Double Inverted Pendulum Research Articles

Sensor Fault Tolerant Controller for a Dou

This paper presents an Internal Model Control based structure to realise fault tolerance towards sensor faults. The proposed design implicitly embeds fault detection and controller elements requirements with considerations to stability and robustness towards uncertainties besides multiple faults environment. The performance of the proposed controller is demonstrated via multi input multi output and unstable system i.e. the double inverted pendulum system. Performance of the controller is compared with the well known H∞ controller. Results show the potential of this controller for implementation to handle systems with multiple sensor faults and uncertainties.

Design and Assessment of a Multiple Sensor Fault Tolerant Robust Control System

This paper presents an enhanced robust control design structure to realise fault tolerance towards sensor faults suitable for multi‐input‐multi‐output (MIMO) systems implementation. The proposed design permits fault detection and controller elements to be designed with considerations to stability and robustness towards uncertainties besides multiple faults environment on a common mathematical platform. This framework can also cater to systems requiring fast responses. A design example is illustrated with a fast, multivariable and unstable system, that is, the double inverted pendulum system. Results indicate the potential of this design framework to handle fast systems with multiple sensor faults.

Optimal output feedback stabilization

We show that optimal stabilization of a linear dynamic plant can be implemented on the basis of the solution of linear matrix inequalities even if the plant state cannot be measured. By way of example, we obtain optimal control laws for a double inverted pendulum assuming that only the lower link deflection angle is measured.

Active fault-tolerant control of a double inverted pendulum

This paper proposes an active fault-tolerant control scheme based on a gain-scheduled H∞ design strategy. Under the assumption that the effects of faults on the system can be of affine parameter dependence, a reconfigurable robust H∞ controller is developed. The resulting controller is a function of the fault effect factors, which can be derived online from the residual vector of the fault detection and isolation (FDI) mechanism. To demonstrate the effectiveness of the proposed method, a non-linear double inverted pendulum system with a fault in the motor tachometer loop is considered. The adaptive fault-tolerant controller recovers well from the unstable system with loop failure.

Decentralized adaptive recurrent neural control structure

This paper presents a novel decentralized variable structure neural control approach for large-scale uncertain systems, which is developed using recurrent high-order neural networks (RHONN). It is assumed that each subsystem belongs to a class of block-controllable nonlinear systems whose vector fields includes interconnection terms, which are bounded by nonlinear functions. A decentralized RHONN structure and the respective learning law are proposed in order to approximate online the dynamical behavior of each nonlinear subsystem. The control law, which is able to regulate and to track the desired reference signals, is designed using the well-known variable structure theory. The stability of the whole system is analyzed via the Lyapunov methodology. The applicability of the proposed decentralized identification and control algorithm is illustrated via simulations as applied to an interconnected double inverted pendulum.

432 部分空間制御法による直列二重倒立振子の振り上げ制御

As a typical control subject, inverted pendulum systems have been used to investigate effectiveness and feature of control methods. In this report, we applied a subspace control and swing up control based on Jacobian elliptic functions to swing up and stabilize a serial double inverted pendulum system. For swinging up pendulum, energy control is a most popular method now. On the other hand, we propose to cause a nonlinear resonance in order to swing up pendulums easily. The effectiveness of new swing up technique is verified by numerical simulation.

Minimal control synthesis adaptive control of nonlinear systems: utilizing the properties of chaos

This paper discusses a novel approach to the control of chaos based on the use of the adaptive minimal control synthesis algorithm. The strategies presented are based on the explicit exploitation of different properties of chaotic systems including the boundedness of the chaotic attractors and their topological transitivity (or ergodicity). It is shown that chaos can be exploited to synthesize more efficient control techniques for nonlinear systems. For instance, by using the ergodicity of the chaotic trajectory, we show that a local adaptive control strategy can be used to synthesize a global controller. An application is to the swing-up control of a double inverted pendulum.

A Linear-Programming-Based Sliding-Mode Control Design for Stabilization of a Double-Inverted Pendulum

A linear programming approach for computation of sliding-mode control inputs is proposed. The method is applied to a double-inverted pendulum system and it takes input and approaching rate constraints into account. The derivation procedure reveals that it is generalizable to a large class of dynamic systems and can take a more general set of constraints into account. The approach preserves the robustness property of the sliding-mode control and enriches it by adding the features of the linear programming. The main feature incorporated into the sliding-mode control is the optimal update of the control inputs under a set of linear constraints. The constraints are specified to meet the sliding-mode conditions and to improve its undesired chattering behaviour.

