A Novel Robust Control of Uncertain Furuta Pendulum Based on a General Lyapunov Function

2019 ◽  
Vol 141 (11) ◽  
Author(s):  
Xinrong Zhang ◽  
Ruiying Zhao ◽  
Jie Ma ◽  
Chul-Hee Lee
Keyword(s):  
Robust Control ◽  
Lyapunov Function ◽  
Control Design ◽  
Uniform Boundedness ◽  
Fast Time ◽  
Ultimate Boundedness ◽  
Pendulum System ◽  
System A ◽  
Uniform Ultimate Boundedness ◽  
Nonlinear Pendulum

AbstractA novel robust approach for the obedience control of Furuta pendulum with uncertainty is proposed. The uncertainty considered in this paper is (possibly fast) time-varying and bounded, which may exist in any stage of the pendulum subsystem. By the Lagrangian formulation of the nonlinear pendulum system, a robust control, based on a general Lyapunov function, is designed to render the Furuta pendulum a position obedience. As a consequence of the Lyapunov approach, the control design is not restricted to linearize the pendulum system. The system performance under the proposed control is guaranteed as uniform boundedness and uniform ultimate boundedness. The salient features of this new control are demonstrated both analytically and numerically. The experiment is conducted in the Furuta pendulum system to prove the validity and effectiveness of the control design.

scholarly journals Robust control design for home pension service mobile robots with passive and servo constraints

2020 ◽  
Vol 103 (3) ◽  
pp. 003685042095221
Author(s):  
Yating Zhao ◽  
Xiaolong Chen ◽  
Han Zhao
Keyword(s):  
Robust Control ◽  
Mobile Robots ◽  
Control Design ◽  
Uniform Boundedness ◽  
Control Force ◽  
Dynamics Modeling ◽  
Ultimate Boundedness ◽  
Uniform Ultimate Boundedness ◽  
Robust Control Design ◽  
Servo Constraints

This paper presents a novel robust control design for a class of home pension service mobile robots (HPSMRs) with non-holonomic passive constraints, based on the Udwadia-Kalaba theory and Udwadia control. The approach has two portions: dynamics modeling and robust control design. The Udwadia-Kalaba theory is employed to deal with the non-holonomic passive constraints. The frame of the Udwadia control is employed to design the robust control to tracking the servo constraints. The designed approach is easy to implement because the analytical solution of the control force can explicitly be obtained even if the non-holonomic passive constraints exists. The uniform boundedness and uniform ultimate boundedness are demonstrated by the theoretical analysis. The effectiveness of the proposed approach is verified through the numerical simulation by a HPSMR.

Periodic solutions to functional differential equations

1985 ◽  
Vol 101 (3-4) ◽  
pp. 253-271 ◽  
Author(s):  
O. A. Arino ◽  
T. A. Burton ◽  
J. R. Haddock
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Uniform Boundedness ◽  
Continuous Functions ◽  
Ultimate Boundedness ◽  
Space Of Continuous Functions ◽  
Uniform Ultimate Boundedness ◽  
Functional Differential ◽  
Image Position

SynopsisWe consider a system of functional differential equationswhere G: R × B → Rn is T periodic in t and B is a certain phase space of continuous functions that map (−∞, 0[ into Rn. The concepts of B-uniform boundedness and B-uniform ultimate boundedness are introduced, and sufficient conditions are given for the existence of a T-periodic solution to (1.1). Several examples are given to illustrate the main theorem.

