Repetitive Control for Rejection of Periodic Multiplicative Disturbances and Adaptive Identification of the Unknown Period

2004 ◽  
Author(s):  
Sandipan Mishra ◽  
Manabu Yamada ◽  
Masayoshi Tomizuka
Keyword(s):  
Control Algorithm ◽  
Closed Loop ◽  
Design Method ◽  
Repetitive Control ◽  
Adaptive Controller ◽  
Least Mean Square ◽  
Closed Loop System ◽  
Internal Model Principle ◽  
Periodic Disturbances ◽  
The Stability

Repetitive control has been used extensively for rejection of periodic disturbances, in systems that have to follow periodic trajectories. To date, most repetitive controllers have focused on rejection of additive periodic disturbances. This paper suggests the use of a repetitive control algorithm for rejection of periodic multiplicative disturbances. The first result is a simple design method of a new controller to reject the multiplicative disturbance effectively, provided that the period of the disturbance is known. This controller is based on the internal model principle and the design method consists of a simple norm condition. It is shown that this repetitive-type controller can reject the disturbance. The second result is an extension of the first one to the case that the period of the disturbance is unknown. A period estimator is added to the control system to identify the period of the multiplicative disturbance. The algorithm, consisting of an adaptive recursive least mean square method, is simple. It is shown that this adaptive controller can reject the disturbance with an uncertain period and guarantee the stability of the adaptive closed-loop system including the period estimator.

scholarly journals Robust adaptive controller design for excavator arm

2019 ◽  
Vol 8 (4) ◽  
pp. 293
Author(s):  
Nga Thi-Thuy Vu
Keyword(s):  
Closed Loop ◽  
Controller Design ◽  
Lyapunov Stability Theory ◽  
Adaptive Controller ◽  
Closed Loop System ◽  
Model Free ◽  
Lagrange Form ◽  
Robust Adaptive ◽  
The Stability ◽  
Robust Adaptive Controller

This paper presents a robust adaptive controller that does not depend on the system parameters for an excavator arm. Firstly, the model of the excavator arm is demonstrated in the Euler-Lagrange form considering with overall excavator system. Next, a robust adaptive controller has been constructed from information of state error. In this paper, the stability of overall system is mathematically proven by using Lyapunov stability theory. Also, the proposed controller is model free then the closed loop system is not affected by disturbances and uncertainties. Finally, the simulation is executed in Matlab/Simulink for both presented scheme and the PD controller under some conditions to ensure that the proposed algorithm given the good performances for all cases.

Fuzzy Adaptive Output Tracking Controller for a Class of Chaotic Systems

2012 ◽  
Vol 488-489 ◽  
pp. 1793-1797
Author(s):  
R. Ghasemi ◽  
M.B. Menhaj ◽  
B. Abdi
Keyword(s):  
Chaotic Systems ◽  
Closed Loop ◽  
Adaptive Controller ◽  
Closed Loop System ◽  
External Disturbances ◽  
Output Tracking ◽  
Fuzzy Adaptive Controller ◽  
Simulation Results ◽  
The Stability ◽  
Fuzzy Adaptive

This paper proposes a new method for designing a fuzzy adaptive controller for a class of non-affine nonlinear chaotic systems in which functions of the systems are unknown. The proposed method is aimed on a class of non-canonical non-affine nonlinear chaotic systems. The stability of the closed loop system is guaranteed based on Lyapunov’s theory. The proposed controller is robust against uncertainties and external disturbances. The simulation results show the effectiveness of the proposed method.

scholarly journals Stability of a Class of Stochastic Nonlinear Systems with Markovian Switching

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Xiaohua Liu ◽  
Wuquan Li
Keyword(s):  
Nonlinear Systems ◽  
Output Feedback ◽  
Closed Loop ◽  
Design Method ◽  
Feedback Controller ◽  
Markovian Switching ◽  
Stochastic Nonlinear Systems ◽  
Closed Loop System ◽  
Output Feedback Controller ◽  
The Stability

This paper investigates the stability of a class of stochastic nonlinear systems with Markovian switching via output-feedback. Based on the backstepping design method and homogeneous domination technique, an output-feedback controller is constructed to guarantee that the closed-loop system has a unique solution and is almost surely asymptotically stable. The efficiency of the output-feedback controller is demonstrated by a simulation example.

