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.

LOCAL BIFURCATION CONTROL IN A ROTOR-MAGNETIC BEARING SYSTEM

2003 ◽  
Vol 13 (04) ◽  
pp. 951-956 ◽  
Author(s):  
J. C. JI ◽  
COLIN H. HANSEN
Keyword(s):  
Hopf Bifurcation ◽  
Feedback Control ◽  
Normal Forms ◽  
Magnetic Bearing ◽  
Linear Feedback ◽  
Nonlinear Feedback Control ◽  
Nonlinear Feedback ◽  
Linear Feedback Control ◽  
Linearized System ◽  
Bearing System

Linear-plus-nonlinear feedback control is used to stabilize Hopf bifurcation in a rotor-magnetic bearing system, for which the linearized system possesses a double zero eigenvalues. The addition of nonlinear (quadratic) terms to the original linear feedback control formulation is used to modify the coefficients of the nonlinear terms in the reduced normal forms. It is found that feedback control incorporating certain quadratic terms renders the Hopf bifurcation supercritical. Finally, illustrative examples are given to verify the analytical results.

scholarly journals Using Sine Function-Based Nonlinear Feedback to Control Water Tank Level

Energies ◽  
2021 ◽  
Vol 14 (22) ◽  
pp. 7602
Author(s):  
Jian Zhao ◽  
Xianku Zhang ◽  
Yilin Chen ◽  
Pengrui Wang
Keyword(s):  
Feedback Control ◽  
Linear Feedback ◽  
Water Tank ◽  
Sine Function ◽  
Proportional Integral Derivative ◽  
Nonlinear Feedback Control ◽  
Nonlinear Feedback ◽  
Linear Feedback Control ◽  
Mathematic Modeling ◽  
Control Water

This manuscript addresses the feasibility and significance of using a sine function to modify the system error of a normal linear feedback control to achieve more efficient capabilities in terms of energy-saving. The associated mathematic modeling and assessment were demonstrated by presenting a case analysis on the capabilities of controlling water level for a single tank. The principle of robust control and the theories and detailed algorithm of Lyapunov stability were applied to assess the result derived by novel nonlinear feedback in the form of sine function for optimizing the robustness of the PID (Proportional–Integral–Derivative) controller and economizing energy. Two control simulations are compared: nonlinear feedback control using a sine function and conventional fuzzy control. The results reveal that using the nonlinear feedback controller, a reduction of up to 32.9% of the average controlled quantity is achieved, and the performance index is improved by 24.0% with satisfactory robustness. The proposed nonlinear feedback control using a sine function provides simplicity, convenient implementation, and energy efficiency.

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.

Semi-global output regulation for discrete-time singular linear systems with input saturation via composite nonlinear feedback control

2016 ◽  
Vol 39 (3) ◽  
pp. 352-360 ◽  
Author(s):  
Xiaoyan Lin ◽  
Dongyun Lin ◽  
Weiyao Lan
Keyword(s):  
Feedback Control ◽  
Linear Systems ◽  
Discrete Time ◽  
Input Saturation ◽  
Output Regulation ◽  
Control Law ◽  
Nonlinear Feedback Control ◽  
Nonlinear Feedback ◽  
Composite Nonlinear Feedback ◽  
Singular Linear Systems

The semi-global output regulation problem of multi-variable discrete-time singular linear systems with input saturation is investigated in this paper. A composite nonlinear feedback control law is constructed by using a low gain feedback technique for semi-global stabilisation of discrete-time singular linear systems with input saturation. The sufficient solvability conditions of the semi-global output regulation problem by composite nonlinear feedback control are established. When the composite nonlinear feedback control law is reduced to a linear control law, the solvability conditions are an exact discrete-time counterpart of the semi-global output regulation problem of continuous-time singular linear systems. With the extra control freedom of the nonlinear part in the composite nonlinear feedback control law, the transient performance of the closed-loop system can be improved by carefully choosing the linear feedback gain and the nonlinear feedback gain. The design procedure of the composite nonlinear feedback control law and the improvement of the transient performance are illustrated by a numerical example.

