Editing and Synthesizing Two‐Character Motions using a Coupled Inverted Pendulum Model

This study aims to develop a controller for use in the online simulation of two interacting characters. This controller is capable of generalizing two sets of interaction motions of the two characters based on the relationships between the characters. The controller can exhibit similar motions to a captured human motion while reacting in a natural way to the opponent character in real time. To achieve this, we propose a new type of physical model called a coupled inverted pendulum on carts that comprises two inverted pendulum on a cart models, one for each individual, which are coupled by a relationship model. The proposed framework is divided into two steps: motion analysis and motion synthesis. Motion analysis is an offline preprocessing step, which optimizes the control parameters to move the proposed model along a motion capture trajectory of two interacting humans. The optimization procedure generates a coupled pendulum trajectory which represents the relationship between two characters for each frame, and is used as a reference in the synthesis step. In the motion synthesis step, a new coupled pendulum trajectory is planned reflecting the effects of the physical interaction, and the captured reference motions are edited based on the planned trajectory produced by the coupled pendulum trajectory generator. To validate the proposed framework, we used a motion capture data set showing two people performing kickboxing. The proposed controller is able to generalize the behaviors of two humans to different situations such as different speeds and turning speeds in a realistic way in real time.     

Energy shaping control of an inverted flexible pendulum fixed to a cart

Control of compliant mechanical systems is increasingly being researched for several applications including flexible link robots and ultra-precision positioning systems. The control problem in these systems is challenging, especially with gravity coupling and large deformations, because of inherent underactuation and the combination of lumped and distributed parameters of a nonlinear system. In this paper we consider an ultra-flexible inverted pendulum on a cart and propose a new nonlinear energy shaping controller to keep the pendulum at the upward position with the cart stopped at a desired location. The design is based on a model, obtained via the constrained Lagrange formulation, which previously has been validated experimentally. The controller design consists of a partial feedback linearization step followed by a standard PID controller acting on two passive outputs. Boundedness of all signals and (local) asymptotic stability of the desired equilibrium is theoretically established. Simulations and experimental evidence assess the performance of the proposed controller.     

Adaptive Nonlinear Control of Wind Energy Conversion System Involving Induction Generator

This paper presents a theoretical framework for adaptive control of a wind energy conversion system (WECS), involving a squirrel cage induction generator (SIG) connected with an AC/DC/AC IGBT‐based PWM converter. A multi‐loop nonlinear controller is designed to meet two main control objectives, i.e., (i) speed reference optimization in order to extract a maximum wind energy whatever the wind speed, and (ii) power factor correction (PFC) to avoid net harmonic pollution. These objectives must be achieved despite the mechanical parameters uncertainty. First, a nonlinear model of the whole controlled system is developed within the Park coordinates. Then, a multi‐loop nonlinear controller is synthesized using the adaptive backstepping design. A formal analysis based on Lyapunov stability is carried out to describe the control system performances. In addition to closed‐loop global asymptotic stability, it is proven that all control objectives (induction generator speed tracking, rotor flux regulation, DC link voltage regulation and unitary power factor) are asymptotically achieved.     

Nonlinear control for rotational movement of cart-pendulum system using homoclinic orbit

In this paper, we deal with the control method for rotational movements of a pendulum using a separatrix. We design a controller that attains a homoclinic motion or a heteroclinic motion of the pendulum and the asymptotic stability of the cart by using a kind of forwarding control design. First, we derive a controller that converges to a homoclinic orbit via a Lyapunov function of the pendulum subsystem. Next, we give a nonlinear stabilizing controller via another Lyapunov function of the cart subsystem. Moreover, using the third Lyapunov function and adding a complementary control input, we guarantee that the pendulum converges to the homoclinic orbit and the cart is stabilized. Finally, the simulation and the experiment using the rapid controller prototyping system based on MATLAB/Simulink are performed to demonstrate the forward upward circling and the giant swing of the pendulum.     

How the brain generates movement

In this study, we assume that the brain uses a general-purpose pattern generator to transform static commands into basic movement segments. We hypothesize that this pattern generator includes an oscillator whose complete cycle generates a single movement segment. In order to demonstrate this hypothesis, we construct an oscillator-based model of movement generation. The model includes an oscillator that generates harmonic outputs whose frequency and amplitudes can be modulated by external inputs. The harmonic outputs drive a number of integrators, each activating a single muscle. The model generates muscle activation patterns composed of rectilinear and harmonic terms. We show that rectilinear and fundamental harmonic terms account for known properties of natural movements, such as the invariant bell-shaped hand velocity profile during reaching. We implement these dynamics by a neural network model and characterize the tuning properties of the neural integrator cells, the neural oscillator cells, and the inputs to the system. Finally, we propose a method to test our hypothesis that a neural oscillator is a central component in the generation of voluntary movement.     

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     

Robust fuzzy control for continuous perturbed time‐delay affine takagi–sugeno fuzzy models

The stability analysis and controller synthesis methodology for a continuous perturbed time‐delay affine (CPTDA) Takagi–Sugeno (T‐S) fuzzy model is proposed in this paper. The CPTDA T‐S fuzzy models include both linear nominal parts and uncertain parameters in each fuzzy rule. The proposed fuzzy control approach is developed based on an iterative linear matrix inequality (ILMI) algorithm to cope with the stability criteria and H_∞ performance constraints for the CPTDA T‐S fuzzy models. Finally, a numerical simulation for the nonlinear inverted pendulum system is given to show the application and availability of the present design approach. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

A new OFRMPC formulation with on‐line synthesis of the dynamic output feedback controller

This paper proposes a new approach for the design of output feedback robust model predictive control (OFRMPC) with a dynamic output feedback controller (DOFC) for linear uncertain systems subject to input and output constraints. The main contribution of this work is the full on‐line synthesis of the DOFC as part of a convex optimization problem, with constraint satisfaction and asymptotic stability guarantees. A numerical example is employed to illustrate the advantage of the proposed control law, as compared with another OFRMPC strategy with partial DOFC synthesis. The present paper also points out an inconsistency in the mathematical development of a previous related OFRMPC formulation (‘improved dynamic output feedback RMPC for linear uncertain systems with input constraints’). Copyright © 2017 John Wiley & Sons, Ltd.     

