scholarly journals LPV H∞ Control with an Augmented Nonlinear Observer for Sawyer Motors

Mathematics ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 18
Author(s):  
Khac Huan Su ◽  
Kwankyun Byeon ◽  
Wonhee Kim ◽  
Youngwoo Lee
Keyword(s):  
State Feedback ◽  
Control Method ◽  
Tracking Error ◽  
Lyapunov Theory ◽  
Feedback Controller ◽  
Nonlinear Observer ◽  
Linear Matrix ◽  
Modulation Scheme ◽  
Error Performance ◽  
State Feedback Controller

This study presents LPV H∞ control with an augmented nonlinear observer (ANOB) to improve both the position and yaw tracking errors for Sawyer motors. The proposed control method consists of the forces and torque modulation scheme, an ANOB, and a Lyapunov-based current controller with the LPV H∞ state feedback controller to guarantee the stability of tracking error dynamics. The ANOB is designed to estimate all the state variables including the position, velocity, current, and disturbance using only position feedback. We propose a vertex expansion technique to solve the influence of the convex interpolation parameters in the LPV system on the tracking error performance. To be robust against disturbance, a state feedback controller with the LPV gain scheduling is determined by applying the H∞ control in the linear-matrix-inequality (LMI) technique. The closed-loop stability is proved through the Lyapunov theory. The effectiveness of the proposed control method is evaluated through simulation results and compared with the conventional proportional-integral-derivative (PID) control method to verify both the improved tracking error performance and a suitable disturbance rejection.

H∞ fuzzy proportional integral state feedback controller of photovoltaic systems under asymmetric actuator constraints

2020 ◽  
pp. 014233122092157
Author(s):  
K Houda ◽  
D Saifia ◽  
M Chadli ◽  
S Labiod
Keyword(s):  
State Feedback ◽  
Reference Model ◽  
Tracking Error ◽  
Control Design ◽  
Atmospheric Condition ◽  
Boost Converter ◽  
Feedback Controller ◽  
Duty Ratio ◽  
Linear Matrix ◽  
State Feedback Controller

This paper presents a new strategy for a robust maximum power point (MPP) tracking fuzzy controller for photovoltaic (PV) systems subject to actuator asymmetric saturation. A DC-DC boost converter is used to connect a PV panel with an output load. The output voltage of the DC-DC boost converter can be adjusted by duty ratio that is limited between 0 and 1. The aim of our control design is to track the MPP under atmospheric condition changes and the presence of the asymmetric saturation of the duty ratio. To minimize tracking error and disturbance effect, the dynamic behaviour of a PV system and its reference model are described by using Takagi–Sugeno fuzzy models. Then, a constrained control based on a fuzzy PI state feedback controller is proposed. The H∞ control approach is used in control design and stability conditions of the closed-loop system are formulated and solved in terms of linear matrix inequalities. Finally, simulation results are given to show the tracking performance of the control design.

scholarly journals Robust Position Control of a Two-Sided 1-DoF Impacting Mechanical Oscillator Subject to an External Persistent Disturbance by Means of a State-Feedback Controller

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-14 ◽  
Author(s):  
Firas Turki ◽  
Hassène Gritli ◽  
Safya Belghith
Keyword(s):  
State Feedback ◽  
Position Control ◽  
External Disturbance ◽  
Feedback Controller ◽  
Linear Matrix ◽  
Stability Conditions ◽  
Mechanical Oscillator ◽  
Impact Oscillator ◽  
State Feedback Controller ◽  
The Impact

This paper proposes a state-feedback controller using the linear matrix inequality (LMI) approach for the robust position control of a 1-DoF, periodically forced, impact mechanical oscillator subject to asymmetric two-sided rigid end-stops. The periodic forcing input is considered as a persistent external disturbance. The motion of the impacting oscillator is modeled by an impulsive hybrid dynamics. Thus, the control problem of the impact oscillator is recast as a problem of the robust control of such disturbed impulsive hybrid system. To synthesize stability conditions, we introduce the S-procedure and the Finsler lemmas by only considering the region within which the state evolves. We show that the stability conditions are first expressed in terms of bilinear matrix inequalities (BMIs). Using some technical lemmas, we convert these BMIs into LMIs. Finally, some numerical results and simulations are given. We show the effectiveness of the designed state-feedback controller in the robust stabilization of the position of the impact mechanical oscillator under the disturbance.

Fault Control for a Class of Nonlinear System with Input Delay

2012 ◽  
Vol 482-484 ◽  
pp. 1801-1804
Author(s):  
Yang Yu ◽  
Wei Wang
Keyword(s):  
Control System ◽  
Nonlinear System ◽  
State Feedback ◽  
Fuzzy Model ◽  
Lyapunov Theory ◽  
Feedback Controller ◽  
Input Delay ◽  
State Feedback Controller ◽  
The Stability ◽  
Delay Dependent

The paper studies fuzzy fault control for a class of nonlinear system with input delay based on T-S fuzzy model. The state feedback controller that ensures the stability of fuzzy tolerant control system is given via Lyapunov theory and derived in terms of LMI and the results are delay-dependent. Simulation examples are given to illustrate the effectiveness of the approach.

