An LQ Approach to Active Control of Vibrations in Helicopters

1996 ◽  
Vol 118 (3) ◽  
pp. 482-488 ◽  
Author(s):  
Sergio Bittanti ◽  
Fabrizio Lorito ◽  
Silvia Strada
Keyword(s):  
Optimal Control ◽  
Active Control ◽  
Linear Quadratic ◽  
Control Effort ◽  
Vibration Effect ◽  
Suitable Definition ◽  
Lq Optimal Control ◽  
The One ◽  
Definition Of ◽  
And Control

In this paper, Linear Quadratic (LQ) optimal control concepts are applied for the active control of vibrations in helicopters. The study is based on an identified dynamic model of the rotor. The vibration effect is captured by suitably augmenting the state vector of the rotor model. Then, Kalman filtering concepts can be used to obtain a real-time estimate of the vibration, which is then fed back to form a suitable compensation signal. This design rationale is derived here starting from a rigorous problem position in an optimal control context. Among other things, this calls for a suitable definition of the performance index, of nonstandard type. The application of these ideas to a test helicopter, by means of computer simulations, shows good performances both in terms of disturbance rejection effectiveness and control effort limitation. The performance of the obtained controller is compared with the one achievable by the so called Higher Harmonic Control (HHC) approach, well known within the helicopter community.

scholarly journals On the optimal control force applied to tuned mass dampers for multi-degree-of-freedom systems

2004 ◽  
Vol 26 (1) ◽  
pp. 1-10
Author(s):  
Nguyen Dong Anh ◽  
Nguyen Chi Sang
Keyword(s):  
Optimal Control ◽  
Numerical Study ◽  
Degree Of Freedom ◽  
Control Force ◽  
Linear Quadratic ◽  
Tuned Mass Dampers ◽  
Coloured Noise ◽  
Optimal Theory ◽  
The One ◽  
Better Than

The design of active TMD for multi-degree-of-freedom systems subjected to second order coloured noise excitation is considered using the linear quadratic optimal theory. A detailed numerical study is carried out for a 2-DOF system. It is shown that the effectiveness of active TMD is better than the one of passive TMD.

scholarly journals Linear-Quadratic Stackelberg Game for Mean-Field Backward Stochastic Differential System and Application

2019 ◽  
Vol 2019 ◽  
pp. 1-17 ◽  
Author(s):  
Kai Du ◽  
Zhen Wu
Keyword(s):  
Optimal Control ◽  
Differential System ◽  
Optimization Problems ◽  
Stackelberg Game ◽  
Mean Field ◽  
Open Loop ◽  
Stackelberg Equilibrium ◽  
Linear Quadratic ◽  
Stackelberg Differential Game ◽  
Lq Optimal Control

This paper is concerned with a new kind of Stackelberg differential game of mean-field backward stochastic differential equations (MF-BSDEs). By means of four Riccati equations (REs), the follower first solves a backward mean-field stochastic LQ optimal control problem and gets the corresponding open-loop optimal control with the feedback representation. Then the leader turns to solve an optimization problem for a 1×2 mean-field forward-backward stochastic differential system. In virtue of some high-dimensional and complicated REs, we obtain the open-loop Stackelberg equilibrium, and it admits a state feedback representation. Finally, as applications, a class of stochastic pension fund optimization problems which can be viewed as a special case of our formulation is studied and the open-loop Stackelberg strategy is obtained.

Acoustic Control Modeling of Conical Bores With Actuating Boundary Conditions

2001 ◽  
Author(s):  
Kevin M. Farinholt ◽  
Donald J. Leo
Keyword(s):  
Boundary Conditions ◽  
Driving Forces ◽  
State Space Model ◽  
Linear Quadratic Regulator ◽  
Mode Shapes ◽  
Linear Quadratic ◽  
Acoustic Control ◽  
Average Control ◽  
The One ◽  
And Control

Abstract An investigation of the natural frequencies and mode shapes associated with sealed conical bores having actuating boundary conditions is presented. Beginning with the one dimensional wave equation for spherically expanding waves, modal characteristics are developed as functions of cone geometry and actuator parameters. This paper presents both analytical and experimental comparisons for the purpose of validating model and development techniques. An investigation of the orthogonality and adjointness of the solution is presented. A discussion of incorporating driving forces in the system model for the purpose of coupling control actuators with internal acoustics is also included. Including these driving forces, a state space model of the system is developed for the purpose of applying modern feedback control. This paper concludes with a study on applying Linear Quadratic Regulator techniques to this system, relating tradeoffs between spatially averaged pressure and control voltages. The results of our simulations indicate that pressure reductions of 30% are attainable with average control voltages of 14.4 volts, given an example geometry.