Force-plate based computation of ankle and hip strategies from double-inverted pendulum model

Using statistical characteristics of the centre of pressure displacement or of the ground reaction forces, it is difficult to have quantitative evaluation of the equilibrium strategy employed (ankle or hip). The purpose of this study is to validate a new force-plate based approach that allows to evaluate postural strategies employed through a method based on a double-inverted pendulum model. This method allows to compute ankle and hip joint motion only from force plate data and relies on inverse kinematics with the centre of mass considered as the end effector. Furthermore, an index, depending on the covariance between hip and ankle angles, is proposed to quantify the strategy used. To validate the method and the strategy index, we compare the results of our computation to an optical stereophotogrammetry measurement of the angles considered as reference value. The experiments demonstrate that our method provides acceptable results. The root mean square error between computed and measured hip and ankle angles stands between 4.5 x 10(-3)degrees for ankle angle in static condition and 1.1 x 10(-1) degrees for hip angle in hip forced condition. The main interest of our method for clinicians is that it allows to retrieve the ankle and hip angles only using a simple and widespread device, the force-plate. Moreover, it proposes a new postural index that can be also be computed without videographic systems.

ACTIVE FAULT-TOLERANT CONTROL OF A DOUBLE INVERTED PENDULUM

This paper proposes an active fault-tolerant control scheme based on gain-scheduled H-infinity control. Under the assumption that the effects of faults on system matrices can be of affine parameter dependence, a reconfigurable robust H-infinity controller is developed. The resulting controller is a function of the fault effect factors which can be derived on-line from the residual vector of the fault detection and isolation (FDI) mechanism. To demonstrate the effectiveness of the proposed method, a double inverted pendulum system with a fault in the tachometer loop of the motor is considered.

A ROBUST CONTROLLER CONFIGURATION FOR MULTIPLE SENSOR FAULT TOLERANCE

This paper presents an enhanced robust control design structure to realise fault tolerance towards sensor faults suitable for multi-input-multi-output (MIMO) systems implementation. The proposed design permits fault detection and controller elements to be designed with considerations to stability and robustness towards uncertainties besides multiple faults environment on a common mathematical platform. This framework can also cater to systems requiring fast responses. A design example is illustrated with a fast, multivariable and unstable system i.e. the double inverted pendulum system. Results indicate the potential of this design framework to handle fast systems with multiple sensor faults.

ACTIVE FAULT-TOLERANT CONTROL FOR UNSTABLE SYSTEMS

This paper concerns active fault-tolerant control (FTC) for unstable systems. A major obstacle to this problem is that the time delay between the fault appears and the FTC controller becomes active may destabilize the system. In this paper, an active FTC scheme based on gain-scheduled H-infinity controller and neural network is proposed. Under the assumption that the effects of faults on system matrices can be of affine parameter dependence, a reconfigurable robust H-infinity controller is developed, which is a function of the fault effect factors that can be derived on-line from the residual vector of the fault detection and isolation (FDI) mechanism. The proposed method is used for successful FTC control of a double inverted pendulum system with a fault in the tachometer loop of the motor.

Decoupling control by hierarchical fuzzy sliding-mode controller

A design method using hierarchical fuzzy sliding-mode (HFSM) decoupling control is proposed to achieve system stability and favorable decoupling performance for a class of nonlinear systems. In this approach, the nonlinear system is decoupled into several subsystems and the state response of each subsystem can be designed to be governed by a corresponding sliding surface. Then the whole system is controlled by a hierarchical sliding-mode controller. In this design, an adaptive law is derived based on the Lyapunov function to tune the coupling factor of the hierarchical sliding-mode controller so as to achieve favorable decoupling performance with guaranteed stability. The proposed design method is applied to investigate the decoupling control of a double inverted pendulum system. Simulations are performed and a comparison between the proposed HFSM decoupling control and a conventional fuzzy sliding-mode (FSM) decoupling control is presented to demonstrate the effectiveness of the proposed design method.

A new tracking algorithm for certain mechanical systems

A new algorithm is proposed for synthesizing a delayed on-off control for tracking slow motions of a certain class of mechanical systems. The conditions for a control to exist are found and examples are given of the solution of the tracking problem for inverted and double inverted pendulums.