Robust piecewise adaptive control for an uncertain semilinear parabolic distributed parameter systems

2022 ◽  
Vol 27 ◽  
pp. 1-20
Author(s):  
Yanfang Lei ◽  
Junmin Li ◽  
Ailiang Zhao
Keyword(s):  
Adaptive Control ◽  
Closed Loop ◽  
Design Method ◽  
External Disturbance ◽  
Adaptive Controller ◽  
Distributed Parameter Systems ◽  
Distributed Parameter ◽  
Closed Loop System ◽  
Semilinear Parabolic ◽  
Parabolic Distributed Parameter Systems

In this study, we focus on designing a robust piecewise adaptive controller to globally asymptotically stabilize a semilinear parabolic distributed parameter systems (DPSs) with external disturbance, whose nonlinearities are bounded by unknown functions. Firstly, a robust piecewise adaptive control is designed against the unknown nonlinearity and the external disturbance. Then, by constructing an appropriate Lyapunov–Krasovskii functional candidate (LKFC) and using the Wiritinger’s inequality and a variant of the Agmon’s inequality, it is shown that the proposed robust piecewise adaptive controller not only ensures the globally asymptotic stability of the closed-loop system, but also guarantees a given performance. Finally, two simulation examples are given to verify the validity of the design method.

Adaptive attitude-tracking control of spacecraft considering on-orbit refuelling

2020 ◽  
pp. 014233122097313
Author(s):  
Yiqi Xu
Keyword(s):  
Tracking Control ◽  
Closed Loop ◽  
Closed Loop System ◽  
Tracking Errors ◽  
Attitude Tracking ◽  
Control Scheme ◽  
Inertia Model ◽  
And Performance ◽  
Attitude Tracking Control ◽  
The Stability

This paper studies the attitude-tracking control problem of spacecraft considering on-orbit refuelling. A time-varying inertia model is developed for spacecraft on-orbit refuelling, which actually includes two processes: fuel in the transfer pipe and fuel in the tank. Based upon the inertia model, an adaptive attitude-tracking controller is derived to guarantee the stability of the resulted closed-loop system, as well as asymptotic convergence of the attitude-tracking errors, despite performing refuelling operations. Finally, numerical simulations illustrate the effectiveness and performance of the proposed control scheme.

A Digital Algorithm for Near-Minimum-Time Control of Robot Manipulators

1987 ◽  
Vol 109 (4) ◽  
pp. 320-327 ◽  
Author(s):  
C. K. Kao ◽  
A. Sinha ◽  
A. K. Mahalanabis
Keyword(s):  
Control Algorithm ◽  
State Feedback ◽  
Closed Loop ◽  
Robot Manipulator ◽  
Minimum Time ◽  
State Feedback Control ◽  
Final States ◽  
Closed Loop System ◽  
Time Control ◽  
Digital Algorithm

A digital state feedback control algorithm has been developed to obtain the near-minimum-time trajectory for the end-effector of a robot manipulator. In this algorithm, the poles of the linearized closed loop system are judiciously placed in the Z-plane to permit near-minimum-time response without violating the constraints on the actuator torques. The validity of this algorithm has been established using numerical simulations. A three-link manipulator is chosen for this purpose and the results are discussed for three different combinations of initial and final states.

Backstepping Based Adaptive Control of Magnetic Levitation System

2013 ◽  
Vol 341-342 ◽  
pp. 945-948 ◽  
Author(s):  
Wei Zhou ◽  
Bao Bin Liu
Keyword(s):  
Parameter Uncertainty ◽  
Closed Loop ◽  
Controller Design ◽  
Magnetic Levitation ◽  
Adaptive Controller ◽  
Closed Loop System ◽  
Actual System ◽  
Levitation System ◽  
Magnetic Levitation System ◽  
Control Accuracy

In view of parameter uncertainty in the magnetic levitation system, the adaptive controller design problem is investigated for the system. Nonlinear adaptive controller based on backstepping is proposed for the design of the actual system with parameter uncertainty. The controller can estimate the uncertainty parameter online so as to improve control accuracy. Theoretical analysis shows that the closed-loop system is stable regardless of parameter uncertainty. Simulation results demonstrate the effectiveness of the presented method.

LPV Based Sliding Mode Control for Limit Protection of Aircraft Engines

2018 ◽  
Author(s):  
Shubo Yang ◽  
Xi Wang
Keyword(s):  
Closed Loop ◽  
Sliding Mode ◽  
Aircraft Engine ◽  
Gain Scheduling ◽  
Engine Control ◽  
Aircraft Engines ◽  
Sliding Surface ◽  
Closed Loop System ◽  
Limit Protection ◽  
The Stability

