scholarly journals Suboptimal Regulation of a Class of Bilinear Interconnected Systems with Finite-Time Sliding Planning Horizons

2008 ◽  
Vol 2008 ◽  
pp. 1-26 ◽  
Author(s):  
M. de la Sen ◽  
Aitor J. Garrido ◽  
J. C. Soto ◽  
O. Barambones ◽  
I. Garrido
Keyword(s):  
Control Law ◽  
State Variables ◽  
Linear Quadratic ◽  
Equivalent Representation ◽  
Quadratic Performance Index ◽  
Matrix Sequence ◽  
Control Scheme ◽  
Quadratic Performance ◽  
System Equations ◽  
Riccati Matrix

This paper focuses on the suboptimization of a class of multivariable discrete-time bilinear systems consisting of interconnected bilinear subsystems with respect to a linear quadratic optimal regulation criterion which involves the use of state weighting terms only. Conditions which ensure the controllability of the overall system are given as a previous requirement for optimization. Three transformations of variables are made on the system equations in order to implement the scheme on an equivalent linear system. This leads to an equivalent representation of the used quadratic performance index that involves the appearance of quadratic weighting terms related to both transformed input and state variables. In this way, a Riccati-matrix sequence, allowing the synthesis of a standard feedback control law, is obtained. Finally, the proposed control scheme is tested on realistic examples.

Dynamic modelling and linear quadratic sliding mode control of a multivariable looper system in hot strip mills

2021 ◽  
Vol 118 (2) ◽  
pp. 215
Author(s):  
Yin Fang-Chen ◽  
Wu Xiang-Cheng
Keyword(s):  
Sliding Mode Control ◽  
Sliding Mode ◽  
Dynamic Modelling ◽  
Control Law ◽  
Linear Quadratic ◽  
Mode Control ◽  
Sliding Motion ◽  
Quadratic Performance ◽  
Hot Strip Mills ◽  
Looper System

This paper introduces a linear quadratic sliding mode control (LQ-SMC) scheme into a looper control system. First, according to a 1700 mm tandem hot mill, the state-space dynamic model of the looper system was established, and then, the optimal control law of the looper system was obtained based on the established model. Finally, the optimal sliding mode and optimal sliding mode control law of the LQ-SMC scheme were designed such that the sliding motion could satisfy the optimal value of the quadratic performance index. Simulation results show that the proposed control scheme has complete robustness to external disturbances that satisfies certain conditions, and the coupling between the looper angle dynamic and strip tension dynamic is also minimized.

Application of optimal control law to laser guided bomb

2018 ◽  
Vol 122 (1251) ◽  
pp. 785-797
Author(s):  
Takieddine Mouada ◽  
Milos V. Pavic ◽  
Bojan M. Pavkovic ◽  
Sasa Z. Zivkovic ◽  
Mirko S. Misljen
Keyword(s):  
Noise Removal ◽  
Control Law ◽  
State Variables ◽  
Linear Quadratic ◽  
State Variable ◽  
Guidance Law ◽  
Optimal Guidance ◽  
Differential Game Theory ◽  
Miss Distance ◽  
Guidance Laws

ABSTRACTThe paper presents a laser guided bomb guidance law based on the linear quadratic differential game theory, where a case of two perpendicular planes with two state variables in each plane has been considered. The Kalman filtering method has been used for noise removal from the measured signals and for estimation of the missing state variable values needed for the optimal guidance law. Optimisation has been conducted with respect to minimisation of the performance index. Comparative analysis of different guidance laws is done. A statistical analysis is performed to obtain the terminal miss distance in dependence on total flight time.

SURVEY OF LINEAR QUADRATIC ROBUST CONTROL

2002 ◽  
Vol 6 (1) ◽  
pp. 19-39 ◽  
Author(s):  
Pierre Bernhard
Keyword(s):  
Robust Control ◽  
Performance Index ◽  
Control Problems ◽  
Linear Quadratic ◽  
Quadratic Problem ◽  
Quadratic Performance Index ◽  
Quadratic Performance ◽  
Per Se

We review several control problems, all related to robust control in some way, that lead to a minimax linear quadratic problem. We stress the fact that although an augmented performance index appears, containing an L2 norm of a disturbance signal, only the nonaugmented quadratic performance index is of interest per se in each case.

On a Problem of Letov in Optimal Control

1965 ◽  
Vol 87 (1) ◽  
pp. 81-89 ◽  
Author(s):  
C. D. Johnson ◽  
W. M. Wonham
Keyword(s):  
Optimal Control ◽  
Present Note ◽  
Control Variable ◽  
Control Law ◽  
Initial Value ◽  
Bounded Control ◽  
Quadratic Performance Index ◽  
Linear Plant ◽  
Quadratic Performance ◽  
Optimal Regulator

In a series of papers [1, 2], A. M. Letov discussed an optimal regulator problem for a linear plant with bounded control variable and quadratic performance index. This problem was also discussed by Chang [3]. Krasovskii and Letov observed later [4] that the solution proposed in [1, 2, and 3] may be correct only for special choices of the initial value of the state vector. In the present note, further aspects of the solution in the general case are described and three examples are given. The possible existence of a regime of unsaturated-nonlinear optimal control is demonstrated. The presence of this regime in the optimal control law was apparently overlooked in [1–4].