Finite-time H∞ synchronization of semi-Markov jump Lur’e systems

2021 ◽  
pp. 2150168
Author(s):  
Xin Huang ◽  
Youmei Zhou ◽  
Muyun Fang ◽  
Jianping Zhou ◽  
Sabri Arik
Keyword(s):  
Finite Time ◽  
State Feedback ◽  
Time Synchronization ◽  
Control Method ◽  
Design Method ◽  
External Disturbance ◽  
Feedback Controller ◽  
Markov Jump ◽  
Lur’E Systems ◽  
State Feedback Controller

This paper investigates the problem of finite-time [Formula: see text] synchronization for semi-Markov jump Lur’e systems with time-varying delay and external disturbance. The purpose of this work is to design a mode-dependent state-feedback controller to ensure that the synchronization-error system achieves finite-time synchronization with a prescribed [Formula: see text] performance index. A criterion for the finite-time synchronization is proposed by using appropriate Lyapunov functional and two recently developed inequalities. Then, a design method for the required state-feedback controller is presented with the application of several decoupling techniques. Finally, an example is provided to illustrate the applicability of the proposed control method.

scholarly journals Robust Mixed H2/H∞ State Feedback Controller Development for Uncertain Automobile Suspensions with Input Delay

Processes ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 359
Author(s):  
Nan Liu ◽  
Hui Pang ◽  
Rui Yao
Keyword(s):  
Feedback Control ◽  
State Feedback ◽  
Actuator Saturation ◽  
Output Feedback Control ◽  
Active Suspension ◽  
Feedback Controller ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Control Approach ◽  
State Feedback Controller

In order to achieve better dynamics performances of a class of automobile active suspensions with the model uncertainties and input delays, this paper proposes a generalized robust linear H2/H∞ state feedback control approach. First, the mathematical model of a half-automobile active suspension is established. In this model, the H∞ norm of body acceleration is determined as the performance index of the designed controller, and the hard constraints of suspension dynamic deflection, tire dynamic load and actuator saturation are selected as the generalized H2 performance output index of the designed controller to satisfy the suspension safety requirements. Second, a generalized H2/H∞ guaranteed cost state-feedback controller is developed in terms of Lyapunov stability theory. In addition, the Cone Complementarity Linearization (CCL) algorithm is employed to convert the generalized H2/H∞ output-feedback control problem into a finite convex optimization problem (COP) in a linear matrix inequality framework. Finally, a numerical simulation case of this half-automobile active suspension is presented to illustrate the effectiveness of the proposed controller in frequency-domain and time-domain.

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 Active Vibration Control of Container Cranes against Earthquake by the Use of LMI Based MixedH2/H∞State-Feedback Controller

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
C. Oktay Azeloglu ◽  
Ahmet Sagirli
Keyword(s):  
State Feedback ◽  
Active Vibration Control ◽  
Time History ◽  
Feedback Controller ◽  
Linear Matrix ◽  
Container Cranes ◽  
State Feedback Controller ◽  
Active Vibration ◽  
Control Forces ◽  
Six Degree Of Freedom

This paper studies the design of a linear matrix inequality (LMI) based mixedH2/H∞state-feedback controller for vibration attenuation problem of seismic-excited container cranes. In order to show effectiveness of the designed controller, a six-degree-of-freedom container crane structural system is modeled using a spring-mass-damper subsystem. The system is then simulated against the real ground motion of El Centro and Northridge earthquakes. Finally, the time history of the crane parts displacements, accelerations, control forces, and frequency responses of both uncontrolled and controlled cases are presented. Additionally, the performance of the designed controller is also compared with a nominal state-feedbackH∞controller performance. Simulations of the designed controller show better seismic performance than a nominal state-feedbackH∞controller. Simulation results show that the designed controller is all effective in reducing vibration amplitudes of crane parts.

scholarly journals Estimation and Synthesis of Reachable Set for Singular Markovian Jump Systems

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Yucai Ding ◽  
Hui Liu
Keyword(s):  
State Feedback ◽  
Sufficient Conditions ◽  
Feedback Controller ◽  
Reachable Set ◽  
Markovian Jump Systems ◽  
Linear Matrix ◽  
Markovian Jump ◽  
State Feedback Controller ◽  
Singular Markovian Jump Systems ◽  
Jump Systems

The problems of reachable set estimation and state-feedback controller design are investigated for singular Markovian jump systems with bounded input disturbances. Based on the Lyapunov approach, several new sufficient conditions on state reachable set and output reachable set are derived to ensure the existence of ellipsoids that bound the system states and output, respectively. Moreover, a state-feedback controller is also designed based on the estimated reachable set. The derived sufficient conditions are expressed in terms of linear matrix inequalities. The effectiveness of the proposed results is illustrated by numerical examples.

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