OUTPUT FEEDBACK ADAPTIVE VARIABLE STRUCTURE CONTROL OF CHAOS IN LORENZ SYSTEM

Based on the variable structure model reference adaptive control (VS-MRAC) theory, a new control system for the control of chaos in Lorenz system, using only the measured output variable, is designed. For the derivation of the control law, it is assumed that the parameters of the model are unknown. Moreover, it is assumed that a disturbance input is present in the system. It is shown that in the closed-loop system, the output variable tracks a given reference trajectory, and the state vector converges to the equilibrium state. Digital simulation results show that the closed-loop system has good transient behavior and robustness to the uncertainties and disturbance input.

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Adaptive Contact Force Control of a Flexible Beam Using Output Feedback

10.1115/imece2000-2312 ◽

2000 ◽

Author(s):

Woosoon Yim

Keyword(s):

Contact Force ◽

Contact Surface ◽

Force Control ◽

Closed Loop ◽

Force Measurement ◽

Transient Behavior ◽

Loop System ◽

Flexible Beam ◽

Reference Trajectory ◽

Closed Loop System

Abstract This paper presents an adaptive force trajectory control of a flexible beam using a piezoceramic actuator. Based on the adaptive backstepping method, a force control system using only force measurement is designed. For the derivation of the control law, it is assumed that parameters of the beam and contact surface stiffness are unknown. It is shown that in the closed-loop system, the contact force tracks a given reference trajectory and the beam vibration is suppressed as well. Digital simulations results show that the closed-loop system has good transient behavior and robust performance in the presence of uncertainties in the parameters of the flexible beam and the contact surface.

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Application of Anytime Control to an Inherently Unstable Physical System

Volume 4A: Dynamics, Vibration, and Control ◽

10.1115/imece2015-51369 ◽

2015 ◽

Author(s):

Wayne Maxwell ◽

Al Ferri ◽

Bonnie Ferri

Keyword(s):

Closed Loop ◽

Initial Conditions ◽

Transient Behavior ◽

Open Loop ◽

Loop System ◽

Closed Loop System ◽

Pendulum System ◽

Inverted Pendulum System ◽

Lqr Controller ◽

Two Stages

This paper extends the use of closed-loop anytime control to systems that are inherently unstable in the open-loop. Previous work has shown that anytime control is very effective in compensating for occasional missed deadlines in the computer processor. When misses occur, the control law is truncated or partially executed. However, the previous work assumed that the open-loop system was stable. In this paper, the anytime strategy is applied to an inverted pendulum system. An LQR controller with estimated state feedback is designed and decomposed into two stages. Both stages are implemented most of the time, but in a small percentage of time, only the first stage is applied, with the resulting closed-loop system being unstable for short periods of time. The statistical performance of the closed-loop system is studied using Monte-Carlo simulations. It is seen that, on average, the closed-loop performance is very close to that of the full-order controller as long as the miss rate is relatively small. However, the variance of the response shows much higher dependence on the miss rate, suggesting that the response becomes more unpredictable. At a critical value of miss rate, the closed-loop system is unstable. The critical miss rate found through simulation is seen to correlate well with the results of a deterministic stability analysis. The statistics on the settling time are also studied, and shown to grow longer as the miss rate increases. The transient behavior of the system is studied for a range of initial conditions.

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Adaptive Robust Quadratic Stabilization Tracking Control for Robotic System with Uncertainties and External Disturbances

Journal of Control Science and Engineering ◽

10.1155/2014/715250 ◽

2014 ◽

Vol 2014 ◽

pp. 1-10 ◽

Cited By ~ 4

Author(s):

Jinzhu Peng ◽

Yan Liu

Keyword(s):

Closed Loop ◽

Robot Manipulator ◽

Variable Structure ◽

Robotic System ◽

Loop System ◽

Closed Loop System ◽

Hybrid Scheme ◽

External Disturbances ◽

Control Approach ◽

Quadratic Stabilization

An adaptive robust quadratic stabilization tracking controller with hybrid scheme is proposed for robotic system with uncertainties and external disturbances. The hybrid scheme combines computed torque controller (CTC) with an adaptive robust compensator, in which variable structure control (VSC) andH∞optimal control approaches are adopted. The uncertain robot manipulator is mainly controlled by CTC, the VSC is used to eliminate the effect of the uncertainties and ensure global stability, andH∞approach is designed to achieve a certain tracking performance of closed-loop system. A quadratic stability approach, which allows separate treatment of parametric uncertainties, is used to reduce the conservatism of the conventional robust control approach. It can be also guaranteed that all signals in closed-loop system are bounded. The validity of the proposed control scheme is shown by computer simulation of a two-link robotic manipulator.

