• Title/Summary/Keyword: lyapunov stability

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Backstepping Sliding Mode-based Model-free Control of Electro-hydraulic Systems

  • Truong, Hoai-Vu-Anh;Trinh, Hoai-An;Ahn, Kyoung-Kwan
    • Journal of Drive and Control
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    • v.19 no.1
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    • pp.51-61
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    • 2022
  • This paper presents a model-free system based on a framework of a backstepping sliding mode control (BSMC) with a radial basis function neural network (RBFNN) and adaptive mechanism for electro-hydraulic systems (EHSs). First, an EHS mathematical model was dedicatedly derived to understand the system behavior. Based on the system structure, BSMC was employed to satisfy the output performance. Due to the highly nonlinear characteristics and the presence of parametric uncertainties, a model-free approximator based on an RBFNN was developed to compensate for the EHS dynamics, thus addressing the difficulty in the requirement of system information. Adaptive laws based on the actor-critic neural network (ACNN) were implemented to suppress the existing error in the approximation and satisfy system qualification. The stability of the closed-loop system was theoretically proven by the Lyapunov function. To evaluate the effectiveness of the proposed algorithm, proportional-integrated-derivative (PID) and improved PID with ACNN (ACPID), which are considered two complete model-free methods, and adaptive backstepping sliding mode control, considered an ideal model-based method with the same adaptive laws, were used as two benchmark control strategies in a comparative simulation. The simulated results validated the superiority of the proposed algorithm in achieving nearly the same performance as the ideal adaptive BSMC.

Design of a real time adaptive controller for industrial robot using TMS320C31 chip (TMS320C31칩을 사용한 산엽용 로보트의 실시간 적응 제어기 설계)

  • Han, S.H.;Kim, Y.T.;Lee, M.H.;Kim, S.K.;Kim, J.O.
    • Journal of the Korean Society for Precision Engineering
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    • v.13 no.10
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    • pp.94-104
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    • 1996
  • This paper presents a new approach to the design of adaptive control system using DSPs(TMS320C31) for robotic manpulators to achieve accurate trajectory tracking by the joint angles Digital signal processors are used in implementing real time adaptive control algorithms to provide an enhanced motion control for robotic manipulators. In the proposed contorl scheme, adaptation laws are derived from the improved Lyapunov second stability analysis method based on the adaptive model reference control theory. The adaptive controller consists of an adaptive feedforward controller, feedback controller, and PID type time varying auxillary control elements. The proposed adaptive control scheme is simple in structure, fast in computation, and suitable for implementation of real-time control. Morever, this scheme does not require an accurate dynamic modeling nor values of manpipulator parameters and payload. Performance of the adaptive controller is illustated by simulation and experimental results for a SCARA robot.

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A Study on I-PID-Based 2-DOF Snake Robot Head Control Scheme Using RBF Neural Network and Robust Term (RBF 신경망과 강인 항을 적용한 I-PID 기반 2 자유도 뱀 로봇 머리 제어에 관한 연구)

  • Sung-Jae Kim;Jin-Ho Suh
    • The Journal of Korea Robotics Society
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    • v.19 no.2
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    • pp.139-148
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    • 2024
  • In this paper, we propose a two-degree-of-freedom snake robot head system and an I-PID (Intelligent Proportional-Integral-Derivative)-based controller utilizing RBF (Radial Basis Function) neural network and adaptive robust terms as a control strategy to reduce rotation occurring in the snake robot head. This study proposes a two-degree-of-freedom snake robot head system to avoid complex snake robot dynamics. This system has a control system independent of the snake robot. Subsequently, it utilizes an I-PID controller to implement a control system that can effectively manage rotation at the snake robot head, the robot's nonlinearity, and disturbances. To compensate for the time delay estimation errors occurring in the I-PID control system, an RBF neural network is integrated. Additionally, an adaptive robust term is designed and integrated into the control system to enhance robustness and generate control inputs responsive to signal changes. The proposed controller satisfies stability according to Lyapunov's theory. The proposed control strategy was tested using a 9-degreeof-freedom snake robot. It demonstrates the capability to reduce rotation in Lateral undulation, Rectilinear, and Sidewinding locomotion.

