Optimal Tuning of a LQR Controller for an Inverted Pendulum Using the Bees Algorithm

Şen, Muhammed Arif; Kalyoncu, Mete

doi:10.18178/joace.4.5.384-387

Cited by 18 publications

(14 citation statements)

References 9 publications

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“…Up to now, in terms of processing practical systems, there are many optimization techniques [53][54] [55][56][57] on the existing researches. Some of optimization techniques, such as PSO algorithm [48][58] [59], genetic algorithm [60], bees algorithm [61], etc. can be applied to adjust optimal LQR weighting matrices.…”

Section: Optimal Controller Design Based On Pso and Lqr Algorithmsmentioning

confidence: 99%

Feedback Linearized Optimal Control Design for Quadrotor With Multi-Performances

Chen

2021

IEEE Access

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Design of tracking controller for quadrotor is an important issue for many engineering fields such as COVID-19 epidemic prevention, intelligent agriculture, military photography and rescue nowadays. This study applies the feedback linearized method and linear quadratic regulator (LQR) method using particle swarm optimization (PSO) to analysis and stabilize the highly nonlinear quadrotor system without applying any nonlinear function approximator that includes neural network approach and fuzzy approach. The article proposes a new method based on the firstly proposed convergence rate formula to achieve the optimal weighting matrices of LQR such that the composite controller can reduce the amplitudes of system control inputs. Determination of the LQR tuning parameters is conventionally achieved via trial and error approach. In addition to being very troublesome, it is difficult to find the globally best tuning matrices with LQR method. This article firstly uses the convergence rate formula of the nonlinear system as the fitness function of LQR approach by using PSO to take the place of the trial and error method. The generalities and implications of proposed approach are globally valid, whereas the Jacobian linearized approach is locally valid due to the Taylor expansion theorem. In addition to these two major achievements, the significant innovation of the proposed method is to possess "simultaneously" additional performances including the almost disturbance decoupling, input amplitude reduction, tuning parameter optimization and globally exponential stability performances. Comparative examples show that the convergence rate with our proposed optimal controller using the PSO algorithm is larger than the fuzzy method, and better than the singular perturbation method with high-gain feedback.INDEX TERMS Almost disturbance decoupling, COVID-19 epidemic prevention , feedback linearized approach, linear quadratic regulator, particle swarm optimization, quadrotor.

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Section: Optimal Controller Design Based On Pso and Lqr Algorithmsmentioning

confidence: 99%

Feedback Linearized Optimal Control Design for Quadrotor With Multi-Performances

Chen

2021

IEEE Access

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“…Một giải thuật tối ưu hóa khác cũng được sử dụng trong điều chỉnh hệ số ma trận tối ưu LQR trên mô hình con lắc ngược, đó là giải thuật bầy đàn PSO (cụ thể là đàn ong: Bees Algorithm) [4]. Kết quả áp dụng đáp ứng hệ con lắc ngược nhanh với thời gian tăng khoảng 1,51s, thời gian ổn định là 3,5s, độ vọt lố thấp 0,1%, sai số góc nghiêng trong khoảng ± 3 độ.…”

Section: Tổng Quan Nghiên Cứuunclassified

“…θ= 0,024 rad/s Kết quả nghiên cứu đã khắc phục được hiện tượng chattering so với phương pháp MOGA và APSO [5]. Bên cạnh đó, thời gian đáp ứng của vị trí và góc nghiêng con lắc cũng đã nhanh hơn 10% so với phương pháp kết hợp giữa giải thuật di truyền GA cùng với bộ điều khiển PID [2] và giảm lên đến 28% so với giải thuật bầy đàn PSO [4].…”

Section: Sử Dụng Giải Thuật DI Truyền (Ga)unclassified

Using Genetic Algorithm in Optimizing the Matrix of LQR Controller for Nonlinear Inverted Pendulum System

Nguyen¹

2019

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In this article, the author used the matlab software to simulate and then compared the results between the classical LQR (Linear Quadratic Regulator) controller and another method to adjust the matrix parameters toward optimization of the LQR controller. It is the GA (Genetic Algorithm) method to optimize the matrix of the LQR controller, and the results have been verified on the nonlinear pendulum model. The Genetic Algorithm is a modern control algorithm, which is widely applied in research and practice. The main objective of this article is to use the GA algorithm in order to optimize the matrix parameters of LQR controller, whichcontrolled the position and angle of the nonlinear inverted pendulum at the stable balance point. The matlab-based simulating results showed that the system has operated properly to the requirements and the output response has reached an equilibrium position of about 2.5 seconds.

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“…However, this algorithm has a problem of having to determine the weight of the control performances in the evaluation function. The Bees Algorithm (BA) is a method for designing weight matrices considering the control performances (Sen, 2016). This method uses an evaluation function for an LQR system.…”

Section: Introductionmentioning

confidence: 99%

“…This method uses an evaluation function for an LQR system. However, the disadvantage is that this evaluation function also needs to determine the weight for control performance (Sen, 2016;Pham, 2009). This paper proposes a weight matrix selection algorithm using SPSA for model predictive control.…”

Section: Introductionmentioning

confidence: 99%

A new weight selection algorithm using SPSA for model predictive control

Cho¹,

Otsuki

Kubota

2019

Mechanical Engineering Journal

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Model Predictive Control (MPC) is one of the control methods for discrete time systems. The optimal input is calculated by using Linear Quadratic Regulator (LQR). The weight matrices in the evaluation function for LQR are determined by a designer with professional experience and a trial & error approach. Therefore, even if the same system is targeted, the performance can differ depending on the designer. This paper proposes a new weight selection algorithm using Simultaneous Perturbation Stochastic Approximation (SPSA) for MPC. A new evaluation function is proposed for the selection algorithm. Numerical values of the overshoot and the settling time are directly applied as the user's requirements in this evaluation function. The optimal weight matrices numerically satisfying those requirements can be selected by the proposed algorithm. Simulation study of a zero momentum spacecraft shows that the proposed method is effective for the weight selection with consideration of performance.

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Optimal Tuning of a LQR Controller for an Inverted Pendulum Using the Bees Algorithm

Cited by 18 publications

References 9 publications

Feedback Linearized Optimal Control Design for Quadrotor With Multi-Performances

Feedback Linearized Optimal Control Design for Quadrotor With Multi-Performances

Using Genetic Algorithm in Optimizing the Matrix of LQR Controller for Nonlinear Inverted Pendulum System

A new weight selection algorithm using SPSA for model predictive control

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