Linear Feedback Control of Position and Contact Force for a Nonlinear Constrained Mechanism

1990 ◽  
Vol 112 (4) ◽  
pp. 640-645 ◽  
Author(s):  
H. McClamroch ◽  
D. Wang
Keyword(s):  
Feedback Control ◽  
Closed Loop ◽  
Control Design ◽  
Algebraic Model ◽  
Differential Algebraic Equations ◽  
Linear Feedback ◽  
Control Law ◽  
Algebraic Equations ◽  
Constraint Force ◽  
Constrained System

A feedback control problem for a constrained mechanism is formulated and solved. The mechanism is controlled by forces applied to the mechanism which are to be adjusted according to a linear control law, based on feedback of the positions and velocities of the mechanism and feedback of the constraint force on the mechanism. The control objective is to achieve accurate and robust local regulation of the motion of the mechanism and of the constraint force on the mechanism. Derivation of a suitable control law is significantly complicated by the nonclassical nature of the differential-algebraic model of the constrained system and by the nonlinear characteristics of the model. The control design approach involves use of a certain nonlinear transformation which leads to a set of decoupled differential-algebraic equations; classical control design methodology can be applied to these latter equations. An example of a planar mechanism is studied in some detail, for two different regulation objectives. Specific control laws are developed using the described methodology. Comparisons are made with a closed loop system, where the control law is derived without proper consideration of the constraint force. Computer simulations are presented to demonstrate the several closed-loop properties.

Pointwise Optimal Control of Dynamical Systems Described by Constrained Coordinates

1999 ◽  
Vol 121 (4) ◽  
pp. 594-598 ◽  
Author(s):  
V. Radisavljevic ◽  
H. Baruh
Keyword(s):  
Optimal Control ◽  
Dynamical Systems ◽  
Feedback Control ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Differential Algebraic Equations ◽  
Control Law ◽  
Algebraic Equations ◽  
The Stability ◽  
The Mathematical Model

A feedback control law is developed for dynamical systems described by constrained generalized coordinates. For certain complex dynamical systems, it is more desirable to develop the mathematical model using more general coordinates then degrees of freedom which leads to differential-algebraic equations of motion. Research in the last few decades has led to several advances in the treatment and in obtaining the solution of differential-algebraic equations. We take advantage of these advances and introduce the differential-algebraic equations and dependent generalized coordinate formulation to control. A tracking feedback control law is designed based on a pointwise-optimal formulation. The stability of pointwise optimal control law is examined.

Active Compressor Surge Control Using Piston Actuation

2011 ◽  
Author(s):  
Nur Uddin ◽  
Jan Tommy Gravdahl
Keyword(s):  
Feedback Control ◽  
Closed Loop ◽  
Linear Feedback ◽  
Control Law ◽  
Asymptotically Stable ◽  
Nonlinear Feedback Control ◽  
Nonlinear Feedback ◽  
Closed Loop System ◽  
Linear Feedback Control ◽  
Surge Control

A novel approach to active surge control in compressors using piston actuation is presented. Two control laws are compared in order to evaluate the feasibility of implementing the concept. The first control law is a nonlinear feedback control derived by using backstepping and the second one is a linear feedback control derived by analyzing the eigenvalues of the linearized system around the operating point. The nonlinear feedback control law makes the closed loop system globally asymptotically stable (GAS) and uses full states feedback. The linear feedback control is only using feedback from plenum pressure and piston velocity and the removal of the mass flow feedback is advantageous for implementation. The closed loop system with the linear feedback control is locally asymptotically stable around the operating point. Simulations show that both controllers are capable of stabilizing surge.

