A Comparison of Different Models for Beam Vibrations From the Standpoint of Control Design

1990 ◽  
Vol 112 (3) ◽  
pp. 349-356 ◽  
Author(s):  
K. A. Morris ◽  
M. Vidyasagar
Keyword(s):  
Distributed System ◽  
Closed Loop ◽  
Control Design ◽  
Viscous Damping ◽  
Closed Loop System ◽  
Rayleigh Damping ◽  
Negative Results ◽  
Finite Dimensional ◽  
Constant Coefficients ◽  
Damping Model

In this paper we analyze different models for beam vibrations from the standpoint of designing finite-dimensional controllers to stabilize the beam vibrations. We show that a distributed system described by an undamped Euler-Bernoulli equation cannot be stabilized by any finite-dimensional controller, i.e., any controller which can be described an ordinary differential equation with constant coefficients. If viscous damping is included, a similar problem occurs in that all the poles can’t be moved to the left of a given vertical line. These negative results should be interpreted as a commentary on the limitations of these models, rather than on the control of real beams. We then show that if a Rayleigh damping model is used, a finite-dimensional controller may be designed to move the closed loop system poles essentially as far to the left in the complex plane as desired. This result will also hold for certain hysteresis damping models. This has implications for the settling time of the vibrations.

Nonlinear Control of Semi-Active MacPherson Suspension System

2012 ◽  
Author(s):  
Olugbenga M. Anubi ◽  
Carl D. Crane
Keyword(s):  
Closed Loop ◽  
Control Design ◽  
Mr Damper ◽  
Suspension System ◽  
Time Domain Simulation ◽  
Closed Loop System ◽  
Output Feedback Controller ◽  
Space Frequency ◽  
Simulation Results ◽  
Active Damper

This paper presents the control design and analysis of a non-linear model of a MacPherson suspension system equipped with a magnetorheological (MR) damper. The model suspension considered incorporates the kinematics of the suspension linkages. An output feedback controller is developed using an ℒ2-gain analysis based on the concept of energy dissipation. The controller is effectively a smooth saturated PID. The performance of the closed-loop system is compared with a purely passive MacPherson suspension system and a semi-active damper, whose damping coefficient is tunned by a Skyhook-Acceleration Driven Damping (SH-ADD) method. Simulation results show that the developed controller outperforms the passive case at both the rattle space, tire hop frequencies and the SH-ADD at tire hop frequency while showing a close performance to the SH-ADD at the rattle space frequency. Time domain simulation results confirmed that the control strategy satisfies the dissipative constraint.

scholarly journals Stabilization of Variable Coefficients Euler-Bernoulli Beam with Viscous Damping under a Force Control in Rotation and Velocity Rotation

2017 ◽  
Vol 9 (6) ◽  
pp. 1
Author(s):  
Bomisso G. Jean Marc ◽  
Tour\'{e} K. Augustin ◽  
Yoro Gozo
Keyword(s):  
Exponential Stability ◽  
Force Control ◽  
Riesz Basis ◽  
Closed Loop ◽  
Variable Coefficients ◽  
Viscous Damping ◽  
Closed Loop System ◽  
Bernoulli Beam ◽  
Spectral System ◽  
Euler Bernoulli Beam

This paper investigates the problem of exponential stability for a damped Euler-Bernoulli beam with variable coefficients clamped at one end and subjected to a force control in rotation and velocity rotation. We adopt the Riesz basis approach for show that the closed-loop system is a Riesz spectral system. Therefore, the exponential stability and the spectrum-determined growth condition are obtained.

scholarly journals Anisochronic Internal Model Control Design

10.14311/482 ◽  
2003 ◽  
Vol 43 (5) ◽  
Author(s):  
T. Vyhlídal ◽  
P. Zítek
Keyword(s):  
System Dynamics ◽  
Internal Model ◽  
Closed Loop ◽  
Control Design ◽  
Internal Model Control ◽  
Loop System ◽  
Closed Loop System ◽  
First Order ◽  
Dominant Pole ◽  
Model Control

