Sensitivity Reduction of Constraint Forces and Position Control for Mechanical Descriptor Systems

1997 ◽  
Vol 119 (2) ◽  
pp. 286-289
Author(s):  
Dan-chi Jiang ◽  
Wei-Yong Yan ◽  
K. L. Teo
Keyword(s):  
State Feedback ◽  
Closed Loop ◽  
Position Control ◽  
Design Procedure ◽  
Descriptor Systems ◽  
Algebraic Riccati Equation ◽  
Systematic Design ◽  
Closed Loop System ◽  
Constraint Forces ◽  
Constrained System

This paper deals with the position and force control for mechanical systems with holonomic constraints. Our concern is the design of a feedback controller such that the closed-loop system has a satisfactory transient response and is less sensitive to various types of disturbances. Using an appropriate transformation, the constrained system is converted into an unconstrained system of lower order. Then, an H∞, control problem involving the reduced system is formulated. In the case of state feedback, a systematic design procedure for solving the problem is presented, where the key step is the solution of an algebraic Riccati equation. An example is given to illustrate the effectiveness of the proposed method.

scholarly journals Indefinite LQ Problem for Irregular Singular Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Qingxiang Fang ◽  
Jigen Peng ◽  
Feilong Cao
Keyword(s):  
Optimal Control ◽  
Riccati Equation ◽  
State Feedback ◽  
Closed Loop ◽  
Singular Systems ◽  
Algebraic Riccati Equation ◽  
Closed Loop System ◽  
State Pair ◽  
Lq Problem ◽  
Control State

The indefinite LQ problem for irregular singular systems is investigated. Under some general conditions, the optimal control-state pair is obtained by solving an algebraic Riccati equation. The optimal control is synthesized as state feedback. All the finite poles of the closed-loop system are located on the left-half complex plane. An example is given to show the validity of the proposed conclusion.

Dissipative Control of Singular Systems by Proportional Plus Derivative State Feedback

2012 ◽  
Vol 246-247 ◽  
pp. 826-831
Author(s):  
Shuang Yun Xing ◽  
Xin Jing ◽  
Yang Cao
Keyword(s):  
State Feedback ◽  
Closed Loop ◽  
Singular Systems ◽  
Uncertain System ◽  
Loop System ◽  
Descriptor Systems ◽  
Control Synthesis ◽  
Closed Loop System ◽  
Dissipative Control ◽  
Derivative Matrix

This article deals with the problem of dissipative control synthesis for a class of descriptor systems with uncertainties in the derivative matrix. Attention is focused on the design of a proportional plus derivative (PD) state feedback, which guarantees that the closed-loop system is robustly stable and strict dissipative. Firstly, a sufficient condition for the closed-loop system is robustly stable and strict dissipative is presented by using a simple idea of changing the problem to the corresponding problem of an augmented uncertain system. Then, a PD controller is constructed by solving LMIs. Finally, a numerical example is given to demonstrate that the proposed method is effective.

scholarly journals Global Stabilization of High-Order Time-Delay Nonlinear Systems under a Weaker Condition

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Nengwei Zhang ◽  
Enbin Zhang ◽  
Fangzheng Gao
Keyword(s):  
Nonlinear Systems ◽  
State Feedback ◽  
Closed Loop ◽  
Design Procedure ◽  
High Order ◽  
Global Stabilization ◽  
Closed Loop System ◽  
System A ◽  
Continuous State ◽  
High Order Time

Under the weaker condition on the system growth, this paper further investigates the problem of global stabilization by state feedback for a class of high-order nonlinear systems with time-varying delays. By skillfully using the homogeneous domination approach, a continuous state feedback controller is successfully designed, which preserves the equilibrium at the origin and guarantees the global asymptotic stability of the resulting closed-loop system. A simulation example is given to demonstrate the effectiveness of the proposed design procedure.

scholarly journals Robust H∞ Loop Shaping Controller Synthesis for SISO Systems by Complex Modular Functions

2021 ◽  
Vol 26 (1) ◽  
pp. 21
Author(s):  
Ahmad Taher Azar ◽  
Fernando E. Serrano ◽  
Nashwa Ahmad Kamal
Keyword(s):  
Design Methodology ◽  
Closed Loop ◽  
Complex Analysis ◽  
Controller Design ◽  
Filter Design ◽  
Design Procedure ◽  
Elliptic Functions ◽  
Loop System ◽  
Closed Loop System ◽  
Loop Shaping

In this paper, a loop shaping controller design methodology for single input and a single output (SISO) system is proposed. The theoretical background for this approach is based on complex elliptic functions which allow a flexible design of a SISO controller considering that elliptic functions have a double periodicity. The gain and phase margins of the closed-loop system can be selected appropriately with this new loop shaping design procedure. The loop shaping design methodology consists of implementing suitable filters to obtain a desired frequency response of the closed-loop system by selecting appropriate poles and zeros by the Abel theorem that are fundamental in the theory of the elliptic functions. The elliptic function properties are implemented to facilitate the loop shaping controller design along with their fundamental background and contributions from the complex analysis that are very useful in the automatic control field. Finally, apart from the filter design, a PID controller loop shaping synthesis is proposed implementing a similar design procedure as the first part of this study.

