Least Squares Adaptive Control for Trajectory Following Robots

1987 ◽  
Vol 109 (2) ◽  
pp. 104-110 ◽  
Author(s):  
C. W. deSilva ◽  
J. Van Winssen
Keyword(s):  
Least Squares ◽  
Reference Model ◽  
Recursive Algorithm ◽  
Adaptive Controller ◽  
Nonlinear Damping ◽  
Feedback Gain ◽  
Online Identification ◽  
Control Scheme ◽  
Trajectory Following ◽  
Time Changes

A control scheme is presented for trajectory following with robotic manipulators. The method employs a feedforward torque for gross compensation and adaptive feedback gain scheduling for correcting deviations from the desired trajectory. The adaptive controller eliminates trajectory errors in the least squares sense without using online identification or a reference model. The control scheme takes into account dynamic nonlinearities (e.g., coriolis and centrifugal accelerations and payload changes), geometric nonlinearities (e.g., nonlinear coordinate expressions for large excursions) and physical nonlinearities (e.g., nonlinear damping) as well as dynamic coupling present in a manipulator. The method can accommodate real-time changes in the desired trajectory. In practice, a recursive algorithm would be needed to accomplish this. Computer simulations are given to demonstrate the feasibility of the control scheme.

Self-tuning proportional, integral and derivative controller based on genetic algorithm least squares

1998 ◽  
Vol 212 (6) ◽  
pp. 437-448 ◽  
Author(s):  
K Warwick ◽  
Y-H Kang
Keyword(s):  
Least Squares ◽  
Adaptive Controller ◽  
Recursive Least Squares ◽  
Industrial Processes ◽  
Industrial Plant ◽  
Parameter Estimator ◽  
Proportional Integral ◽  
Control Scheme ◽  
Self Tuning ◽  
Real Plant

A self-tuning proportional, integral and derivative control scheme based on genetic algorithms (GAs) is proposed and applied to the control of a real industrial plant. This paper explores the improvement in the parameter estimator, which is an essential part of an adaptive controller, through the hybridization of recursive least-squares algorithms by making use of GAs and the possibility of the application of GAs to the control of industrial processes. Both the simulation results and the experiments on a real plant show that the proposed scheme can be applied effectively.

Optimal Model Reference Control Scheme Design for Nonlinear Strict-Feedback Systems

2020 ◽  
Vol 38 (9A) ◽  
pp. 1342-1351
Author(s):  
Musadaq A. Hadi ◽  
Hazem I. Ali
Keyword(s):  
Reference Model ◽  
Feedback System ◽  
Optimization Method ◽  
Feedback Systems ◽  
Model Reference ◽  
Scheme Design ◽  
Model Reference Control ◽  
Control Scheme ◽  
Lyapunov Stability Analysis ◽  
Strict Feedback

In this paper, a new design of the model reference control scheme is proposed in a class of nonlinear strict-feedback system. First, the system is analyzed using Lyapunov stability analysis. Next, a model reference is used to improve system performance. Then, the Integral Square Error (ISE) is considered as a cost function to drive the error between the reference model and the system to zero. After that, a powerful metaheuristic optimization method is used to optimize the parameters of the proposed controller. Finally, the results show that the proposed controller can effectively compensate for the strictly-feedback nonlinear system with more desirable performance.

scholarly journals Lithium-Ion Battery SOC Estimation Based on Adaptive Forgetting Factor Least Squares Online Identification and Unscented Kalman Filter

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1733
Author(s):  
Hao Wang ◽  
Yanping Zheng ◽  
Yang Yu
Keyword(s):  
Kalman Filter ◽  
Least Squares ◽  
Unscented Kalman Filter ◽  
Equivalent Circuit Model ◽  
Lithium Ion ◽  
Forgetting Factor ◽  
Soc Estimation ◽  
Online Identification ◽  
Adaptive Forgetting Factor ◽  
Adaptive Forgetting

In order to improve the estimation accuracy of the battery state of charge (SOC) based on the equivalent circuit model, a lithium-ion battery SOC estimation method based on adaptive forgetting factor least squares and unscented Kalman filtering is proposed. The Thevenin equivalent circuit model of the battery is established. Through the simulated annealing optimization algorithm, the forgetting factor is adaptively changed in real-time according to the model demand, and the SOC estimation is realized by combining the least-squares online identification of the adaptive forgetting factor and the unscented Kalman filter. The results show that the terminal voltage error identified by the adaptive forgetting factor least-squares online identification is extremely small; that is, the model parameter identification accuracy is high, and the joint algorithm with the unscented Kalman filter can also achieve a high-precision estimation of SOC.

Online parameter estimation and adaptive control with limited information in structures

2021 ◽  
pp. 107754632110191
Author(s):  
Fereidoun Amini ◽  
Elham Aghabarari
Keyword(s):  
Parameter Estimation ◽  
Adaptive Control ◽  
Least Squares ◽  
Control Algorithm ◽  
Least Squares Method ◽  
Recursive Least Squares ◽  
Limited Information ◽  
Online Identification ◽  
Recursive Least Squares Method ◽  
Adaptive Control Algorithm

An online parameter estimation is important along with the adaptive control, that is, a time-dependent plant. This study uses both online identification and the simple adaptive control algorithm with velocity feedback. The recursive least squares method was used to identify the stiffness and damping parameters of the structure’s stories. Identification was carried out online without initial estimation and only by measuring the structural responses. The limited information regarding sensor measurements, parameter convergence, and the effects of the covariance matrix is examined. The integration of the applied online identification, the appropriate reference model selection in simple adaptive control, and adopting the proportional integral filter was used to limit the structural control response error. Some numerical examples are simulated to verify the ability of the proposed approach. Despite the limited information, the results show that the simultaneous use of online identification with the recursive least squares method and simple adaptive control algorithm improved the overall structural performance.