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Modeling and Dynamic Behaviors of a Rotor Suspended in Electromagnetic Bearings

13th Biennial Conference on Mechanical Vibration and Noise: Modal Analysis, Modeling, Diagnostics, and Control — Analytical and Experimental ◽

10.1115/detc1991-0366 ◽

1991 ◽

Author(s):

Jiankang Xu ◽

Youbai Xie ◽

Junhong Mao

Keyword(s):

Closed Loop ◽

Dynamic Stiffness ◽

Digital Simulation ◽

Loop System ◽

Closed Loop System ◽

Electromagnetic Forces ◽

Dynamic Behaviors

Abstract A closed loop system composed of a rotor in electromagnetic bearings and a PID (proportion-integration-differentiation) controller is developed. With the active electromagnetic forces the rotor 50 millimeters in diameter can be fully suspended in two radial electromagnetic bearings and can be driven from zero up to 3000 rpm. This closed loop system is modeled and its dynamic behaviors are analized by digital simulation. The influence of controller parameters on motion of the rotor and the relation between controller parameters and dynamic stiffness of the electromagnetic bearings are presented.

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Adaptive Control of a Smart Projectile Fin With Unknown High-Frequency Gain by Piezoelectric Actuation

Volume 9: Mechanical Systems and Control, Parts A, B, and C ◽

10.1115/imece2007-41216 ◽

2007 ◽

Author(s):

Venkat Mudupu ◽

Sahjendra Singh ◽

Woosoon Yim

Keyword(s):

Adaptive Control ◽

Control System ◽

High Frequency ◽

Closed Loop ◽

Aerodynamic Force ◽

Angular Rate ◽

Loop System ◽

Reference Trajectory ◽

Piezoelectric Bimorph ◽

Closed Loop System

This paper delves into adaptive control of a smart projectile fin with unknown high frequency gain using a piezoelectric bimorph. The hollow projectile smart fin is actuated using a cantilevered piezoelectric bimorph that is completely enclosed within the fin. The model of the smart fin system includes the aerodynamic moment which is a function of the angle of attack of the projectile. The rotation angle of the fin is controlled by deforming the piezoelectric bimorph which is hinged at the tip of the rigid fin. It is assumed that fin parameters as well as the high frequency gain of the model are unknown. Moreover, the model includes an unknown bounded time varying aerodynamic disturbance. An adaptive control system using the Nussbaum gain is designed. The structure of the control system is independent of the dimension of the flexible fin model. This is important because the fin model has large number of flexible modes. For the design of the control law, a linear combination of the fin angle and fin angular rate is chosen as the controlled output variable. In the closed loop system, all the signals are bounded and the fin angle tracks the reference trajectory. Simulation results are presented along with the experimental validation done using the subsonic wind tunnel at the University of Nevada, Las Vegas (UNLV). Both simulation and experimental results show that in the closed-loop system, the fin angle is precisely controlled in spite of the uncertainties in the fin parameters and the aerodynamic force.

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Sliding Mode Control and Elastic Mode Stabilization of a Robotic Arm With Flexible Links

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.2896473 ◽

1991 ◽

Vol 113 (4) ◽

pp. 669-676 ◽

Cited By ~ 33

Author(s):

P. J. Nathan ◽

S. N. Singh

Keyword(s):

Closed Loop ◽

Joint Angle ◽

Sliding Mode ◽

Variable Structure ◽

Terminal State ◽

Loop System ◽

Robotic Arm ◽

Closed Loop System ◽

Elastic Mode ◽

Mode Stabilization

This paper treats the question of control of an elastic robotic arm of two links based on variable structure system (VSS) theory and pole assignment technique for stabilization. A discontinuous joint angle control law, based on VSS theory, is designed which accomplishes asymptotic decoupled joint angle trajectory tracking. In the closed-loop system, the trajectories are attracted toward a chosen hypersurface in the state space and then slide along it. Although, joint angles are controlled using variable structure control (VSC) law, the flexible modes of the links are excited. Using center manifold theory, it is shown that the closed-loop system, including the sliding mode controller, is stable. Based on a linearized model about the terminal state, a stabilizer is designed using pole assignment technique to control the elastic oscillations of the links. A control logic is included which switches the stabilizer at the instant when the joint angle trajectory enters a specified neighborhood of the terminal state. Simulation results are presented to show that in the closed-loop system, accurate joint angle trajectory tracking, and elastic mode stabilization are accomplished in the presence of payload uncertainty.

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