The Ball and Beam System: Cascaded LQR-FLC Design and Implementation

Muhammad Ridho Rosa,Muhammad Zakiyullah Romdlony,Bambang Riyanto Trilaksono 제어·로봇·시스템학회 2023 International Journal of Control, Automation, and Vol.21 No.1

This paper aims to derive a dynamic model of ball and beam systems (BBS), design, and implement the optimal controller linear quadratic regulator (LQR) with cascaded feedback linearization controller (FLC). It is known that missing information of the parameter of the system model can cause undesired tracking results. The LQR-FLC can solve the tracking problem caused by model uncertainty. The LQR controller, the inner-loop controller, is designed based on the derived BBS dynamics model. Then FLC, the outer-loop controller, is designed to get the desired tracking error dynamics. By using LQR-FLC, one can use the simple PD controller to design the tracking error dynamics. In addition, the estimator is designed to provide the controller with the full-states information. This research is worth investigating because the LQR-FLC scheme for controlling the BBS is missing in the literature. The experiment is carried out using a hardware in loop (HIL) scheme where MATLAB-Simulink is connected to a microcontroller. Simulation and experimental results show the effectiveness of the proposed cascaded LQR-FLC.

Hybrid Fuzzy Learning Controller for an Unstable Nonlinear System

Chung, Byeong-Mook,Lee, Jae-Won,Joo, Hae-Ho,Lim, Yoon-Kyu Korean Society for Precision Engineering 2000 International Journal of Precision Engineering and Vol.1 No.1

Although it is well known that fuzzy learning controller is powerful for nonlinear systems, it is very difficult to apply a learning method if they are unstable. An unstable system diverges for impulse input. This divergence makes it difficult to learn the rules unless we can find the initial rules to make the system table prior to learning. Therefore, we introduced LQR(Linear Quadratic Regulator) technique to stabilize the system. It is a state feedback control to move unstable poles of a linear system to stable ones. But, if the system is nonlinear or complicated to get a liner model, we cannot expect good results with only LQR. In this paper, we propose that the LQR law is derived from a roughly approximated linear model, and next the fuzzy controller is tuned by the adaptive on-line learning with the real nonlinear plant. This hybrid controller of LQR and fuzzy learning was superior to the LQR of a linearized model in unstable nonlinear systems.

LQR-퍼지논리제어기에 의한 2중 차량 구조 역진자 시스템의 제어

허열(Yue Xu),최병재(Byung-Jae Choi) 한국지능시스템학회 2013 한국지능시스템학회논문지 Vol.23 No.3

임의의 비선형 시스템을 제어하기 위한 새로운 방법의 제어 알고리즘이 널리 보고되고 있으며, 그 유용성을 입증하기 위한 제어 대상 시스템으로 역진자 시스템이 널리 활용되고 있다. 본 논문에서는 스프링으로 연결된 2개의 차량에 장착된 역진자를 제어하는 알고리즘을 제시한다. 여기서 두 개의 차량 중 하나는 구동용, 다른 하나는 역진자를 장착한 무구동용이다. 이를 위한 시스템 모델링을 제시하고, 퍼지논리제어 시스템 기반의 양질의 제어기 설계를 제안한다. 본 논문에서는 퍼지논리제어기의 입력변수로 사용될 6개의 변수를 2개로 축소하기 위하여 LQR(Linar Quadratic Regulator) 기법을 도입하며, 이를 통하여 퍼지논리제어기 설계의 복잡성을 줄일 수 있음을 보인다. 더욱이 개선된 2-입력 퍼지논리제어기의 제어 규칙표가 skew-symmetric의 특성을 가지는 성질로부터 다시 단일입력 퍼지논리제어기 설계를 제안한다. 제안한 방법의 유용성을 입증하기 위하여 시뮬레이션을 수행하며, 이를 통하여 제안한 방법의 우수성을 입증한다. Any new method for controlling a nonlinear system has widely been reported. An inverted pendulum system has typically been used as a target system for demonstrating its usefulness. In this paper, we propose an algorithm to control a flexible joint cart based inverted pendulum system. Two carts are connected with a spring and one is a driving cart and the other is no driving cart with a pole. We here present a system modeling and a good fuzzy logic based control algorithm. We also introduce LQR (Linar Quadratic Regulator) technique for reducing the number of control variables. By using this technique, the number of input variables for a fuzzy logic controller is become only two not six. So the computational complexity is largely reduced. Moreover, a two-input fuzzy logic controller has a control rule table with a skew-symmetric property. And it will lead the design of a single-input fuzzy logic controller. In order to demonstrate the usefulness of the proposed method and prove the superiority of the proposed method, some computer simulations are presented..