The features of internal model control (IMC) design based on the first order anisochronic model are investigated in this paper. The structure of the anisochronic model is chosen in order to fit both the dominant pole and the dominant zero of the system dynamics being approximated. Thanks to its fairly plain structure, the model is suitable for use in IMC design. However, use of the anisochronic model in IMC design may result in so-called neutral dynamics of the closed loop. This phenomenon is studied in this paper via analysing the spectra of the closed loop system.

scholarly journals Dynamic Feedback Backstepping Control for a Class of MIMO Nonaffine Block Nonlinear Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Hai-Yan Li ◽  
Yun-An Hu ◽  
Jian-Cun Ren ◽  
Min Zhu
Keyword(s):  
Nonlinear Systems ◽  
Feedback Linearization ◽  
Closed Loop ◽  
Sliding Mode ◽  
Design Method ◽  
Control Design ◽  
Backstepping Control ◽  
Dynamic Feedback ◽  
Closed Loop System ◽  
Linearization Techniques

For a class of MIMO nonaffine block nonlinear systems, a neural network- (NN-) based dynamic feedback backstepping control design method is proposed to solve the tracking problem. This problem is difficult to be dealt with in the control literature, mainly because the inverse controls of block nonaffine systems are not easy to resolve. To overcome this difficulty, dynamic feedback, backstepping design, sliding mode-like technique, NN, and feedback linearization techniques are incorporated to deal with this problem, in which the NNs are used to approximate and adaptively cancel the uncertainties. It is proved that the whole closed-loop system is stable in the sense of Lyapunov. Finally, simulations verify the effectiveness of the proposed scheme.

scholarly journals From stable walking to steering of a 3D bipedal robot with passive point feet

Robotica ◽  
2012 ◽  
Vol 30 (7) ◽  
pp. 1119-1130 ◽  
Author(s):  
Ching-Long Shih ◽  
J. W. Grizzle ◽  
Christine Chevallereau
Keyword(s):  
Closed Loop ◽  
Control Design ◽  
Asymptotically Stable ◽  
Closed Loop System ◽  
Bipedal Robot ◽  
Walking Gait ◽  
Straight Line ◽  
Natural Symmetry ◽  
Single Support Phase ◽  
Support Phase

SUMMARYThis paper exploits a natural symmetry present in a 3D robot in order to achieve asymptotically stable steering. The robot under study is composed of 5-links and unactuated point feet; it has 9 DoF (degree-of-freedom) in the single-support phase and six actuators. The control design begins with a hybrid feedback controller that stabilizes a straight-line walking gait for the 3D bipedal robot. The closed-loop system (i.e., robot plus controller) is shown to be equivariant under yaw rotations, and this property is used to construct a modification of the controller that has a local, but uniform, input-to-state stability (ISS) property, where the input is the desired turning direction. The resulting controller is capable of adjusting the net yaw rotation of the robot over a step in order to steer the robot along paths with mild curvature. An interesting feature of this work is that one is able to control the robot's motion along a curved path using only a single predefined periodic motion.

Control Design for the System of Manipulator Handling a Flexible Payload With Input Constraints

2018 ◽  
Author(s):  
Shuyang Liu ◽  
Reza Langari ◽  
Yuanchun Li
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Closed Loop ◽  
Semigroup Theory ◽  
Control Design ◽  
Hyperbolic Function ◽  
Control Law ◽  
Input Constraints ◽  
Closed Loop System ◽  
Simulation Results

In this paper, we consider the control design for manipulator handling a flexible payload in the presence of input constraints. The dynamics of the system is described by coupled ordinary differential equation and a partial differential equation. Considering actuators saturation, the proposed control law applies a smooth hyperbolic function to handle the effect of the input constraints. The asymptotic stability of the closed-loop system is proved by using semigroup theory and extended LaSalle’s Invariance Principle. Simulation results show that the proposed controller is effective.