Optimization approach to the constrained regulation problem for linear continuous-time fractional-order systems

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Xindong Si ◽  
Hongli Yang
Keyword(s):  
Feedback Control ◽  
Fractional Order ◽  
State Feedback Control ◽  
Invariant Sets ◽  
Linear Feedback ◽  
Control Law ◽  
Optimization Approach ◽  
Fractional Order Systems ◽  
Linear Feedback Control ◽  
Computational Point

AbstractThis paper deals with the Constrained Regulation Problem (CRP) for linear continuous-times fractional-order systems. The aim is to find the existence conditions of linear feedback control law for CRP of fractional-order systems and to provide numerical solving method by means of positively invariant sets. Under two different types of the initial state constraints, the algebraic condition guaranteeing the existence of linear feedback control law for CRP is obtained. Necessary and sufficient conditions for the polyhedral set to be a positive invariant set of linear fractional-order systems are presented, an optimization model and corresponding algorithm for solving linear state feedback control law are proposed based on the positive invariance of polyhedral sets. The proposed model and algorithm transform the fractional-order CRP problem into a linear programming problem which can readily solved from the computational point of view. Numerical examples illustrate the proposed results and show the effectiveness of our approach.

An implicit class of continuous dynamical system with data-sample outputs: a robust approach

2019 ◽  
Vol 37 (2) ◽  
pp. 589-606
Author(s):  
Raymundo Juarez ◽  
Vadim Azhmyakov ◽  
A Tadeo Espinoza ◽  
Francisco G Salas
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Dynamical Systems ◽  
Nonlinear Models ◽  
Differential Algebraic Equations ◽  
Linear Feedback ◽  
Continuous Systems ◽  
Algebraic Equations ◽  
Nonlinear Dynamical ◽  
Ellipsoid Method ◽  
Invariant Ellipsoid

Abstract This paper addresses the problem of robust control for a class of nonlinear dynamical systems in the continuous time domain. We deal with nonlinear models described by differential-algebraic equations (DAEs) in the presence of bounded uncertainties. The full model of the control system under consideration is completed by linear sampling-type outputs. The linear feedback control design proposed in this manuscript is created by application of an extended version of the conventional invariant ellipsoid method. Moreover, we also apply some specific Lyapunov-based descriptor techniques from the stability theory of continuous systems. The above combination of the modified invariant ellipsoid approach and descriptor method makes it possible to obtain the robustness of the designed control and to establish some well-known stability properties of dynamical systems under consideration. Finally, the applicability of the proposed method is illustrated by a computational example. A brief discussion on the main implementation issue is also included.

Dynamic Modeling and Simulation of Parallel Mechanisms Using the Virtual Spring Approach

2000 ◽  
Author(s):  
Jiegao Wang ◽  
Clément M. Gosselin ◽  
Li Cheng
Keyword(s):  
Closed Loop ◽  
Differential Algebraic Equations ◽  
Parallel Mechanisms ◽  
Algebraic Equations ◽  
New Approach ◽  
Flexible Links ◽  
Simulation Results ◽  
Loop Constraints ◽  
Virtual Springs ◽  
Good Agreement

Abstract A new approach for the dynamic simulation of parallel mechanisms or mechanical systems is presented in this paper. This approach uses virtual springs and dampers to include the closed-loop constraints thereby avoiding the solution of differential-algebraic equations. Examples illustrating the approach are given and include the four-bar mechanism with both rigid and flexible links as well as the 6-dof Gough-Stewart platform. Simulation results are given for the four-bar linkages and the 6-dof manipulator. The results achieve a good agreement with the results obtained from other conventional approaches.

scholarly journals Continuous-Time Perfect Control Algorithm—A State Feedback Approach

2021 ◽  
Vol 11 (16) ◽  
pp. 7466
Author(s):  
Marek Krok ◽  
Wojciech P. Hunek ◽  
Paweł Majewski
Keyword(s):  
Design Process ◽  
Process Simulation ◽  
Continuous Time ◽  
Control Algorithm ◽  
State Feedback ◽  
Closed Loop ◽  
Control Design ◽  
Control Law ◽  
New Approach

In this paper, a new approach to the continuous-time perfect control algorithm is given. Focusing on the output derivative, it is shown that the discussed control law can effectively be implemented in terms of state-feedback scenarios. Moreover, the application of nonunique matrix inverses is also taken into consideration during the perfect control design process. Simulation examples given within this work allow us to showcase the main properties obtained for continuous-time perfect control closed-loop plants.

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