Optimal design for robust control parameter for active roll control system: a fuzzy approach

2017 ◽  
Vol 24 (19) ◽  
pp. 4575-4591 ◽  
Author(s):  
Hao Sun ◽  
Ye-Hwa Chen ◽  
Han Zhao ◽  
Shengchao Zhen
Keyword(s):  
Control System ◽  
Robust Control ◽  
Optimal Design ◽  
Ride Comfort ◽  
Initial Conditions ◽  
Dynamic Performance ◽  
Control Design ◽  
Uniform Boundedness ◽  
Roll Control ◽  
Active Roll Control

In this paper, we investigate the dynamical model of an active roll control system (ARCS) which can impose an anti-roll moment quickly by active actuators to prevent a vehicle rolling when the vehicle generates the roll tendency and effectively enhances the vehicle dynamic performance without sacrificing ride comfort. In the dynamic model of the ARCS, we consider the sprung mass of the vehicle which is (possibly) time-varying and the initial conditions are the uncertain parameters which are described by fuzzy set theory. A new optimal robust control which is deterministic and is not the usual if–then rules-based control is proposed. The desired controlled system performance is twofold: one deterministic, which includes uniform boundedness and uniform ultimate boundedness, and one fuzzy, which enhances the cost consideration. We then formulate an optimal design problem associated with the control as a constrained optimization problem. The resulting control design is systematic and is able to guarantee the deterministic performance and minimize the average fuzzy performance. Numerical simulations show that the control design renders the ARCS practically stable and achieves constraints following maneuvering.

scholarly journals Robust Control Design for Kaplan Turbine

2021 ◽  
Vol 2141 (1) ◽  
pp. 012006
Author(s):  
Hernando González Acevedo
Keyword(s):  
Robust Control ◽  
Dynamic Model ◽  
Transient Response ◽  
Reference Signal ◽  
Control Design ◽  
Parameter Uncertainties ◽  
Robust Controller ◽  
System A ◽  
Kaplan Turbine ◽  
Robust Control Design

Abstract The paper presents the dynamic model of a Kaplan turbine coupled to a DC generator, which is part of the H112D didactic system. A robust controller is designed using two different techniques: H ∞ mixed sensitivity and Quantitative feedback Theory (QFT). The robustness of the controller was analysed with three indicators: analysis of parameter uncertainties, transient response given a variable reference signal and robustness against disturbances.

Deterministic Controllers for a Class of Mismatched Systems

1994 ◽  
Vol 116 (1) ◽  
pp. 17-23 ◽  
Author(s):  
Sandeep
Keyword(s):  
Dynamical Systems ◽  
Uniform Boundedness ◽  
Sufficient Condition ◽  
Ultimate Boundedness ◽  
Matching Conditions ◽  
Uncertain Dynamical Systems ◽  
Uniform Ultimate Boundedness

In this paper a class of nonlinear uncertain dynamical systems, which do not satisfy the matching conditions, is considered. This class of mismatched systems is more general than one considered earlier. A sufficient condition, in terms of a critical mismatch threshold, is given, which ensures uniform boundedness and uniform ultimate boundedness. The theory is illustrated by an example of controlled aircraft take-off under windshear conditions.

scholarly journals Robust Control Design for an Uncertain Macroeconomic Dynamical System with Unknown Characteristics and Inequality Control Constraint

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Xiaorui Xie ◽  
Ye-Hwa Chen
Keyword(s):  
Dynamical System ◽  
Robust Control ◽  
Design Procedure ◽  
Control Design ◽  
Uniform Boundedness ◽  
Salient Feature ◽  
Uncertain System ◽  
Stabilization Policy ◽  
Bounded Controls ◽  
Robust Control Design

The stabilization problem of a macroeconomic dynamical system is considered in this paper. The main features of this system are that the system uncertainties may be unknown functions of state and time but with known bounds. Furthermore, the control inputs are subject to constraints, which is a salient feature in an economic control problem. To ensure that the controls are within the specified boundaries, in our control design procedure, a creative diffeomorphism, which converts bounded controls into unbounded corresponding signals by choosing an appropriate transformation function, is proposed. For the uncertain system, a deterministic robust control is designed to render the practical stability: uniform boundedness and uniform ultimate boundedness. The range of the input bounds is related to the uncertainties and can be designed according to the actual situation. Numerical simulations are performed to verify the effectiveness of the stabilization policy.

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