Optimal Control Design of a Bimorph Optical Beam Deflector

2001 ◽  
Author(s):  
Chang-Po Chao ◽  
Jeng-Sheng Huang ◽  
Ching-Lung Ou Yung ◽  
Rong-Fong Fung
Keyword(s):  
Optimal Control ◽  
Position Control ◽  
Angular Position ◽  
Control Design ◽  
Element Model ◽  
Optical Beam ◽  
Optimal Feedback Control ◽  
Central Position ◽  
Control Effort ◽  
And Control

Abstract The optical beam deflector is composed of two piezoelectric layers, one sandwiched brass layer in the middle with both ends clamped and a mirror attached to the upper surface of the top piezoelectric layer in the central position. This structure is designed to deflect the mirror to a certain angular position by applying external voltage supply to piezo-layers. This study proposes an optimal angular position control scheme of the attached mirror. The governing partial differential equations are first derived for the ensuing analysis and control design, which is followed by the establishment of finite element model in ten nodes specified at some longitudinal points of the optical beam deflector. In order to achieve a faster convergent rate for the deflector to reach the desired angular position, the optimal control of LQ regulator with final states fixed is employed to explore the possibility of shorter transient response and less cost of control effort and states. The optimal feedback control is obtained based on solving a dynamic Riccati equation backward in time. The numerical simulation results are finally provided to validate the theoretical control design.

scholarly journals Delayed Stochastic Linear-Quadratic Control Problem and Related Applications

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
Li Chen ◽  
Zhen Wu ◽  
Zhiyong Yu
Keyword(s):  
Optimal Control ◽  
Differential Equations ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Stochastic Differential Equations ◽  
Backward Stochastic Differential Equations ◽  
Delay System ◽  
Linear Quadratic ◽  
Stochastic Linear System ◽  
And Control

We discuss a quadratic criterion optimal control problem for stochastic linear system with delay in both state and control variables. This problem will lead to a kind of generalized forward-backward stochastic differential equations (FBSDEs) with Itô’s stochastic delay equations as forward equations and anticipated backward stochastic differential equations as backward equations. Especially, we present the optimal feedback regulator for the time delay system via a new type of Riccati equations and also apply to a population optimal control problem.

scholarly journals Study on Indefinite Stochastic Linear Quadratic Optimal Control with Inequality Constraint

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Guiling Li ◽  
Weihai Zhang
Keyword(s):  
Optimal Control ◽  
Dynamic Programming Algorithm ◽  
Inequality Constraint ◽  
Terminal State ◽  
State Feedback Control ◽  
Programming Algorithm ◽  
Necessary Condition ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Lq Optimal Control

This paper studies the indefinite stochastic linear quadratic (LQ) optimal control problem with an inequality constraint for the terminal state. Firstly, we prove a generalized Karush-Kuhn-Tucker (KKT) theorem under hybrid constraints. Secondly, a new type of generalized Riccati equations is obtained, based on which a necessary condition (it is also a sufficient condition under stronger assumptions) for the existence of an optimal linear state feedback control is given by means of KKT theorem. Finally, we design a dynamic programming algorithm to solve the constrained indefinite stochastic LQ issue.

Microclimate control of a greenhouse by adaptive Generalized Linear Quadratic strategy

2018 ◽  
Vol 11 (1) ◽  
pp. 377 ◽  
Author(s):  
Mohamed Essahafi ◽  
Mustapha Ait Lafkih
Keyword(s):  
Optimal Control ◽  
Least Squares ◽  
Recursive Least Squares ◽  
Linear Quadratic ◽  
Linear Quadratic Gaussian ◽  
Advanced Technique ◽  
Online Identification ◽  
State Models ◽  
The Cost ◽  
And Control

