Development and performance evaluation of an infinite horizon LQ optimal tracker

Bauer, Péter; Bokor, József

doi:10.1016/j.ejcon.2017.10.001

Cited by 5 publications

(4 citation statements)

References 16 publications

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“…First, we consider a general multi-input multi-output continuous linear time-invariant (LTI) dynamic system as described in (2). The objective is to design a controller in such a way that the closed-loop system exhibits satisfactory transient response to a given reference trajectory and zero steady-state error, which are desired for many test scenarios on full vehicle test benches.…”

Section: Problem Descriptionmentioning

confidence: 99%

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Linear Quadratic Tracking Control of Car-in-the-Loop Test Bench using Model learnt via Bayesian Optimization

Gao,

Jardin,

Rinderknecht

2024

Preprint

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In this paper, we introduce a control method for the linear quadratic tracking (LQT) problem with zero steady-state error. It is achieved by augmenting the original system with an additional state representing the integrated error between the reference and actual outputs. In its essence, it is a linear quadratic integral (LQI) control embedded in a general LQT control framework, with the reference trajectory generated by a linear exogenous system. During the simulative implementation for the specific real-world system Car-in-the-Loop (CiL) test bench, we assume that the 'real' system is completely known. Therefore, for the model-based control, we can have a perfect model identical to the 'real' system. It becomes clear that stable solutions can scarcely be achieved with controller designed with the perfect model of the 'real' system. Contrary, we show that a model learnt via Bayesian Optimization (BO) can facilitate a much bigger set of stable controllers. It exhibits an improved control performance. To the best of the authors' knowledge, this discovery is the first in the LQT related literature.

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Section: Problem Descriptionmentioning

confidence: 99%

“…It is advantageous from an implementation point of view, especially for industrial systems. A good overview and performance evaluation of LQT for discrete time-invariant systems is given in [2]. For the case of finite horizon, recursive solutions for controls with fixed terminal states is proposed in [3].…”

Section: Introductionmentioning

confidence: 99%

Linear Quadratic Tracking Control of Car-in-the-Loop Test Bench using Model learnt via Bayesian Optimization

Gao,

Jardin,

Rinderknecht

2024

Preprint

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“…As in Section 3.2, the linear system given by Equation (10) was considered to determine a linear quadratic (LQ) optimal control [31][32][33][34] for the two-link robot arm.…”

Section: Linear Quadratic Optimal Controlmentioning

confidence: 99%

MPC Control and LQ Optimal Control of A Two-Link Robot Arm: A Comparative Study

et al. 2018

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This study examined the control of a planar two-link robot arm. The control approach design was based on the dynamic model of the robot. The mathematical model of the system was nonlinear, and thus a feedback linearization control was first proposed to obtain a linear system for which a model predictive control (MPC) was developed. The MPC control parameters were obtained analytically by minimizing a cost function. In addition, a simulation study was done comparing the proposed MPC control approach, the linear quadratic (LQ) control based on the same feedback linearization, and a control approach proposed in the literature for the same problem. The results showed the efficiency of the proposed method.

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“…LQ tracker is a well-established traditional method based on optimal control, and the controller consists of a feedback controller (i.e., nominal controller) and a feedforward controller (i.e., compensator), see [17,18]. However, the solution is obtained by calculating the recursive algebraic Raccati equations (ARE) and auxiliary differential equations, and thereby the reference is assumed to be known in advance, which restricts its practical application [18,19]. A solution for this problem is to design an online controller calculated without knowing the reference ahead of time.…”

Section: Introductionmentioning

confidence: 99%

H2/H∞ Output Tracking Control with a Performance Compensator for Aeroengines

et al. 2020

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A robust output tracking controller is necessary for the safe and reliable operation of aeroengines. This paper aims at developing an H 2 / H ∞ output tracking approach for aeroengines. In order to improve the tracking performance of the traditional robust tracker, the proposed control structure is designed as a combination of a nominal controller and a compensator. Concretely, an H 2 / H ∞ nominal controller is derived from game algebraic Raccati equation (GARE), which facilitates establishing a compensator for the system. Since the reference is usually unknown in advance for practical application, the proposed compensator is calculated online according to the nominal controller and the current reference. The solvability of the compensator and the stability of the system is guaranteed for both stable and bounded unstable references. Simulation examples for a turbofan engine are provided to demonstrate the effectiveness of the proposed algorithm.

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Development and performance evaluation of an infinite horizon LQ optimal tracker

Cited by 5 publications

References 16 publications

Linear Quadratic Tracking Control of Car-in-the-Loop Test Bench using Model learnt via Bayesian Optimization

Linear Quadratic Tracking Control of Car-in-the-Loop Test Bench using Model learnt via Bayesian Optimization

MPC Control and LQ Optimal Control of A Two-Link Robot Arm: A Comparative Study

H2/H∞ Output Tracking Control with a Performance Compensator for Aeroengines

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