Limit protection, which frequently exists as an auxiliary part in control systems, is not the primary motive of control but is a necessary guarantee of safety. As in the case of aircraft engine control, the main objective is to provide the desired thrust based on the position of the throttle; nevertheless, limit protection is indispensable to keep the engine operating within limits. There are plenty of candidates that can be applied to design the regulators for limit protection. PID control with gain-scheduling technique has been used for decades in the aerospace industry. This classic approach suggests linearizing the original nonlinear model at different power-level points, developing PID controllers correspondingly, and then scheduling the linear time-invariant (LTI) controllers according to system states. Sliding mode control (SMC) is well-known with mature theories and numerous successful applications. With the one-sided convergence property, SMC is especially suitable for limit protection tasks. In the case of aircraft engine control, SMC regulators have been developed to supplant traditional linear regulators, where SMC can strictly keep relevant outputs within their limits and improve the control performance. In aircraft engine control field, we all know that the plant is a nonlinear system. However, the present design of the sliding controller is carried out with linear models, which severely restricts the valid scope of the controller. Even if the gain scheduling technique is adopted, the stability of the whole systems cannot be theoretically proved. Research of linear parameter varying (LPV) system throws light on a class of nonlinear control problems. In present works, we propose a controller design method based on the LPV model to solve the engines control problem and achieve considerable effectiveness. In this paper, we discuss the design of a sliding controller for limit protection task of aircraft engines, the plant of which is described as an LPV system instead of LTI models. We define the sliding surface as tracking errors and, with the aid of vertex property, present the stability analysis of the closed-loop system on the sliding surface. An SMC law is designed to guarantee that the closed-loop system is globally attracted to the sliding surface. Hot day (ISA+30° C) takeoff simulations based on a reliable turbofan model are presented, which test the proposed method for temperature protection and verify its stability and effectiveness.

scholarly journals A stable proportional–proportional integral tracking controller with self-organizing fuzzy-tuned gains for parallel robots

2019 ◽  
Vol 16 (1) ◽  
pp. 172988141881995
Author(s):  
Francisco G Salas ◽  
Jorge Orrante-Sakanassi ◽  
Raymundo Juarez-del-Toro ◽  
Ricardo P Parada
Keyword(s):  
Stability Analysis ◽  
Performance Index ◽  
Closed Loop ◽  
Tracking Error ◽  
Parallel Robots ◽  
Control Loop ◽  
Closed Loop System ◽  
Proportional Integral ◽  
The Stability ◽  
Self Organizing

Parallel robots are nowadays used in many high-precision tasks. The dynamics of parallel robots is naturally more complex than the dynamics of serial robots, due to their kinematic structure composed by closed chains. In addition, their current high-precision applications demand the innovation of more effective and robust motion controllers. This has motivated researchers to propose novel and more robust controllers that can perform the motion control tasks of these manipulators. In this article, a two-loop proportional–proportional integral controller for trajectory tracking control of parallel robots is proposed. In the proposed scheme, the gains of the proportional integral control loop are constant, while the gains of the proportional control loop are online tuned by a novel self-organizing fuzzy algorithm. This algorithm generates a performance index of the overall controller based on the past and the current tracking error. Such a performance index is then used to modify some parameters of fuzzy membership functions, which are part of a fuzzy inference engine. This fuzzy engine receives, in turn, the tracking error as input and produces an increment (positive or negative) to the current gain. The stability analysis of the closed-loop system of the proposed controller applied to the model of a parallel manipulator is carried on, which results in the uniform ultimate boundedness of the solutions of the closed-loop system. Moreover, the stability analysis developed for proportional–proportional integral variable gains schemes is valid not only when using a self-organizing fuzzy algorithm for gain-tuning but also with other gain-tuning algorithms, only providing that the produced gains meet the criterion for boundedness of the solutions. Furthermore, the superior performance of the proposed controller is validated by numerical simulations of its application to the model of a planar three-degree-of-freedom parallel robot. The results of numerical simulations of a proportional integral derivative controller and a fuzzy-tuned proportional derivative controller applied to the model of the robot are also obtained for comparison purposes.

scholarly journals Distance-Based Formation Control for Quadrotors with Collision Avoidance via Lyapunov Barrier Functions

2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Jawhar Ghommam ◽  
Luis F. Luque-Vega ◽  
Maarouf Saad
Keyword(s):  
Collision Avoidance ◽  
Tracking Control ◽  
Formation Control ◽  
Closed Loop ◽  
Group Formation ◽  
Closed Loop System ◽  
Relative Localization ◽  
Formation Pattern ◽  
Set Up ◽  
The Stability

In this paper, group formation control with collision avoidance is investigated for heterogeneous multiquadrotor vehicles. Specifically, the distance-based formation and tracking control problem are addressed in the framework of leader-follower architecture. In this scheme, the leader is assigned the task of intercepting a target whose velocity is unknown, while the follower quadrotors are arranged to set up a predefined rigid formation pattern, ensuring simultaneously interagent collision avoidance and relative localization. The adopted strategy for the control design consists in decoupling the quadrotor dynamics in a cascaded structure to handle its underactuated property. Furthermore, by imposing constraints on the orientation angles, the follower will never be overturned. Rigorous stability analysis is presented to prove the stability of the entire closed-loop system. Numerical simulation results are presented to validate the proposed control strategy.

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