Design and analysis of controllers for a double inverted pendulum

A physical control problem is studied with the H ∞ and the μ methodology. The issues of modeling, uncertainty modeling, performance specification, controller design, and laboratory implementation are discussed. The laboratory experiment is a double inverted pendulum placed on a cart. The limitations in the system with respect to performance are the limitation in the control signal and the limitation of the movement of the cart. It is shown how these performance limitations will effect the design of H ∞ and μ controllers for the system.

Stabilization Control for a Serial Double Inverted Pendulum with Observation-Time-Delay Using Delayed Feedback

In this paper, the stabilization problem of a plant with known delay in observation is studied. Although several methods, the Smith predictor or the state predictive control, have already been proposed about the control of plant with time delay, theoretical limitations and the practical inconvenience were left to be solved; e. g., the Smith predictor can only treat the stable systems, and the numerical integration of the exponential function is difficult in the state predictive control. The presented method combines the state feedback control with the delayed feedback control, which can stabilize the unstable systems and can be easily performed. The numerical simulation of the stabilization of the serial double inverted pendulum shows that the proposed method can he applied to stabilization of the unstable system and is effective for the impulsive disturbance.

DECENTRALIZED NEURONAL CONTROL STRUCTURE

A novel decentralized variable structure neural control approach for large-scale uncertain systems is developed using Recurrent High Order Neural Networks (RHONN). It is assumed that each subsystem belongs to a class of block-controllable nonlinear systems whose vector fields includes interconnections terms. The interconnection terms are bounded by nonlinear functions. A decentralized RHONN structure and the respective learning law, are propposed in order to approximate on-line the dynamical behaviour of each nonlinear subsystem. The control law, which is able to regulate and to track the desired reference signals, is designed using the well known variable structure theory. The stability of the whole system is analyzed via the Lyapunov methodology. The applicability of proposed decentralized identification and control algorithm is illustrated via simulations as applied to stabilize an interconnected double inverted pendulum.

Swing-Up Control of a Serial Cart-Type Double Inverted Pendulum System

In this paper, a swing up control scheme for a serial double inverted pendulum system is proposed. The pendulum system is cart-type and the swing upcontrol includes a position control of the cart. The control scheme is to swing up the pendulum in three steps, Step 1 : to swing up the first pendulum. Step 2 : to swing up the second pendulum while stabilizing the first pendulum at the upright position, and Step 3 : to stabilize the two pendulums around the unstable equilibrium state. In each step a control scheme and a switching rule from a step to the next step are given. And the position control of the cart by using feedback stabilization control is included in the controller of each step. For the controller of Step 1, the energy control method based on Lyapunov method is applied to swing up the first pendulum and the feedback stabilization controller of a cart position is added so as to satisfy the condition of Lyapunov method of the first pendulum. For the controller of Step 2, the proposed method combines a stabilization control method of the first pendulum and the cart position using sliding mode control method, and a swing-up control method of the second pendulum using energy control method. And for the controller in Step 3, the sliding mode controller stabilizing both of the pendulums and the cart position is used. A numerical simulation and an experimental result are given to show the effectiveness of the proposed scheme

Passive fault tolerant control of a double inverted pendulum—a case study

A passive fault tolerant control scheme is suggested, in which a nominal controller is augmented with an additional block, which guarantees stability and performance after the occurrence of a fault. The method is based on the YJBK parameterization, which requires the nominal controller to be implemented in observer based form. The proposed method is applied to a double inverted pendulum system, for which an H ∞ controller has been designed and verified in a lab setup. In this case study, the fault is a degradation of the tacho loop.

Hardware implementation of the quadruple inverted pendulum with single motor

Inverted pendulums are always used to verify some qualities and effect of certain control theory or method. Single or double inverted pendulum control system has been extensively studied for education and research purposes. However how to control a triple inverted pendulum is a difficult problem, which just a couple of control experts can solve including us. Undoubtedly, to implement controlling of a quadruple inverted pendulum is a very difficult problem, but we first successfully accomplished it using variable universe adaptive fuzzy control method in August, 2002. In this paper, a controller for a quadruple inverted pendulum is demonstrated using the variable universe adaptive fuzzy control theory.