A Note on Pole Placement of Mechanical Systems

1991 ◽  
Vol 113 (3) ◽  
pp. 420-421 ◽  
Author(s):  
C. Minas ◽  
D. J. Inman
Keyword(s):  
Least Squares ◽  
Canonical Form ◽  
Output Feedback ◽  
Closed Loop ◽  
Weighted Least Squares ◽  
Mechanical Systems ◽  
Pole Placement ◽  
Feedback Gain ◽  
Closed Loop System ◽  
Feedback Method

An output feedback method is developed, that systematically places a desired number of poles of a closed-loop system at or near desired locations. The system is transformed to its equivalent controllable canonical form, where the output feedback gain matrix is calculated in a weighted least squares scheme, that minimizes the change of the remaining modes of the system. The advantage of this method over other pole placement routines is the fact that the influence on the remaining unplaced modes of the system is minimum, which is particularly important in preserving closed-loop stability.

Exakte posenabhängige Strukurmodelle*/Accurate virtual machine tool structures - Online-identification of the general model of a lightweight machine tool structure with pose-dependent dynamic behavior

2017 ◽  
Vol 107 (05) ◽  
pp. 323-328
Author(s):  
S. Apprich ◽  
F. Wulle ◽  
A. Prof. Pott ◽  
A. Prof. Verl
Keyword(s):  
Machine Tool ◽  
Least Squares ◽  
Dynamic Behavior ◽  
Natural Frequencies ◽  
Recursive Least Squares ◽  
Machine Model ◽  
Online Identification ◽  
Working Space ◽  
Machine Tool Structure ◽  
Machine Tool Structures

Serielle Werkzeugmaschinenstrukturen weisen ein posenabhängiges, dynamisches Verhalten auf, wobei die Eigenfrequenzen um mehrere Hertz im Arbeitsraum variieren können. Die genaue Kenntnis dieses Verhaltens gestattet eine verbesserte Regelung der Strukturen. Ein generelles parametrisches Maschinenmodell, dessen Parameter online durch einen Recursive-Least-Squares-Algorithmus an das reale Maschinenverhalten angepasst werden, stellt Informationen über dieses Maschinenverhalten bereit.   Serial machine tool structures feature a pose-dependent dynamic behavior with natural frequencies varying by serveral hertz within the working space. The accurate knowledge of this behavior allows an improved control of the structures. A general parametric machine model, whose parameters are adapted online to the actual machine tool behavior by a Recursive Least Squares algorithm, provides information about the pose-dependent dynamic behavior.

High-Sideslip Model Reference Adaptive Flight Control for Aileron Locked Aircraft

2014 ◽  
Vol 651-653 ◽  
pp. 751-756
Author(s):  
Peng Fei Cheng ◽  
Cheng Fu Wu ◽  
Yue Guo
Keyword(s):  
Flight Control ◽  
Control Method ◽  
Reference Model ◽  
Sideslip Angle ◽  
Model Reference ◽  
Control Scheme ◽  
Adaptive Flight Control ◽  
Random Initialization ◽  
Model Reference Adaptive ◽  
The Given

This paper develops a high-sideslip flight control scheme based on model reference adaptive control (MRAC) to stabilize aircraft under aileron deadlock of one side. Firstly, the cascaded flight control scheme for high-sideslip straight flight is presented and how the control signals transfer is also analyzed. After that, the control structure and laws of MRAC for attitude inner-loop connected with sideslip command are designed. Finally, the control scheme is verified under a nonlinear aircraft model in conditions of no fault and one side aileron deadlock respectively. The simulation results show that when one side aileron deadlock occurs in accompany with the plant’s aerodynamic data perturbation and random initialization of controller parameters, this control method could utilize operation points of no-fault aircraft to force the faulty aircraft following the given reference model responses and finally tracking given sideslip angle command without static error robustly.

scholarly journals Tracking—A

2021 ◽  
pp. 163-192
Author(s):  
Jean Walrand
Keyword(s):  
Kalman Filter ◽  
Linear Regression ◽  
Least Squares ◽  
Recursive Algorithm ◽  
Nonlinear Function ◽  
Random Variables ◽  
Random Variable ◽  
Linear Least Squares ◽  
Least Squares Estimate ◽  
Related Notion

AbstractThis chapter explains how to estimate an unobserved random variable or vector from available observations. This problem arises in many examples, as illustrated in Sect. 9.1. The basic problem is defined in Sect. 9.2. One commonly used approach is the linear least squares estimate explained in Sect. 9.3. A related notion is the linear regression covered in Sect. 9.4. Section 9.5 comments on the problem of overfitting. Sections 9.6 and 9.7 explain the minimum means squares estimate that may be a nonlinear function of the observations and the remarkable fact that it is linear for jointly Gaussian random variables. Section 9.8 is devoted to the Kalman filter, which is a recursive algorithm for calculating the linear least squares estimate of the state of a system given previous observations.

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