Non-linear stable inversion-based output tracking control for a spherical inverted pendulum

We design an exact output tracking control law for a four degree of freedom spherical inverted pendulum based on the non-linear stable inversion tool proposed by Devasia et al. (1989). The pendulum is a slim cylindrical beam attached to a horizontal plane via a universal joint; the joint is free to move in the plane under the influence of a planar force. The upright position is an unstable equilibrium of the uncontrolled system because of gravity. The objective is to design a controller so that the pendulum can be steered to track some smooth desired translational trajectories while keeping the pendulum tightly around the upright position. The design proceeds in three steps: 1. identification of the internal dynamics; 2. feedforward control design for achievable trajectories; 3. feedback design to stabilize the achievable trajectories. The computer simulations show that the proposed controller can deliver excellent tracking performance.     

Attitude control of a triple inverted pendulum

The paper is concerned with the attitude control of a triple inverted pendulum. The lowest hinge is free for rotation and the torques of the upper two hinges are manipulated not only to stabilize the pendulum but also to control its attitude. The control system is designed by using CAD developed by the author and is realized by a minicomputer. The designed controller is a robust servo controller for a linearized model in the neighbourhood of the upright position of triple inverted pendulum. Experimental results show that the designed controller works satisfactorily.     

Stabilization of the inverted spherical pendulum via Lyapunov approach

In this paper a nonlinear controller is presented for the stabilization of the spherical inverted pendulum system. The control strategy is based on the Lyapunov approach in conjunction with LaSalle's invariance principle. The proposed controller is able to bring the pendulum to the unstable upright equilibrium point with the position of the movable base at the origin. The obtained closed‐loop system has a very large domain of attraction, that can be as large as desired, for any initial position of the pendulum which lies above the horizontal plane. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Nearly optimal neural network stabilization of bipedal standing using genetic algorithm

In this work, stability control of bipedal standing is investigated. The biped is simplified as an inverted pendulum with a foot-link. The controller consists of a general regression neural network (GRNN) feedback control, which stabilizes the inverted pendulum in a region around the upright position, and a PID feedback control, which keeps the pendulum at the upright position. The GRNN controller is also designed to minimize an energy-related cost function while satisfying the constraints between the foot-link and the ground. The optimization has been carried out using the genetic algorithm (GA) and the GRNN is directly trained during optimization iteration process to provide the closed loop feedback optimal controller. The stability of the controlled system is analyzed using the concept of Lyapunov exponents, and a stability region is determined. Simulation results show that the controller can keep the inverted pendulum at the upright position while nearly minimizing an energy-related cost function and keeping the foot-link stationary on the ground. The work contributes to bipedal balancing control, which is important to the development of bipedal robots.     

An Output Feedback Position/Speed Regulator for a Torque—driven Inertia Wheel Pendulum

This paper presents a position/speed regulator for a torque–driven inertia wheel pendulum where only position measurements are available for feedback. Our contribution is to introduce a controller that does not need joint velocity measurements, and instead it uses the output of a linear filtering of weighted joint position errors to add damping. The proposed controller allows bringing the nonactuated pendulum rod towards its upright position, while the wheel spins asymptotically to a desired constant speed. A complete stability analysis based on Barbashin–Krasovskii’s theorem is presented together with an estimate of domain of attraction. Simulation results upon a torque–driven inertia wheel pendulum model illustrate the performance of the proposed controller.

     

Systematic design method of stabilization fuzzy controllers for pendulum systems

A systematic method to construct stabilization fuzzy controllers for a single pendulum system and a series-type double pendulum system is presented based on the single input rule modules (SIRMs) dynamically connected fuzzy inference model. The angle and angular velocity of each pendulum and the position and velocity of the cart are selected as the input items. Each input item is given with a SIRM and a dynamic importance degree. All the SIRMs have the same rule setting. The dynamic importance degrees use the absolute value(s) of the angle(s) of the pendulum(s) as the antecedent variable(s). The dynamic importance degrees are designed such that the upper pendulum angular control takes the highest priority and the cart position control takes the lowest priority when the upper pendulum is not balanced upright. The control priority orders are automatically adjusted according to control situations. The simulation results show that the proposed fuzzy controllers have high generalization ability to completely stabilize a wide range of single pendulum systems and series-type double pendulum systems in short time. By extending the architecture, a stabilization fuzzy controller for a series-type triple pendulum system is even possible. © 2001 John Wiley & Sons, Inc.     

