Design of Finite Time Settling Regulators for Linear Systems

1994 ◽  
Vol 116 (4) ◽  
pp. 602-609 ◽  
Author(s):  
Slim Choura
Keyword(s):  
Finite Time ◽  
Feedforward Control ◽  
Linear Quadratic Regulator ◽  
Control Law ◽  
Control Input ◽  
Linear Quadratic ◽  
Control Laws ◽  
Performance Specifications ◽  
The Time Domain ◽  
State Responses

Earlier development of finite time settling controllers focused on the structure of the control law which consists of feedback and feedforward parts. In this structure, the feedback part is designed separately to satisfy certain performance specifications in the frequency and/or the time domain. The feedforward part is determined from the feedback control law, and therefore, there exists one-way coupling of both parts. In this paper, we propose a modification in the control structure that enables the designer to regulate the bounds of the control input and the state responses. We show that the finite time settling control problem can be transformed into a linear quadratic regulator one. This transformation results in a two-way coupling of the feedback and the feedforward control laws. We verify that the robustness property of the control strategy is preserved despite its structural change. In addition, we give guidelines for the selection of the feedforward control law.

Robust tracking control with discrete-time LQR control for micromanipulators

2018 ◽  
Vol 32 (18) ◽  
pp. 1850201
Author(s):  
Liu Yang ◽  
Dongjie Li ◽  
Donghao Xu
Keyword(s):  
Discrete Time ◽  
Tracking Control ◽  
Feedforward Control ◽  
Vertical Plane ◽  
Small Displacement ◽  
Control Input ◽  
Robust Tracking ◽  
Linear Quadratic ◽  
Robust Tracking Control ◽  
Lqr Control

This paper presents a robust tracking control with discrete-time linear quadratic regulation (LQR) method for micromanipulators. The micromanipulator is composed of three piezoelectric actuators (PEAs), which results in achieving three-degree-of-freedom motion. PEAs have been widely used in micromanipulation for biomedicine because of the advantages of its infinitely small displacement resolution and precision. However, owning to the nonlinear effects of PEAs, mainly hysteresis, can drastically degrade the tracking control accuracy. Therefore, it is desirable to develop advanced controllers to compensate hysteresis effect for improving the trajectory tracking performance. Before the controller design, a compensation for motion coupling error in vertical plane is concerned. Then, a controller consisting of three parts which are a nominal feedforward control input, a LQR control input and a control input based on system uncertainties compensation is designed. At last, the robust stability of the designed controller is proved through a Lyapunov stability analysis. The simulation results demonstrate that the proposed controller is effective in tracking applications, which can provide a high resolution performance.

A Stochastic Regulator for Integrated Communication and Control Systems: Part II—Numerical Analysis and Simulation

1991 ◽  
Vol 113 (4) ◽  
pp. 612-619 ◽  
Author(s):  
Luen-Woei Liou ◽  
Asok Ray
Keyword(s):  
Control Systems ◽  
Numerical Procedure ◽  
Linear Quadratic Regulator ◽  
State Feedback Control ◽  
Control Law ◽  
Linear Quadratic ◽  
Simulation Experiments ◽  
Integrated Communication ◽  
And Control ◽  
Future Work

A state feedback control law has been derived in Part I [1] of this two-part paper on the basis of an augmented plant model [2, 3, 4] that accounts for the randomly varying delays induced by the network in Integrated Communication and Control Systems (ICCS). The control algorithm was formulated as a linear quadratic regulator problem and then solved using the principle of dynamic programming and optimality. This paper, which is the second of two parts, presents (i) a numerical procedure for synthesizing the control parameters and (ii) results of simulation experiments for verification of the above control law using the flight dynamic model of an advanced aircraft. This two-part paper is concluded with recommendations for future work.

Point-to-Point Positioning of Flexible Structures Using a Time Domain LQ Smoothness Constraint

1992 ◽  
Vol 114 (3) ◽  
pp. 416-421 ◽  
Author(s):  
S. P. Bhat ◽  
D. K. Miu
Keyword(s):  
Time Domain ◽  
Finite Time ◽  
Flexible Structures ◽  
Control Input ◽  
Time Control ◽  
Smoothness Constraint ◽  
Point Control ◽  
Point To Point ◽  
The Time Domain ◽  
Different Order

An analytical procedure to implement optimal smoothing of the finite-time control waveform for point-to-point control problem is presented, which minimizes an optimality constraint consisting of a linear combination of the quadratic norms of its time derivatives. It is shown that the resulting control input is essentially the minimum norm solution augmented to satisfy some additional continuity requirements in the time domain. Application of the proposed technique to finite-time maneuvering of flexible structures is experimentally demonstrated and performances are compared using control torques evaluated based on different order of the smoothness constraint and order of the truncated plant model.