Robust and Non-fragile H Controller Design Algorithm for Time-delayed System with Randomly Occurring Uncertainties and Disturbances ) (임의발생 불확실성 및 외란을 고려한 시간지연시스템의 강인비약성 H 제어기 설계 알고리듬)

  • Yang, Seung Hyeop;Paik, Seung Hyun;Lee, Jun Yeong;Park, Hong Bae
    • Journal of the Institute of Electronics and Information Engineers
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    • v.52 no.12
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    • pp.89-98
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    • 2015
  • This paper provides a robust and non-fragile $H_{\infty}$ controller design algorithm for time-delayed systems with randomly occurring polytopic uncertainties and disturbances. First, we design time-delayed system considering randomly occurring uncertainties and disturbances. Next, The sufficient condition for the existence of robust and non-fragile $H_{\infty}$ controller is presented by LMI(linear matrix inequality) using Lyapunov stability analysis and $H_{\infty}$ performance measure. Since the obtained condition can be expressed as a PLMI(parameterized linear matrix inequality) by changes of variables and Schur complement, all solutions including controller gain, degrees of controller satisfying non-fragility, $H_{\infty}$ norm bound ${\gamma}$ can be calculated simultaneously. Finally, numerical examples are given to illustrate the performance and the effectiveness of the proposed robust and non-fragile $H_{\infty}$ controller compared with the deterministic uncertainty model even though there exists randomly occurring uncertainties, disturbances and time delays.

Design of Robust Fuzzy Controllers via Inverse Optimal Approach (역최적화 방법을 이용한 강인한 퍼지 제어기의 설계)

  • 곽기호;임재환;박주영
    • Journal of the Korean Institute of Intelligent Systems
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    • v.11 no.6
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    • pp.477-486
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    • 2001
  • In this paper , we study the problem of designing TS(Takagi-Sugeno) fuzzy controllers for the systems that can be approximated or represented by the TS fuzzy model. The main strategy used in this paper is the inverse optimal approach, in which the cost function is determined later than the Lyapunov function and its corresponding control input satisfying the design requirements such as stability, decay rate, and robustness against uncertainty. This approach is useful because it yields controllers satisfying the inherent robustness of optimal controllers as well as the considered design goals. The design procedures established in this paper are all in the from of solving LMIs(Iinear matrix inequalities). Since the LMIs arising in the design procedures can be solved within a given tolerance by the interior point methods. the design method of the paper are efficient in practice. The applicability of the proposed design procedures is demonstrated by design examples.

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A study on simulation and performance improvement of industrial robot manipulator controller using adaptive model following control method (적응모델추종제어기법에 의한 산업용 로봇 매니퓰레이터 제어기의 성능개선 및 시뮬레이션에 관한 연구)

  • 허남수;한성현;이만형
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.15 no.2
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    • pp.463-477
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    • 1991
  • This study proposed a new method to design a robot manipulator control system capable of tracking the trajectories of joint angles in a reasonable accuracy to cover with actual situation of varying payload, uncertain parameters, and time delay. The direct adaptive model following control method has been used to improve existing industrial robot manipulator control system design. The proposed robot manipulator controller is operated by adjusting its gains based on the response of the manipulator in such a way that the manipulator closely matches the reference model trajectories predefined by the designer. The manipulator control system studied has two loops: they are an inner loop on adaptive model following controller to compensate nonlinearity in the manipulator dynamic equation and to decouple the coupling terms and an outer loop of state feedback controller with integral action to guarantee the stability of the adaptive scheme. This adaptation algorithm is based on the hyperstability approach with an improved Lyapunov function. The coupling among joints and the nonlinearity in the dynamic equation are explicitly considered. The designed manipulator controller shows good tracking performance in various cases, load variation, parameter uncertainties. and time delay. Since the proposed adaptive control method requires only a small number of parameters to be estimated, the controller has a relatively simple structure compared to the other adaptive manipulator controllers. Therefore, the method used is expected to be well suited for a high performance robot controller under practical operation environments.

Controlling robot by image-based visual servoing with stereo cameras

  • Fan, Jun-Min;Won, Sang-Chul
    • Proceedings of the Korea Society of Information Technology Applications Conference
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    • 2005.11a
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    • pp.229-232
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    • 2005
  • In this paper, an image-based "approach-align -grasp" visual servo control design is proposed for the problem of object grasping, which is based on the binocular stand-alone system. The basic idea consists of considering a vision system as a specific sensor dedicated a task and included in a control servo loop, and we perform automatic grasping follows the classical approach of splitting the task into preparation and execution stages. During the execution stage, once the image-based control modeling is established, the control task can be performed automatically. The proposed visual servoing control scheme ensures the convergence of the image-features to desired trajectories by using the Jacobian matrix, which is proved by the Lyapunov stability theory. And we also stress the importance of projective invariant object/gripper alignment. The alignment between two solids in 3-D projective space can be represented with view-invariant, more precisely; it can be easily mapped into an image set-point without any knowledge about the camera parameters. The main feature of this method is that the accuracy associated with the task to be performed is not affected by discrepancies between the Euclidean setups at preparation and at task execution stages. Then according to the projective alignment, the set point can be computed. The robot gripper will move to the desired position with the image-based control law. In this paper we adopt a constant Jacobian online. Such method describe herein integrate vision system, robotics and automatic control to achieve its goal, it overcomes disadvantages of discrepancies between the different Euclidean setups and proposes control law in binocular-stand vision case. The experimental simulation shows that such image-based approach is effective in performing the precise alignment between the robot end-effector and the object.

