Trajectory Tracking Using Linear State Feedback Controller for a Mecanum Wheel Omnidirectional

2021 ◽  
pp. 411-421
Author(s):  
Nguyen Hong Thai ◽  
Trinh Thi Khanh Ly ◽  
Nguyen Thanh Long ◽  
Le Quoc Dzung
Keyword(s):  
Trajectory Tracking ◽  
State Feedback ◽  
Feedback Controller ◽  
State Feedback Controller ◽  
Linear State ◽  
Mecanum Wheel

Tracking a Chaotic System Using an Observer-Based Nonlinear State-Feedback Controller

2011 ◽  
Vol 403-408 ◽  
pp. 4643-4648
Author(s):  
Tanushree Roy ◽  
Aparajita Sengupta
Keyword(s):  
Nonlinear System ◽  
Trajectory Tracking ◽  
State Feedback ◽  
Duffing Oscillator ◽  
Feedback Controller ◽  
Nonlinear Observer ◽  
Single Input Single Output ◽  
State Feedback Controller ◽  
Single Output ◽  
Nonlinear State

This paper attempts to design a Luenberger-like nonlinear observer and a nonlinear state-feedback controller for trajectory tracking of a single-input/single-output nonlinear system exhibiting chaotic dynamics. Using a nonlinear transformation, the nonlinear system is first transformed into a linear system and thereafter a control law is designed for trajectory tracking. The controller, designed on the basis of an input-output linearized model, is applied on both the linearized as well as the nonlinear system. The results are validated through simulation on a Duffing oscillator.

scholarly journals Observer-based trajectory tracking control with preview action for a class of discrete-time Lipschitz nonlinear systems and its applications

2020 ◽  
Vol 12 (7) ◽  
pp. 168781402092265
Author(s):  
Xiao Yu ◽  
Fucheng Liao
Keyword(s):  
Nonlinear Systems ◽  
Discrete Time ◽  
Trajectory Tracking ◽  
Tracking Control ◽  
State Feedback ◽  
Feedback Controller ◽  
Matrix Inequality ◽  
State Feedback Controller ◽  
Lipschitz Nonlinear Systems ◽  
Reference Knowledge

In this article, the observer-based preview tracking control problem is investigated for a class of discrete-time Lipschitz nonlinear systems. To convert the observer-based trajectory tracking problem into a regulation problem, the classical difference technique is used to construct an augmented error system containing tracking error signal and previewable reference knowledge. Then, a state feedback controller with specific structures is taken into consideration. Sufficient design condition is established, based on the Lyapunov function approach, to guarantee the asymptotic stability of the closed-loop system. By means of some special mathematical derivations, the bilinear matrix inequality condition is successfully transformed into a tractable linear matrix inequality. Meanwhile, the gains of both observer and tracking controller can be computed simultaneously only in one step. As for the original system, the developed tracking control law is composed of an integrator, an observer-based state feedback controller, and a preview action term related to the reference signal. Finally, two numerical examples are provided to demonstrate the effectiveness of the theoretical method.

Some Ideas on the Local Control of Nonlinear Systems With Time-Periodic Coefficients

1999 ◽  
Author(s):  
Alexandra Dávid ◽  
S. C. Sinha
Keyword(s):  
Normal Form ◽  
Local Control ◽  
State Feedback ◽  
Feedback Controller ◽  
Periodic Systems ◽  
State Feedback Controller ◽  
Linearized System ◽  
Linear State ◽  
Time Invariant ◽  
Time Periodic

Abstract In this paper ideas on local control of linear and nonlinear time-periodic systems are presented. Our first goal is to stabilize the system far away from bifurcation points. In this case, the classical linear state feedback stabilization based on pole placement is generalized such that it is applicable to time-periodic systems. The linear state-feedback controller design involves computation of the fundamental solution matrix of the system in a symbolic form as function of the control parameters. Next, we focus on the bifurcation control of time-periodic systems. When the linearized system is in a critical case of stability (i.e. when it has Floquet multipliers on the unit circle of the complex plane) and the critical modes are uncontrollable in the linear sense, then a purely nonlinear state-feedback controller is designed to stabilize the equilibrium at the bifurcation point and ensure the stability of the bifurcated nontrivial solution. When the linearized system is linearly controllable, then it is shown that an appropriately chosen linear state-feedback control can also modify the nonlinear features of the bifurcations, such as stability or size of the limit cycles or quasi-periodic limit sets. The control techniques are based on a series of transformations that convert the system into a time-invariant form. First, the Lyapunov-Floquet transformation is used to make the linear part of the periodic system time-invariant. Then, time-periodic center manifold reduction and time-dependent normal form theory are applied to obtain the simplest nonlinear form of a system undergoing bifurcation. For most codimension one bifurcations the normal form is completely time-invariant and therefore, it is a rather simple task to choose the appropriate control gains. These ideas are illustrated by an example of a parametrically excited simple pendulum undergoing symmetry breaking bifurcation.

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