scholarly journals Optimization of parameters of a modal active control in a beam of composite material

2018 ◽  
Vol 211 ◽  
pp. 19002
Author(s):  
Camila Albertin Xavier da Silva ◽  
Erik Taketa ◽  
Edson Hideki Koroishi ◽  
Fabian Andres Lara-Molina ◽  
Albert Willian Faria
Keyword(s):  
Composite Material ◽  
Active Control ◽  
Active Vibration Control ◽  
Linear Quadratic Regulator ◽  
Optimization Methods ◽  
Linear Matrix ◽  
Linear Quadratic ◽  
Electromagnetic Actuators ◽  
Optimization Of Parameters ◽  
The Time Domain

The present work proposes the active vibration control in a beam of composite material, using electromagnetic actuators, in order to obtain a reduction in the response of the displacement of the system associated to a reduction in energy consumption. The control theory used was the linear quadratic regulator solved by linear matrix inequalities. The electromagnetic actuator was then linearized using a methodology similar to that used in magnetic bearings. The work also proposes to study the optimization of parameters applied in this active control, by means of the heuristic optimization methods. From numerical simulations, the system´s response was obtained in the time domain that demonstrated the efficiency of the proposed technique in the active control of vibrations.

scholarly journals Design of Composite Feedback and Feedforward Control Law for Aircraft Inertially Stabilized Platforms

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Valerii Azarskov ◽  
Anatoly Tunik ◽  
Olha Sushchenko
Keyword(s):  
Control Systems ◽  
Feedforward Control ◽  
Design Method ◽  
Synergetic Effect ◽  
Measurement Unit ◽  
Control Law ◽  
Control Laws ◽  
Robustness Criterion ◽  
Two Stages ◽  
Invariance Theory

The design of the control systems of the inertially stabilized platforms (ISPs) as part of airborne equipment for the majority of aircraft has its peculiarity. The presence of rate gyros in the inertial measurement unit gives the possibility to measure the rotation rate of the ISP base, which is the main disturbance interfering with the ISP accuracy. Inclusion of the feedforward disturbance gain in the control law with the simplest PI feedback significantly improves the accuracy of stabilization by the invariance theory. A combination of feedback and feedforward controllers produces a synergetic effect, thus, improving ISP accuracy. This article deals with the design of the airborne ISP control systems consisting of two stages: the parametric optimization of the PI feedback control based on composite “performance-robustness” criterion and the augmentation of the obtained system with feedforward gain. To prove the efficiency of the proposed control laws, the simulation of the ISP was undertaken. We have used a simulation of the heading-hold system of the commuter aircraft Beaver and the yaw rate output of this closed-loop system we have used as a source of the disturbance. The results of modeling proved the efficiency of the proposed design method.

Payload Pendulation Reduction Using a Variable-Geometry-Truss Architecture with LQR and Fuzzy Controls

2003 ◽  
Vol 9 (7) ◽  
pp. 805-837 ◽  
Author(s):  
Paolo Dadone ◽  
Walter Lacarbonara ◽  
Ali H. Nayfeh ◽  
Hugh F. Vanlandingham
Keyword(s):  
Control Point ◽  
Broad Band ◽  
Ship Motions ◽  
Control Input ◽  
Variable Geometry ◽  
Linear Quadratic ◽  
Control Laws ◽  
Band Frequency ◽  
Input Acceleration ◽  
Variable Geometry Truss

We investigate the feasibility of a variable-geometry truss (VGT) based architecture for suppressing payload pendulations in ship-mounted cranes. The VGT assembly is conceived to be retrofitted onto the boom tip of ship-mounted cranes. A simplified planar model is developed. A control point along the cable hoisting the payload is constrained to move along a straight path with a given control input (acceleration) imparted via the actuators embedded in the VGT assembly. Control laws based on either linear quadratic or fuzzy control methodologies are developed in order to minimize an assigned cost functional. Their effectiveness is compared through extensive numerical simulations. The performance of the VGT architecture and associated control laws is analyzed when the crane is subject to the most severe combination of resonant excitations: a primary resonant roll excitation at the natural frequency of the controlled system, and a principal-parametric resonant heave excitation, both corresponding to sea state three and higher. The proposed strategy exhibits enough control authority over the system dynamics, greatly reducing the severe and undesirable resonant pendulations caused by the ship motions in a broad-band frequency range. Moreover, its disturbance-rejection capabilities are exerted with feasible control efforts, which are localized in the segment of the crane where they are needed.

scholarly journals Optimal Design of Fault-Tolerant Controller for an Electric Power Steering System with Sensor Failures Using Genetic Algorithm

