An optimal control method for linear systems with time delay

Cai, Guo‐Ping; Huang, J.S.T.; Yang, Simon X.

doi:10.1016/s0045-7949(03)00146-9

Cited by 70 publications

(46 citation statements)

References 14 publications

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“…Linear-quadratic-regulator (LQR) is a part of optimal control strategy which has been widely developed and used in various applications [10]. LQR design is based on the selection of feedback gains K such that the cost function J is minimized.…”

Section: B Lqr Controllermentioning

confidence: 99%

Performance Analysis of Aircraft Pitch Control By Linear Quadratic Regulator and Fuzzy Controller

Singh¹

2017

IJRASET

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Today's aircraft consist of number of automatic controller that helps the airplane crew in airplane management and piloting the aircraft. Usually, the control strategies of aircraft can be grouped into two categories as follows: lateral and longitudinal control. In longitudinal control, the pitch angle has been employed for an aircraft system. Pitch of an aircraft may be described as a rotation around the lateral axis. An elevator is used to control pitch of aircraft which is located at the back of an airplane. So in this paper, a pitch control of an aircraft has been implemented by using Fuzzy controller. The stability of aircraft system is of major concern in real interface system. Thus, aircraft system must be accurate having stable response of aircraft system and should approaches to reference over a certain interval of time i.e. it should not oscillate over a long time. So this work exhibits the design of fuzzy control strategy for controlling the pitch angle of an aircraft. Two control strategies: Linear quadratic regulator (LQR) control and Fuzzy control strategies have been employed and compared. After that a comparative analysis of these control strategies has been done. The whole system has been implemented in MATLAB SIMULINK environment. Keywords: Pitch control, longitudinal l control, Lateral control, Fuzzy controller, linear quadratic regulator (LQR). I.INTRODUCTION Pitch control is a longitudinal control; therefore longitudinal model of an aircraft is used to design the pitch angle controller of an aircraft. Roll control is a lateral control. Therefore lateral model of an aircraft is required to design the roll angle controller of an aircraft. The roll angle is used to control the rolling motion of an aircraft. Elevator is used to control pitch of an aircraft and ailerons are used to control roll of an aircraft. The ultimate aim is to follow the elevator and ailerons command with minimum delay and maximum accuracy. To reduce the complexity of system, assume aircraft as a rigid body and aircraft's motion consist of a small deviation from its equilibrium flight condition [1]. In addition, the aircraft control system can be divided into two parts, namely longitudinal and lateral control [2]. In longitudinal control, the elevator controls pitch or the longitudinal motion of aircraft system whereas in lateral control lateral motion (roll and yaw) of aircraft system is controlled. Pitch of an aircraft may be described as a rotation around the lateral axis. It might be calculated as the angle between the direction of speed in a horizontal line and vertical plane Pitch of aircraft is control by elevator which usually situated at the rear of the airplane running parallel to the wing that houses the ailerons [3]. Elevator is used to control pitch or to control the tail planes of an aircraft which is located at the back of an airplane. The elevator pivoted at the rear of an aircraft work in pairs; when the right elevator goes up, the left elevator also goes up. The linear zed mathematical model is o...

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Section: B Lqr Controllermentioning

confidence: 99%

Performance Analysis of Aircraft Pitch Control By Linear Quadratic Regulator and Fuzzy Controller

Singh¹

2017

IJRASET

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“…If this is the case, the weighting matrices N N N andR R R in Eqs. (14)- (16) become N N N = 0 and R R R = R R R since B B B d1 = 0. Hence, the Riccati equation (16) becomes …”

Section: Remarkmentioning

confidence: 99%

“…For example, Park et al provided a dynamic output-feedback linear quadratic (LQ) controller by applying the continuous reduction [15]. Cai and his coworkers proposed two different optimal controls for the dynamic system with input delays [16,17], one based on the continuous reduction and the other based on a discrete reduction.…”

Section: Introductionmentioning

confidence: 99%

A new reduction-based LQ control for dynamic systems with a slowly time-varying delay

Liu

Haraguchi

2009

Acta Mech Sin

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Time delays in the feedback control often deteriorate the control performance or even cause the instability of a dynamic system. This paper presents a control strategy for the dynamic system with a constant or a slowly timevarying input delay based on a transformation, which simplifies the time-delay system into a delay-free one. Firstly, the relation is discussed for two existing reduction-based linear quadratic controls. One is continuous and the other is discrete. By extending the relation, a new reduction-based control is then developed with a numerical algorithm presented for practical control implementation. The controller suggested by the proposed method has such a promising property that it can be used for the cases of different values of an input time delay without redesign of controller. This property provides the potential for stabilizing the dynamic system with a time-varying input delay. Consequently, the application of the proposed method to the dynamic system with a slowly time-varying delay is discussed. Finally, numerical simulations are given to show the efficacy and the applicability of the method.

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“…7,12 The first three methods work well with some small time delay problems but cannot deal with large time delay ones. Two direct design methods 7,12 are to design a timedelay controller directly from a time-delay differential equation and no assumption is made in the entire design process and they are suitable for both small and large time delays. Cai and Chen 8,13 verified these two methods by conducting an experiment using several flexible structures as research objects.…”

Section: Introductionmentioning

confidence: 99%

Robust H-infinity Control of Building Structures with Time Delay

Liu¹,

Chen²,

Cai³

et al. 2017

IJAV

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In this paper, a robust H ∞ controller for a building structure with a time delay is studied. Firstly, the motion equation of the structural system with an explicit time delay is introduced. Then, the state space representation of a dynamic equation without any explicit time delay is deduced by a specific integral transformation to the time-delay equation. Secondly, a robust control method is applied to the H ∞ time-delay controller design and, due to the compensation of the time delay, the proposed controller contains not only the state term of the current step, but also a linear combination of some former steps of the control. Finally, numerical simulations and comparisons of a six-story building using the proposed time-delay controller are carried out. The simulation results indicate that the control performance will deteriorate if the time delay is not taken into account in the control design. The proposed H ∞ time-delay controller in this paper can effectively compensate for a time delay in order to get better control effectiveness. Besides, this delay controller is robust to both structural parameter and time delay uncertainties.

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An optimal control method for linear systems with time delay

Cited by 70 publications

References 14 publications

Performance Analysis of Aircraft Pitch Control By Linear Quadratic Regulator and Fuzzy Controller

Performance Analysis of Aircraft Pitch Control By Linear Quadratic Regulator and Fuzzy Controller

A new reduction-based LQ control for dynamic systems with a slowly time-varying delay

Robust H-infinity Control of Building Structures with Time Delay

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