A new algebraic LQR weight selection algorithm for tracking control of 2 DoF torsion system

Abstract

This paper proposes a novel linear quadratic regulator (LQR) weight selection algorithm by synthesizing the algebraic Riccati equation (ARE) with the Lagrange multiplier method for command following applications of a 2 degree of freedom (DoF) torsion system. The optimal performance of LQR greatly depends on the elements of weighting matrices Q and R. However, normally these weighting matrices are chosen by a trial and error approach which is not only time consuming but cumbersome. Hence, to address this issue, blending the design criteria in time domain with the ARE, we put forward an algebraic weight selection algorithm, which makes the LQR design both simple and modular. Moreover, to estimate the velocity of a servo angle, a high gain observer (HGO) is designed and integrated with the LQR control scheme. The efficacy of the proposed control scheme is tested on a benchmark 2 DoF torsion system for a trajectory tracking application. Both the steady state and dynamic characteristics of the proposed controller are assessed. The experimental results accentuate that the proposed HGO based LQR scheme can guarantee the system to attain the design requirements with minimal vibrations and tracking errors.

New genetic algorithm for structural active control by considering the effect of time delay

“…Here, Q and R are the weighted matrices that indicate the importance of the state and control variables in the minimization process (Elumalai and Subramanian, 2017;Oliveira et al, 2015). Moreover, the equivalent critical damping method called ECD determines the actuator force by applying the critical damping theory to the first vibration's mode (Alamatian and Rezaeepazhand, 2011;Karimpour et al, 2014)…”

Determination of LQR weights by Bayesian optimization method using multiple earthquake waves

“…For example, Kohiyama et al presented a method that estimates the responses for the MDOF model by using the complex-complete-quadratic-combination (CCQC) method [5]. Elumalai et al have shown the weighting matrices can be yielded by solving the inverse problem for MDOF models [6]. However, if a building model is high-DOF system, many damping ratios and natural frequencies have to be chosen to calculate the weighting matrices.…”

A new weight selection algorithm using SPSA for model predictive control

“…The desired performance can generally be represented by using damping ratio and natural frequency in second-order system for Single-Input-Single-Output (SISO) systems. Elumalai & Subramanian (2017) proposed the method to select the weight matrix by synthesizing the Algebraic Riccati Equation (ARE) with the Lagrange multiplier method. However, the calculation of synthesizing must be done for each model, because a coefficient matrix is different for each model.…”

“…Some previous research for weight tuning algorithm used algebraic calculation, Particle Swarm Optimization(PSO), Genetic Algorithm(GA), and Simultaneous Perturbation Stochastic Approximation (SPSA). Elumalai & Subramanian (2017) selected the weight matrix using algebraic calculation, but only targeted SISO systems. Tuning LQR using PSO algorithm provides better performance than PID controller.…”