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Xue Liu ◽  
Hui Pang ◽  
Yuting Shang ◽  
Wen Wu
Keyword(s):  
Genetic Algorithm ◽  
Electric Power ◽  
Fault Tolerant ◽  
Linear Quadratic Regulator ◽  
State Feedback Control ◽  
Control Law ◽  
Linear Quadratic ◽  
Electric Power Steering ◽  
Sensor Failures ◽  
Power Steering

This paper focuses on the fault-tolerant control (FTC) problem for an electric power steering (EPS) system subjected to stochastic sensor failures, and a novel fault-tolerant controller is proposed based on the genetic algorithm (GA). A mathematical model of the EPS system with sensor failures is first established, and the state feedback control law is solved by using linear quadratic regulator techniques to stabilize the closed-loop control system. Then, the dynamic response errors of the EPS system with and without sensor faults are chosen as the optimization objective function. Furthermore, the appropriate weighting matrices are evaluated to obtain the optimal fault control law by using GA. Finally, simulation results are presented to illustrate the effectiveness of the proposed control strategy.

Use of Rotor State Feedback to Improve Closed-Loop Stability and Handling Qualities

2012 ◽  
Vol 57 (2) ◽  
pp. 1-10 ◽  
Author(s):  
Joseph F. Horn ◽  
Wei Guo ◽  
Gurbuz Taha Ozdemir
Keyword(s):  
Disturbance Rejection ◽  
State Feedback ◽  
Closed Loop ◽  
Linear Quadratic Regulator ◽  
Linear Analysis ◽  
Dynamic Inversion ◽  
Control Law ◽  
Linear Quadratic ◽  
Handling Qualities ◽  
Model Following

A rotorcraft control law that uses rotor state feedback (RSF) is presented and demonstrated in simulation. The baseline control law uses a model following/dynamic inversion approach to control the roll, pitch, and yaw axes. The RSF control law was designed to integrate seamlessly with the baseline control law and can be readily engaged or disengaged. The RSF control gains were designed using linear quadratic regulator synthesis. Linear analyses showed that RSF could allow for the feedback gains on rates and attitude to be increased to values that would result in closed-loop instability without the use of RSF. The increased gains can be used to increase bandwidth and improve disturbance rejection. The controller was tested on a nonlinear model in both non–real-time and piloted simulations, and results confirmed the linear analysis. The RSF control law design has potential to improve handling qualities by allowing higher bandwidth and better disturbance rejection with reduced risk of closed-loop instability.

scholarly journals ANALYSIS OF CONTROL QUALITY OF AIRCRAFT LATERAL MOTION DURING APPROACH WITH THE USE OF DIFFERENT CONTROL LAWS

Aviation ◽  
2006 ◽  
Vol 10 (3) ◽  
pp. 21-29 ◽  
Author(s):  
Grzegorz Kopecki
Keyword(s):  
Linear Quadratic Regulator ◽  
Lateral Motion ◽  
Linear Quadratic ◽  
Control Laws ◽  
Model Following Control ◽  
Model Following ◽  
Lack Of Information ◽  
Incomplete Measurement ◽  
The Difference

The article presents different methods of control of the lateral motion of aircraft during approach with the use of ILS‐LOC. Results of computer simulations are presented. An assessment of the quality with and without cross‐wind was made with the use of quality coefficients. The control laws are based on PID regulator and its modifications. Moreover, the application of the model‐following control in case of incomplete measurement, i.e. lack of information about the track angle, is presented. For interception, the model is used as the generator of the desired trajectory. The difference between the real and model trajectory is used for wind compensation, instead of the integration in LOC regulator. For control law synthesis for stabilization, linear quadratic regulator method was used.

Finite-Time Settling Control of a Flexible Arm

1994 ◽  
Vol 208 (2) ◽  
pp. 79-87 ◽  
Author(s):  
S Choura
Keyword(s):  
Control Strategy ◽  
Finite Time ◽  
Position Control ◽  
Feedforward Control ◽  
Control Strategies ◽  
State Space Model ◽  
Control Law ◽  
Flexible Beam ◽  
Flexible Arm ◽  
Finite Set

This paper considers the position control of a flexible beam attached to a rotating rigid hub. The control torque is applied at the hub through a motor. A state-space model describing the motion of the flexible beam is developed and is employed in the design of the control law. The finite-time settling control strategy that combines feedback and feedforward is applied to the beam problem. The feedback part is separately designed to resolve the issues of asymptotic stability and robustness to uncertainties. The feedforward part simultaneously suppresses the rigid-body mode and a finite set of flexible modes at the end of manoeuvre and, therefore, it is the part responsible for the finite-time settling of the beam to its final configuration. It is shown that if the finite-time settling control is compared with previously developed control strategies under the same input bound constraint, it leads to a better suppression of vibrations at the end of manoeuvre, provided that a sufficient number of flexible modes are incorporated in the computation of the feedforward control law. A robustness test is carried out to show the viability of the control strategy supported by computer simulations.

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