<p>To highlight the conceptual aspects related to the implementation of techniques optimal control in the form state, we present in this paper, the identification and control of the temperature and humidity of the air inside a greenhouse. Using respectively an online identification based on the recursive least squares with forgotten Factor method and the multivariable adaptive linear quadratic Gaussian approach which the advanced technique (LQG) is presented.  The design of this controller parameters is based on state models identified directly from measured greenhouse data. hence the performances of the controller developed are illustrated by different tests and simulations on identified models of a greenhouse. Discussions on the results obtained are then processed in the paper to show the effectiveness of the controller in terms of stability and optimization of the cost of control.</p>

Multi-Dimension Uncertain Linear Quadratic Optimal Control with Cross Term

2015 ◽  
Vol 19 (5) ◽  
pp. 670-675 ◽  
Author(s):  
Yuefen Chen ◽  
◽  
Bo Li
Keyword(s):  
Differential Equation ◽  
Optimal Control ◽  
Linear Feedback ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Riccati Differential Equation ◽  
Cross Term ◽  
Lq Optimal Control ◽  
Quadratic Optimal Control ◽  
Feedback Optimal Control

In this paper, we consider a multi-dimension uncertain linear quadratic (LQ) optimal control with cross term. With the aid of the equation of optimality of a general multi-dimension uncertain optimal control, we present a necessary and sufficient condition for the existence of optimal linear feedback optimal control which is associated with a Riccati differential equation. Moreover, some properties of the solution for the Riccati differential equation are discussed. Furthermore, the uniqueness of the feedback optimal control for the uncertain linear quadratic optimal control with cross term is proved. Finally, as an application, an example is presented to illustrate the theory obtained.

A Sealed System and Compressor Model for Optimal Control of Household Refrigerators

2012 ◽  
Author(s):  
Bahman Abbasi ◽  
Keith Wait ◽  
Michael Kempiak
Keyword(s):  
Optimal Control ◽  
Control Systems ◽  
Effective Means ◽  
Evaporator Temperature ◽  
Efficient Manner ◽  
Control Effort ◽  
Industry Standards ◽  
Flow Phenomena ◽  
And Performance ◽  
And Control

Increasingly stringent industry standards have posed significant challenges on manufacturers to enhance the design and performance of household refrigerators. One of the least expensive and most effective means of improving the system is optimizing the control strategy. Some of the most promising control systems, such as adaptive and optimal control methods, require an accurate model of the system to guide the control effort. However, the complexity and interconnectedness of thermal and refrigerant flow phenomena make developing modern control systems a particularly challenging aspect of designing refrigerators, in spite of many decades of research and development. There exist models to correlate the desired compartments’ temperatures to that of the evaporator coil. However, there is a lack of a general approach to translate the required evaporator temperature to a compressor speed that provides it in an energy efficient manner. This work introduces a method to make that connection. The technique developed in this work can be adjusted for implementation on various refrigerator sizes and platforms to help modulate and control the compressor speed in real time.

scholarly journals Active Vibration Control of the Sting Used in Wind Tunnel: Comparison of Three Control Algorithms

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Xing Shen ◽  
Yuke Dai ◽  
Mingxuan Chen ◽  
Lei Zhang ◽  
Li Yu
Keyword(s):  
Optimal Control ◽  
Wind Tunnel ◽  
Vibration Control ◽  
Control Algorithm ◽  
Active Vibration Control ◽  
Linear Quadratic Regulator ◽  
Real Time Control ◽  
Linear Quadratic ◽  
Control Effort ◽  
Active Vibration

In wind tunnel tests, cantilever stings are often used as model-mount in order to reduce flow interference on experimental data. In this case, however, large-amplitude vibration and low-frequency vibration are easily produced on the system, which indicates the potential hazards of gaining inaccurate data and even damaging the structure. This paper details three algorithms, respectively, Classical PD Algorithm, Artificial Neural Network PID (NNPID), and Linear Quadratic Regulator (LQR) Optimal Control Algorithm, which can realize active vibration control of sting used in wind tunnel. The hardware platform of the first-order vibration damping system based on piezoelectric structure is set up and the real-time control software is designed to verify the feasibility and practicability of the algorithms. While the PD algorithm is the most common method in engineering, the results show that all the algorithms can achieve the purpose of over 80% reduction, and the last two algorithms perform even better. Besides, self-tuning is realized in NNPID, and with the help of the Observer/Kalman Filter Identification (OKID), LQR optimal control algorithm can make the control effort as small as possible. The paper proves the superiority of NNPID and LQR algorithms and can be an available reference for vibration control of wind tunnel system.

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