Interconnection and damping assignment passivity-based control of mechanical systems with underactuation degree one

Interconnection and damping assignment passivity-based control is a new controller design methodology developed for (asymptotic) stabilization of nonlinear systems that does not rely on, sometimes unnatural and technique-driven, linearization or decoupling procedures but instead endows the closed-loop system with a Hamiltonian structure with a desired energy function-that qualifies as Lyapunov function for the desired equilibrium. The assignable energy functions are characterized by a set of partial differential equations that must be solved to determine the control law. We prove in this paper that for a class of mechanical systems with underactuation degree one the partial differential equations can be explicitly solved. Furthermore, we introduce a suitable parametrization of assignable energy functions that provides the designer with a handle to address transient performance and robustness issues. Finally, we develop a speed estimator that allows the implementation of position-feedback controllers. The new result is applied to obtain an (almost) globally stabilizing scheme for the vertical takeoff and landing aircraft with strong input coupling, and a controller for the pendulum in a cart that can swing-up the pendulum from any position in the upper half plane and stop the cart at any desired location. In both cases we obtain very simple and intuitive position-feedback solutions.     

模糊规则控制一种绝对不稳定系统

本文设计了一个高精度、高分辨率的模糊控制器，并用以控制二阶倒立摆获得成功。提出了一种处理多变量系统的新观点，给出了模糊控制二阶倒立摆的控制规则；和一种强有力的清晰化方法，从而使模糊控制器的输出更加细腻，应用上述理论设计的高精度、高分辨率的模糊控制器，对二阶倒立摆进行实时控制获得成功。     

Stabilization of the inverted pendulum around its homoclinic orbit

The inverted pendulum has been used as a benchmark for motivating the study of nonlinear control techniques. We propose a simple controller for balancing the inverted pendulum and raise it to its upper equilibrium position while the cart displacement is brought to zero. The control strategy is based on an energy approach of the cart and pendulum system.     

A Modular Fuzzy Control Approach for Two-Wheeled Wheelchair

Wheelchairs on two wheels are becoming essential part of life for disabled persons. But designing control strategies for such wheelchairs is a challenging task due to the fact that they are highly nonlinear and unstable systems. The subtle design of the system mimics a double inverted pendulum with three actuators, one for each wheel, and one for chair position. The system starts to work with lifting the front wheels (casters) to the upright position and further with stabilizing in the upright position. The challenge resides in the design and implementation of suitable control strategies for the two-wheeled wheelchair so as to perform comparably similar to a normal four-wheeled wheelchair. A two-level modular fuzzy logic controller is proposed in this paper. A model of the standard wheelchair is also developed as a test and verification platform using Visual Nastran software integrated with Matlab.     

Global stabilization of the unstable Reaction-Wheel Pendulum

The paper deals with the problem of the Reaction Wheel Pendulum stabilization about unstable (inverted) position for arbitrary initial conditions. Considered mechanical system consists of a physical pendulum with a symmetric disk attached to the end of the pendulum, which is free to spin about an axis parallel to the axis of rotation of the pendulum. The disk is actuated by a DC-motor. The coupling torque generated by the angular acceleration of the disk is used to control of the pendulum. The switching control law is proposed to swinging up the pendulum and balancing it about the inverted position. The nonlinear swinging up control law is proposed ensuring global stabilization of the pendulum about inverted position. The Energy-based Speed-gradient (EBSG) control scheme is used to designing the swinging-up controller. The modification of the EBSG method is proposed to ensure attainability of the inverted position of the pendulum for all initial states of the system. The balance controller is designed on the basis of the Variable Structure Control with forced sliding mode. Numerical simulation results are presented showing achievement of the posed control goal by means of the control action of small magnitude.     

Computer control of a double inverted pendulum

A double inverted pendulum is successfully stabilized at the upright position by using a computer control. The control system is designed based on the state space approach by using a computer aided design program named CADOS developed for this purpose. CADOS was used not only for the analysis and design, but also for the simulation to evaluate the designed system. The controller designed consists of the state variable feedback and the observer. The state variable feedback is determined based on either pol-locations or as the optimal control for the quadratic criterion function. As the observer, the minimal order state observer or a linear functional observer is employed, and it is theoretically proved that the linear functional observer for a multiple inverted pendulum can always be realized by the first order. The designed controller is implemented in the mini-computer used for CADOS and could work satisfactorily. The controller using a linear functional observer requires less computation time and controls the system in more stable way.     

基于快速起摆的Furuta摆切换控制系统

针对由一个驱动臂和一个未驱动摆杆组成的欠驱动Furuta摆系统,设计了实现其稳定的切换控制系统.控制任务是将未驱动摆杆稳定在上方不稳定平衡点的同时,将驱动臂控制到零点,分为两部分:首先基于部分反馈线性化技术设计一个饱和的状态反馈控制器,将摆杆快速控制到上方不稳定平衡点附近;然后切换到一个线性的全状态反馈控制器,实现系统的稳定控制.仿真实验验证了控制器的有效性.     