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The Control of Flexible Robot Arm using Adaptive Control Theory (적응제어 이론을 이용한 유연한 로봇팔의 제어)

  • Han, Jong-Kil
    • The Journal of the Korea institute of electronic communication sciences
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    • v.7 no.5
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    • pp.1139-1144
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    • 2012
  • The ration of payload to weight of industrial robot amounts form 1:10 to 1:30. Compared with man who have a ration of 3:1, it is very low. One of the goals for the next generation of robots will be a ration. This might be possible only by developing lightweight robots. When two-link flexible arm is rotated about an joint axis, transverse vibration may occur. In this paper, vibration dynamics of flexible arm is modeled by using Bernoulli-Euler beam theory and Lagrange equation. Using the fact that matrix $\dot{D}-2C$ is skew symmetric, new controllers which have a simplified structure with less computational burden is proposed by using Lyapunov stability theory. We propose deterministic and adaptive control laws for two link flexible arm, and the validity of the proposed control scheme is shown in computer simulation for two-link flexible arm.

Flight Control of Tilt-Rotor Airplane In Rotary-Wing Mode Using Adaptive Control Based on Output-Feedback (출력기반 적응제어기법을 이용한 틸트로터 항공기의 회전익 모드 설계연구)

  • Ha, Cheol-Keun;Im, Jae-Hyoung
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.38 no.3
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    • pp.228-235
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    • 2010
  • This paper deals with an autonomous flight controller design problem for a tilt-rotor aircraft in rotary-wing mode. The inner-loop algorithm is designed using the output-based approximate feedback linearization. The model error originated from the feedback linearization is cancelled within allowable tolerance by using single-hidden-layer neural network. According to Lyapunov direct stability theory, the adaptive update law is derived to run the neural network on-line, which is based on the linear observer dynamics. Moreover, the outer-loop algorithm is designed to track the trajectory generated from way-point guidance. Especially, heading and flight-path angle line-of-sight guidance are applied to the outer-loop to improve accuracy of the landing tracking performance. The 6-DOF nonlinear simulation shows that the overall performance of the flight control algorithm is satisfactory even though the collective input response shows instantaneous actuator saturation for a short time due to the lack of the neural network and the saturation protection logic in that loop.

Structural vibration control using $H_{\infty}$ control theory : unceratinty model ($H_{\infty}$제어이론을 이용한 구조진동제어 - 불확실성 모델)

  • 송병석
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 1995.04a
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    • pp.240-245
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    • 1995
  • 제어이론의 역사적 발전사를 고찰해보면 1930년대부터 1960년대까지를 고전 제어(classical control) 시대로 분류되고 이때 주로 사용되었던 용어들은 주파수역(frequency domain)에서 사용된 개념인 극점(pole), 영점(zero), Nyquist, 근궤적(root-Locus) 선도(plot)등으로 대표된다. 그 다음단계인 현대 제어(modern control) 시대 (1960년대-1980년대)때는 새로운 개념들이 도입 되었는데 시간역(time domain)에서 사용되는 상태공간(state-space) 모델, 가제어성(controllability), 가관측성(observability), Kalman 필터, LQG 제어 등이다. 1980년대부터 현재까지를 강인제어(robust control) 시대로 분류하는데 이것의 특징들은 극점이나 영점 대신 상태공간 모델을 사용하여 주파수역에서 정의되는 개념들인 H$_{\infty}$ 합성법, .$\mu$ 해석법, LQG/LTR 및 QFT, Lyapunov 등으로 대표된다. 현대제어시대때는 제어기 K는 공칭 플랜트 모델 G$_{0}$를 기준으로 설계되었으나 실제로 공칭 플랜트 모델은 실제 플랜트와 항상 같을 수가 없었다. 따라서 실제 플랜트 G는 G=G$_{0}$ + .DELTA.G로 표현되며 여기서 .DELTA.G는 플랜트 불 확실성(plant uncertainty), 즉 실제 플랜트와 공칭 플랜트의 차이를 나타낸 다. 이 플랜트 불확실성은 제어기가 실제 응용되어 사용되었을 때 제대로 작동하지 않는 주요 이유중에 하나이다. 이와 같은 상황에서 안정도 강인성 (stability robustness) 및 성능 강인성(performance rosubtness)의 보장은 상 당히 중요한 문제로 대두되었으며 주어진 플랜트 불확실성하에서 이러한 강이성들이 보장되는 제어이론들 중 H$_{\infty}$ 제어이론이 많이 연구/응용 되고 있다. 특히 공칭 플랜트 모델과 함께 사용되는 플랜트 모델과 함께 사용되는 플랜트 불확실성 모델은 직접적으로 성능 및 안정도에 영향을 미치므로 주의 깊게 선정해야 한다.

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