The Swing Control of Cranes with Variable Rope Length Based on Linear Time Varying System Theory

2012 ◽  
Vol 461 ◽  
pp. 763-767
Author(s):  
Li Fu Wang ◽  
Zhi Kong ◽  
Xin Gang Wang ◽  
Zhao Xia Wu
Keyword(s):  
State Feedback ◽  
Closed Loop ◽  
Linear Time ◽  
Feedback Stabilization ◽  
Time Varying ◽  
Closed Loop System ◽  
Overhead Cranes ◽  
Time Varying Systems ◽  
Time Invariant ◽  
Time Invariant System

In this paper, following the state-feedback stabilization for time-varying systems proposed by Wolovich, a controller is designed for the overhead cranes with a linearized parameter-varying model. The resulting closed-loop system is equivalent, via a Lyapunov transformation, to a stable time-invariant system of assigned eigenvalues. The simulation results show the validity of this method.

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.

Global fixed-time stabilization for a class of uncertain high-order nonlinear systems with dead-zone input nonlinearity

2018 ◽  
Vol 41 (7) ◽  
pp. 1888-1895
Author(s):  
Fangzheng Gao ◽  
Yanling Shang ◽  
Yuqiang Wu ◽  
Yanhong Liu
Keyword(s):  
Nonlinear Systems ◽  
State Feedback ◽  
Closed Loop ◽  
Dead Zone ◽  
Fixed Time ◽  
High Order ◽  
Closed Loop System ◽  
Sign Function ◽  
Input Nonlinearity ◽  
Power Integrator

This paper considers the problem of global fixed-time stabilization for a class of uncertain high-order nonlinear systems. One distinct characteristic of this work is that the system under consideration possesses the dead-zone input nonlinearity. By delicately combining the sign function with a power integrator technique, a state feedback controller is designed such that the states of the resulting closed-loop system converge to the origin within a fixed time. A simulation example is provided to illustrate the effectiveness of the proposed approach.

Observer-Based Control of a Class of Switched Fuzzy Systems

2014 ◽  
Vol 945-949 ◽  
pp. 2539-2542
Author(s):  
Hong Yang ◽  
Huan Huan Lü ◽  
Le Zhang
Keyword(s):  
Fuzzy System ◽  
Fuzzy Systems ◽  
Function Method ◽  
State Feedback ◽  
Closed Loop ◽  
External Disturbance ◽  
Asymptotically Stable ◽  
Closed Loop System ◽  
Lyapunov Function Method ◽  
Switching State

For the non-measurable states, a control of switched fuzzy systems is presented based on observer. Using switching technique and multiple Lyapunov function method, the fuzzy observer is built to ensure that for all allowable external disturbance the relevant closed-loop system is asymptotically stable. Moreover, switching strategy achieving system global asymptotic stability of the switched fuzzy system is given. In this model, a switching state feedback controller is presented. A simulation shows the feasibility and the effectiveness of the method.

scholarly journals Conventional and Fuzzy Force Control in Robotised Machining

2013 ◽  
Vol 210 ◽  
pp. 178-185 ◽  
Author(s):  
Zenon Hendzel ◽  
Andrzej Burghardt ◽  
Piotr Gierlak ◽  
Marcin Szuster
Keyword(s):  
Neural Networks ◽  
Artificial Neural Networks ◽  
Force Control ◽  
Closed Loop ◽  
Position Control ◽  
Control Strategies ◽  
Closed Loop System ◽  
Fuzzy Logic Systems ◽  
Complex Control System ◽  
Artificial Neural

This article presents an application of the hybrid position-force control of the robotic manipulator with use of artificial neural networks and fuzzy logic systems in complex control system. The mathematical description of the manipulator and a closed-loop system are presented. In the position control were used the PD controller and artificial neural networks, which compensate nonlinearities of the manipulator. The paper presents mainly the application of various strategies of the force control. The force control strategies using conventional controllers P, PI, PD, PID and fuzzy controllers are presented and discussed. All of the control methods were verified on the real object in order to make a comparison of a control quality.

Positive Finite-Time Stabilization for Discrete-Time Linear Systems

2014 ◽  
Vol 137 (1) ◽  
Author(s):  
Wenping Xue ◽  
Kangji Li
Keyword(s):  
Linear Systems ◽  
Discrete Time ◽  
Finite Time ◽  
State Feedback ◽  
Closed Loop ◽  
Linear Matrix ◽  
Closed Loop System ◽  
Initial State ◽  
Finite Time Stability ◽  
Time Linear

In this paper, a new finite-time stability (FTS) concept, which is defined as positive FTS (PFTS), is introduced into discrete-time linear systems. Differently from previous FTS-related papers, the initial state as well as the state trajectory is required to be in the non-negative orthant of the Euclidean space. Some test criteria are established for the PFTS of the unforced system. Then, a sufficient condition is proposed for the design of a state feedback controller such that the closed-loop system is positively finite-time stable. This condition is provided in terms of a series of linear matrix inequalities (LMIs) with some equality constraints. Moreover, the requirement of non-negativity of the controller is considered. Finally, two examples are presented to illustrate the developed theory.

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