Compound control for autonomous docking to a three-axis tumbling target

2018 ◽  
Vol 41 (4) ◽  
pp. 911-924
Author(s):  
Dong Ye ◽  
Wei Lu ◽  
Zhongcheng Mu
Keyword(s):  
Feedback Control ◽  
Attitude Control ◽  
Sliding Mode ◽  
Control Law ◽  
Nonlinear Feedback Control ◽  
Nonlinear Feedback ◽  
Integral Sliding Mode ◽  
Compound Control ◽  
Tumbling Target ◽  
Autonomous Docking

This paper investigates the coupled position and attitude control problem of an on-orbit servicing spacecraft autonomous docking to a three-axis freely tumbling target in space. A compound control law is presented to guarantee that the docking port of servicing spacecraft is always directing towards the docking port of tumbling target, which is accomplished through the combination of the coupled relative position tracking and relative attitude control. For the purpose of avoiding collision between the two spacecraft, a two-phased approach for the terminal approaching the tumbling target is proposed. Also, the compound control is composed of a nonlinear feedback control law and an integral sliding mode control law. The nonlinear feedback control law is mainly used to track the system command and the integral sliding mode control law is mainly used to deal with the external disturbances and system uncertainties to enhance the robustness of the control system. Furthermore, the control saturation problem is considered. In addition, the characteristic of integral sliding mode under the control constraint and measurement noise is also analyzed. Finally, several numerical simulations are performed to verify the effectiveness and robustness of the compound control law for autonomous docking to a three-axis freely tumbling target.

Compound Control of Attitude Synchronization for Autonomous Docking to a Tumbling Satellite

2013 ◽  
Vol 394 ◽  
pp. 470-476 ◽  
Author(s):  
Xue Yan An ◽  
Wei Lu ◽  
Zhang Ren
Keyword(s):  
Feedback Control ◽  
Control Law ◽  
Nonlinear Feedback Control ◽  
Nonlinear Feedback ◽  
External Disturbances ◽  
Compound Control ◽  
Bounded Disturbances ◽  
System Uncertainties ◽  
Attitude Synchronization ◽  
Autonomous Docking

In order to solve the attitude synchronization control problem for an on-orbit servicing spacecraft autonomous docking to a tumbling satellite in the presence of unknown bounded disturbances and system uncertainties, a compound control law is presented in this paper. The compound control law is composed of a nonlinear feedback control law and a compensate control law. The nonlinear feedback control law is mainly used to track the system command and the compensate control law is mainly used to deal with the external disturbances and system uncertainties to enhance the robustness of the control system. Simulation results verified the effectiveness of the designed compound control law, and the robustness to the unknown bounded disturbances, system uncertainties is also demonstrated.

scholarly journals Linear Feedback Synchronization Used in the Three-Dimensional Duffing System

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Jian-qun Han ◽  
Xu-dong Shi ◽  
Hong Sun
Keyword(s):  
Feedback Control ◽  
Chaotic System ◽  
Control Method ◽  
Three Dimensional ◽  
Lyapunov Stability Theory ◽  
Linear Feedback ◽  
Nonlinear Feedback ◽  
Linear Feedback Control ◽  
Duffing System ◽  
Feedback Control Method

It has been realized that synchronization using linear feedback control method is efficient compared to nonlinear feedback control method due to the less computational complexity and the synchronization error. For the problem of feedback synchronization of Duffing chaotic system, in the paper, we firstly established three-dimensional Duffing system by method of variable decomposition and, then, studied the synchronization of Duffing chaotic system and designed the control law based on linear feedback control and Lyapunov stability theory. It is proved theoretically that the two identical integer order chaotic systems are synchronized analytically and numerically.

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