Swing-up control strategies for a reaction wheel pendulum

Control of a reaction wheel pendulum, a prototype of an under-actuated system, is easily done using switching control strategies, which combines swing-up control and balancing control schemes. In this article, two novel swing-up control strategies for a reaction wheel pendulum have been proposed. The first swing-up control strategy treats the oscillations of the pendulum as perturbations from the bottom equilibrium point. The second swing-up control is based on interconnection and damping assignment-passivity based control (IDA-PBC). IDA-PBC preserves Euler Lagrangian structure of the system and gives more physical insight about any mechanical system. Any balancing controller can be coupled with the proposed swing-up control strategies to stabilise the pendulum at the top unstable equilibrium position. The control task of balancing the pendulum in top upright position is completed by switching from swing-up scheme to the balancing scheme at the point where the pendulum is very near to the top equilibrium point. Proposed swing-up control strategies have been implemented in real time in switching mode. The two proposed swing-up control schemes provide fast responses as compared to existing energy based schemes.     

基于DSP实现的一阶倒立摆控制

倒立摆是控制领域中典型的被控对象。本文通过智能控制算法实现倒立摆的起摆控制。当摆杆的角度进入稳定区域时,通过PID控制算法使摆杆稳定。整个控制过程由基于DSP(DigitalSignalProcessor)为核心的控制器来实现。经过实物检验,成功地实现了一级倒立摆的稳摆和起摆控制。     

Swing-up and stabilization of a cart–pendulum system under restricted cart track length

This paper describes the swing-up and stabilization of a cart–pendulum system with a restricted cart track length and restricted control force using generalized energy control methods. Starting from a pendant position, the pendulum is swung up to the upright unstable equilibrium configuration using energy control principles. An “energy well” is built within the cart track to prevent the cart from going outside the limited length. When sufficient energy is acquired by the pendulum, it goes into a “cruise” mode when the acquired energy is maintained. Finally, when the pendulum is close to the upright configuration, a stabilizing controller is activated around a linear zone about the upright configuration. The proposed scheme has worked well both in simulation and a practical setup and the conditions for stability have been derived using the multiple Lyapunov functions approach.     

基于Lyapunov能量函数的倒立摆稳定控制

倒立摆是一种复杂的非线性控制系统.通过对其进行控制能够检验控制器的鲁棒性.基于一个能量形式的Lyapunov函数设计了倒立摆稳定控制器使得摆趋于上平衡位置,并且使得小车位移和角度都收敛于零.该控制策略基于系统的总能量,利用其耗散特性设计了Lyapunov函数,并证明了控制系统的稳定性.理论分析及仿真试验表明该控制器对于倒立摆控制具有很强的鲁棒性.     

Two relay controller for real time trajectory generation and its application to inverted orbital stabilization of inertia wheel pendulum via quasi‐continuous HOSM

A quasi‐continuous high‐order sliding mode (QC‐HOSM) control is developed to solve the tracking control problem for an inertia wheel pendulum. A first step towards the solution of the tracking control problem in underactuated systems is to find the set of reference trajectories. A reference model based on the two relay controller idea is then developed for generating a set of desired periodic trajectories for the pendulum centered at its upright position. The two relay controller produces oscillations at the scalar output of the reference underactuated system where the desired amplitude and frequency are reached by choosing its gains. The HOSM will be capable of making the pendulum move, tracking the prescribed reference signals determined by the trajectory generator. Performance issues of the controller constructed are illustrated in an experimental study. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Incremental Evolutionary Design of TSK Fuzzy Controllers

This paper proposes a novel method for the incremental design and optimization of first order Tagaki-Sugeno-Kang (TSK) fuzzy controllers by means of an evolutionary algorithm. Starting with a single linear control law, the controller structure is gradually refined during the evolution. Structural augmentation is intertwined with evolutionary adaptation of the additional parameters with the objective not only to improve the control performance but also to maximize the stability region of the nonlinear system. From the viewpoint of optimization the proposed method follows a divide-and-conquer approach. Additional rules and their parameters are introduced into the controller structure in a neutral fashion, such that the adaptations of the less complex controller in the previous stage are initially preserved. The proposed scheme is evaluated at the task of TSK fuzzy controller design for the upswing and stabilization of a rotational inverted pendulum. In the first case, the objective is a time optimal controller that upswings the pendulum in to the upper equilibrium point in shortest time. The stabilizing controller is designed as a state optimal controller. In a second application the optimization method is applied to the design of a fuzzy controller for vision-based mobile robot navigation. The results demonstrate that the incremental scheme generates solutions that are similar in control performance to pure parameter optimization of only the gains of a TSK system. Even more important, whereas direct optimization of control systems with more than 35 rules fails to identify a stabilizing control law, the incremental scheme optimizes fuzzy state-space partitions and gains for hundreds of rules.     

Swinging up the spherical pendulum via stabilization of its first integrals

This paper presents a new controller for swinging up the spherical pendulum. The problem of stabilizing the upright equilibrium of the spherical pendulum is typically solved in two steps: First, a controller is used to swing up the pendulum so that it enters some vicinity of the upright equilibrium, and then a locally stabilizing controller is used. The contribution of this paper is the design of a controller that solves the first subproblem for almost all initial conditions. The controller stabilizes the two-dimensional stable manifold of the hyperbolic upright equilibrium. The proposed technique is based on the passivity properties of the spherical pendulum.