웨이블렛 신경회로망 제어기를 이용한 비선형 시스템의 위치 제어에 관한 연구

이재현,Lee, Jae-Hyun 한국정보통신학회 2008 한국정보통신학회논문지 Vol.12 No.12

본 논문에서는 비선형 시스템의 위치 제어를 위하여 웨이블렛 신경회로망 제어기를 구성하였으며, 웨이블렛 신경회로망은 LQR 제어기의 성능을 향상 시킬 목적으로 사용한다. 불안전한 비선형 시스템을 선형화 시키고 안정화된 선형 시스템을 만들기 위하여 LQR를 사용하며, 외란에 효과적으로 적응하기 위하여 웨이블렛 신경회로망 제어기를 사용한다. 이 제어기를 비선형 시스템의 위치 제어에 적용하여 실험을 통해 그 유효성을 검정하였다. In this paper, applications of wavelet neural network controller to position control of nonlinear system are considered. Wavelet neural network is used in the objectives which improve the efficiency of LQR controllers. It is possible to make unstable nonlinear systems stable by using LQR(Linear Quadratic Regulator) technique. And, in order to be adapted to disturbance effectively in this system it uses wavelet neural network controller. Applying this method to the position control of nonlinear system, its usefulness is verified from the results of experiment.

PD제어와 LQR을 이용한 병진 시스템의 제어특성 연구

김택현,정상화,이동하 한국공작기계학회 2001 한국생산제조학회지 Vol.10 No.5

The translation system is made up of springs, masses and a dashpot. This precise piece of equipment is controlled electro-mechanically by a motor and operating program. The control strategy of the system can be changed by spring stiffness, change of mass, and the damping coefficient of the dashpot. This system proves the necessity and effect of a closed loop control. In this paper, PD control experiments were implemented for the translation system. When the notch filter was added on the PD controller, we compared the response characteristics of the two systems. The state feedback controller minimized scalar control gains and the resulting response characteristics of the system were studied using the LQR design. Finally, we improved the response characteristics of the translation system which are rising time, settling time, steady state error, and overshoot. LQR was better as compared with PD control.

반작용 휠의 LQR 제어를 통한 Cubli 프레임의 균형유지

김용훈 ( Yonghun Kim ),박준모 ( Junmo Park ),한승오 ( Seungoh Han ) 한국센서학회 2018 센서학회지 Vol.27 No.3

A single-axis Cubli frame realized simply with an IMU sensor and DC motor is presented herein. To maintain the balance on the Cubli frame, an LQR controller based on a Lagrangian derivation of the dynamics was designed, which utilized the state variables of the frame angle and its angular acceleration, as well as the wheel angle and its angular acceleration. The designed LQR controller showed a settling time balancing capability of approximately two seconds and 40% of the maximum overshoot in Matlab/Simulink simulations. Our experimental results of the fabricated Cubli frame matched with the simulation results. It maintained balancing at the reference position even though an initial offset as well as external disturbance during the balancing was applied.