scholarly journals Robust Optimal Attitude Controller for MIMO Uncertain Hexarotor MAVs: Disturbance Observer-Based

2016 ◽  
Vol 2016 ◽  
pp. 1-24 ◽  
Author(s):  
Nurul Dayana Salim ◽  
Dafizal Derawi ◽  
Hairi Zamzuri ◽  
Kenzo Nonami ◽  
Mohd Azizi Abdul Rahman
Keyword(s):  
Nonlinear Dynamics ◽  
Attitude Control ◽  
Disturbance Observer ◽  
Closed Loop ◽  
Control Design ◽  
Loop System ◽  
Parametric Uncertainties ◽  
Time Varying ◽  
Closed Loop System ◽  
External Time

This paper proposes a robust optimal attitude control design for multiple-input, multiple-output (MIMO) uncertain hexarotor micro aerial vehicles (MAVs) in the presence of parametric uncertainties, external time-varying disturbances, nonlinear dynamics, and coupling. The parametric uncertainties, external time-varying disturbances, nonlinear dynamics, and coupling are treated as the total disturbance in the proposed design. The proposed controller is achieved in two simple steps. First, an optimal linear-quadratic regulator (LQR) controller is designed to guarantee that the nominal closed-loop system is asymptotically stable without considering the total disturbance. After that, a disturbance observer is integrated into the closed-loop system to estimate the total disturbance acting on the system. The total disturbance is compensated by a compensation input based on the estimated total disturbance. Robust properties analysis is given to prove that the state is ultimately bounded in specified boundaries. Simulation results illustrate the robustness of the disturbance observer-based optimal attitude control design for hovering and aggressive flight missions in the presence of the total disturbance.

scholarly journals Model Updating for Systems with General Proportional Damping Using Complex FRFs

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Xinhai Wu ◽  
Huan He ◽  
Yang Liu ◽  
Guoping Chen
Keyword(s):  
Model Updating ◽  
Damping Ratio ◽  
Viscous Damping ◽  
Rayleigh Damping ◽  
Damping Matrix ◽  
Modal Damping Ratio ◽  
Modal Damping ◽  
Resonance Frequencies ◽  
Updating Procedure ◽  
Damping Model

In this paper, we propose a model updating method for systems with nonviscous proportional damping. In comparison to the traditional viscous damping model, the introduction of nonviscous damping will not only reduce the vibration of the system but also change the resonance frequencies. Therefore, most of the existing updating methods cannot be directly applied to systems with nonviscous damping. In many works, for simplicity, the Rayleigh damping model has been applied in the model updating procedure. However, the assumption of Rayleigh damping may result in large errors of damping for higher modes. To capture the variation of modal damping ratio with frequency in a more general way, the diagonal elements of the modal damping matrix and relaxation parameter are updated to characterize the damping energy dissipation of the structure by the proposed method. Spatial and modal incompleteness are both discussed for the updating procedure. Numerical simulations and experimental examples are adopted to validate the effectiveness of the proposed method. The results show that the systems with general proportional damping can be predicted more accurately by the proposed updating method.

H∞ CONTROL DESIGN OF A MULTITANK SYSTEM

2020 ◽  
Vol 70 (3) ◽  
pp. 26-33
Author(s):  
Andrey Yonchev ◽  
Martin Mladenov
Keyword(s):  
Mathematical Model ◽  
Modeling And Simulation ◽  
Closed Loop ◽  
Controller Design ◽  
Control Design ◽  
Loop System ◽  
Optimal Controller ◽  
Closed Loop System ◽  
Pump Operation ◽  
Physical Plant

This paper considers MATLAB® modeling and simulation of H∞ controller and its realization on the Multitank System. The first task is to study the physical plant of the laboratory Multitank System and to apply a given mathematical model for optimal controller design. The general objective of the derived regulator is to reach and stabilize the level in the tanks by an adjustment of the pump operation or/and valves settings. Finally, it is necessary to simulate the obtained closed-loop system and to test its workability.

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