A Control Scheme for an Opposed Recumbent Tandem Human-Powered Bicycle

1996 ◽  
Vol 12 (4) ◽  
pp. 480-492
Author(s):  
Scott O. Cloyd ◽  
Mont Hubbard ◽  
LeRoy W. Alaways
Keyword(s):  
Feedback Control ◽  
Linear Quadratic Regulator ◽  
Optimal Feedback Control ◽  
State Variables ◽  
Linear Quadratic ◽  
Lateral Deviation ◽  
Control Scheme ◽  
Control Schemes ◽  
Lean Angle ◽  
Human Powered

Feedback control of a human-powered single-track bicycle is investigated through the use of a linearized dynamical model in order to develop feedback gains that can be implemented by a human pilot in an actual vehicle. The object of the control scheme is to satisfy two goals: balance and tracking. The pilot should be able not only to keep the vehicle upright but also to direct the forward motion as desired. The two control inputs, steering angle and rider lean angle, are assumed to be determined by the rider as a product of feedback gains and “measured” values of the state variables: vehicle lean, lateral deviation from the desired trajectory, and their derivatives. Feedback gains are determined through linear quadratic regulator theory. This results in two control schemes, a “full” optimal feedback control and a less complicated technique that is more likely to be usable by an inexperienced pilot. Theoretical optimally controlled trajectories are compared with experimental trajectories in a lane change maneuver.

H∞-Based LQR Control for Flexible Air-Breathing Hypersonic Vehicles with Pole Placement

2013 ◽  
Vol 787 ◽  
pp. 938-943
Author(s):  
Xue Zhang ◽  
Xiao Geng Liang
Keyword(s):  
Linear Quadratic Regulator ◽  
Pole Placement ◽  
Control Law ◽  
Linear Quadratic ◽  
External Disturbances ◽  
Air Breathing ◽  
Lqr Control ◽  
Flight Vehicles ◽  
Quadratic Performance ◽  
Linearized Model

Focusing on a nonlinear longitudinal dynamical model for air-breathing hypersonic flight vehicles (AHFV), we propose a state feedback linearized model on a nominal trim condition. To stabilize the flight of an AHFV in the presence of external disturbances, a newHbased Linear Quadratic Regulator (LQR) control law with pole placement is designed. Indexes forHperformance, quadratic performance and pole placement are considered together. As a result, the robustness of system is improved and the AHFV system is effectively stabilized. Numerical simulation shows that the controller can effectively stabilize the AHFV system with some disturbances and assign the poles into a desired region.

Research on Unmanned Aerial Vehicles Autonomous Soft Landing Based on Optimal Control

2012 ◽  
Vol 562-564 ◽  
pp. 1442-1446
Author(s):  
Ze Yin Xu ◽  
Xiao Hu Xia ◽  
Yun Jian Ge
Keyword(s):  
Optimal Control ◽  
Time Varying ◽  
Unmanned Helicopter ◽  
Linear Quadratic ◽  
Soft Landing ◽  
Quadratic Performance Index ◽  
Input Signals ◽  
Model Helicopter ◽  
Output System ◽  
Quadratic Performance

This paper deals with the autonomous soft landing of unmanned helicopter aiming to enhance its application. Soft landing means to reduce the shock force upon ground during the helicopters land. Helicopter is a multi-input multi-output system and for which optimal control provides graceful and coordinated controls. Firstly, the experimental platform configuration for autonomous soft-landing system is introduced, which is based on the model helicopter. The time-varying gains and time-varying quadratic performance index Linear Quadratic control for autonomous soft landing of miniature helicopter is applied to unmanned helicopter. Simulation shows that the outputs of the system can respond the input signals accurately.

Design of nonlinear optimal tracking control law based on finite-time stability for quadratic performance index

2021 ◽  
pp. 2150031
Author(s):  
Di Wang ◽  
Can Liu ◽  
Suixiang Gao ◽  
Fucheng Liao
Keyword(s):  
Finite Time ◽  
Performance Index ◽  
Tracking Control ◽  
Design Method ◽  
Control Law ◽  
Time Stability ◽  
Finite Time Stability ◽  
Optimal Tracking ◽  
Quadratic Performance Index ◽  
Quadratic Performance

In this paper, a design method of optimal tracking control based on finite-time stability for quadratic performance index is proposed. Finite-time stability of tracking control involves dynamical systems whose actual output can track desired output in finite time while satisfying Lyapunov stability. A nonlinear control law which guaranteed finite-time stability is designed depending on the core idea of dynamic programming. By using Hamilton–Jacobi–Bellman (HJB) equation and finite-time stability theory, sufficient conditions involving V-function are provided, and design steps for nonlinear finite-time tracking control law are derived by constructing augmented systems. In addition, the V-function is constructed to obtain corresponding law for given systems, which verified that the design method is feasible. Simulation examples validate the efficiency of the results.

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