation, which predigests the design of a controller. The special contribution is that novel auxiliary systems are developed to compensate both the tracking errors and desired control laws, based on which the explored controller can still provide effective tracking of velocity and altitude commands when the inputs are saturated. Finally, reference trajectory tracking simulation shows the effectiveness of the proposed method in its application to air-breathing hypersonic vehicle control.

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