Off-Policy 학습 기반 LQR을 이용한 파라미터 추정 및 전력 시스템 동기 탈조 판별을 위한 외란 관측기 설계

양선직(Sun Jick Yang),장수영(Su Young Jang),손영익(Young Ik Son) 대한전기학회 2021 전기학회논문지 Vol.70 No.1

In this paper, a reinforcement learning-based Linear Quadratic Regulator(LQR) design method has been adopted to identify unknown system parameters. The off-policy learning-based LQR can obtain the optimal control gain through an iteration technique known as policy iteration, without using the system model parameters. Augmented states, using the system output integration, can help to alleviate the rank condition on the proposed parameter estimation method. Increasing the system model information accuracy allows the disturbance observers to detect various system faults with the least amount of estimation error. The line fault detection ability of a power system for out-of-step prediction has been studied by applying the proposed parameter estimation scheme to a single machine infinite bus system. Simulation results show that both the system parameters and the external disturbance can be successfully estimated through the proposed method.

Characteristics Comparison of Motion Controllers through Experiments

정승현,왕준,한창욱,박정일,Jung, Seung-Hyun,Wang, Jun,Han, Chang-Wook,Park, Jung-Il Institute of Control 2008 제어·로봇·시스템학회 논문지 Vol.14 No.11

Through the motion control experiment using Industrial Emulator(Model 220 by ECP), the performance comparison of three kinds of controllers such as PID, RIC and LQR was carried out. It was shown that RIC has the best performance in the presence of disturbances such as step one, sinusoidal one and Coulomb friction for the rigid body. LQR using feedback state variables has the best tracking performance far the flexible body. The performance of PID controller is low compared to other controllers, but the design process is simple. The most advanced controller is LQR. In order to attenuate disturbance, an additional state observer should be used to estimate it, making more complex control system. RIC lies between PID and LQR in view of complexity of design. Even though RIC is not complicated, it has good disturbance rejection ability and less tracking error. By considering these aspects, the RIC is suggested as high precision controller to be used in motion control system.

Characteristics Comparison of Motion Controllers through Experiments

Seung Hyun Jung(정승현),Jun Wang(왕준),Chang Wook Han(한창욱),Jung-Il Park(박정일) 제어로봇시스템학회 2008 제어·로봇·시스템학회 논문지 Vol.14 No.11

Through the motion control experiment using Industrial Emulator(Model 220 by ECP), the performance comparison of three kinds of controllers such as PID, RIC and LQR was carried out. It was shown that RIC has the best performance in the presence of disturbances such as step one, sinusoidal one and Coulomb friction for the rigid body. LQR using feedback state variables has the best tracking performance for the flexible body. The performance of PID controller is Jow compared to other controllers, but the design process is simple. The most advanced controller is LQR. In order to attenuate disturbance, an additional state observer should be used to estimate it, making more complex control system. RIC lies between PlD and LQR in view of complexity of design. Even though RIC is not complicated, it has good disturbance rejection ability and less tracking error. By considering these aspects, the RIC is suggested as high precision controller to be used in motion control system.

통합 섀시 제어를 위한 LQR의 가중치 변화에 대한 민감도 해석

임성진(Seonjin Yim) 제어로봇시스템학회 2017 제어·로봇·시스템학회 논문지 Vol.23 No.4

This article presents a sensitivity analysis on the weight of the linear quadratic regulator (LQR) for integrated chassis control. Electronic stability control (ESC) and active front steering (AFS) are used as actuators needed to generate a control tire force. After computing the control yaw moment in the upper-level controller, the lower-level controller was used to distribute the control yaw moment into the control tire forces generated by ESC and AFS. In this paper, the LQR was used to design the upper-level controller. The Taguchi method was used to complete a sensitivity analysis on the weight of the linear quadratic (LQ) objective function in the LQR. For the sensitivity analysis, simulation was performed using CarSim, a vehicle simulation package. From the sensitivity analysis, the effect of the LQ objective function weight on the control performance was checked. Based on this sensitivity analysis, it was determined that the weights on lateral acceleration and yaw rate error had the largest effect on the control performance.