NETWORK‐INDUCED DELAY‐DEPENDENT H∞ CONTROLLER DESIGN FOR A CLASS OF NETWORKED CONTROL SYSTEMS

This paper is concerned with the problem of robust H_∞ controller design for a class of uncertain networked control systems (NCSs). The network‐induced delay is of an interval‐like time‐varying type integer, which means that both lower and upper bounds for such a kind of delay are available. The parameter uncertainties are assumed to be normbounded and possibly time‐varying. Based on Lyapunov‐Krasovskii functional approach, a robust H_∞ controller for uncertain NCSs is designed by using a sum inequality which is first introduced and plays an important role in deriving the controller. A delay‐dependent condition for the existence of a state feedback controller, which ensures internal asymptotic stability and a prescribed H_∞ performance level of the closed‐loop system for all admissible uncertainties, is proposed in terms of a nonlinear matrix inequality which can be solved by a linearization algorithm, and no parameters need to be adjusted. A numerical example about a balancing problem of an inverted pendulum on a cart is given to show the effectiveness of the proposed design method.     

不确定平面二级倒立摆的鲁棒自适应控制

为提高倒立摆控制系统的抗扰动能力,降低其对未建模动态等的敏感度,研究了不确定平面二级倒立摆的鲁棒自适应控制器的设计方法。把倒立摆动力学模型分解为确定和不确定两部分,用一个非线性参数化模糊逻辑系统逼近平面二级倒立摆的不确定动态,采用李雅普诺夫稳定性理论推导出使平面二级倒立摆的状态误差渐近收敛的鲁棒控制器及自适应律。理论分析和仿真结果表明所提出的控制算法是有效的。     

EVOLUTIONARY SEARCH FOR LIMIT CYCLE AND CONTROLLER DESIGN IN MULTIVARIABLE NONLINEAR SYSTEMS

A feature of many practical control systems is a Multi‐Input Multi‐Output (MIMO) interactive structure with one or more gross nonlinearities. A primary controller design task in such circumstances is to predict and ensure the avoidance of limit cycling conditions followed by achieving other design objectives. This paper outlines how such a system may be investigated using the Sinusoidal Input Describing Function (SIDF) philosophy quantifying magnitude, frequency and phase of any possible limit cycle operation. While Sinusoidal Input Describing function is a suitable linearization technique in the frequency domain for assessment of stability and limit cycle operation, it can not be employed in time domain. In order to be able to incorporate the time domain requirements in an overall controller design technique, the appropriate linearization technique suggested here is the Exponential Input Describing Function (EIDF). First, an evolutionary search based on a multi‐objective formulation is employed for the direct solution of the harmonic balance system matrix equation. The search is based on Multi‐Objective Genetic Algorithms (MOGA) and is capable of predicting specified modes of theoretically possible limit cycle operation. Second, the design requirements in time as well as frequency domain are formulated by a set of constraint inequalities. A numerical synthesis procedure also based on Multi‐Objective Genetic Algorithm is employed to adjust the initial compensator parameters to meet the imposed constraints. Robust stability and robust performance are investigated with respect to linearization uncertainty within the context of multiobjective formulation. In order to make the Genetic Algorithm (GA) search more amenable to design trade‐off between different and often contradictory specifications, a weighted sum of the functions is introduced. This criterion is subsequently optimized subject to the nonlinear system dynamics and a set of design requirements. Examples of use are given to illustrate the effectiveness of the proposed approach.     

An indirect model reference robust fuzzy adaptive control for a class of SISO nonlinear systems

In this paper we are interested in robust adaptive fuzzy control of nonlinear SISO systems in the presence of parametric uncertainties. The plant model structure is represented by the Takagi-Sugeno (T-S) type fuzzy system. An indirect adaptive fuzzy controller based on model reference control scheme is proposed to provide asymptotic tracking of reference signal. The controller parameters are computed at each time. The plant state tracks asymptotically the state of the reference model for any bounded reference input signal. Inverted pendulum and mass spring damper are used to check the performance of the proposed controller.     

Comment on ‘Stability analysis and controller synthesis for discrete linear time-delay systems with state saturation nonlinearities’

A recently reported paper (Ji, X., Liu, T., Sun, Y., and Su, H. (2011), ‘Stability analysis and controller synthesis for discrete linear time-delay systems with state saturation nonlinearities’, International Journal of Systems Science, 42, 397–406) for the global asymptotic stability analysis and controller synthesis for a class of discrete linear time delay systems employing state saturation nonlinearities is reviewed. It is claimed in Ji, Liu, Sun and Su (2011) that a previous approach by Kandanvli and Kar (Kandanvli, V.K.R and Kar, H. (2009), ‘Robust stability of discrete-time state-delayed systems with saturation nonlinearities: Linear matrix inequality approach’, Signal Processing, 89, 161–173) is recovered from their approach as a special case. It is shown that this claim is not justified.     

基于模糊加权的倒立摆混合控制

针对小车倒立摆系统,提出了一种线性状态反馈控制和滑模控制模糊加权的控制方法.滑模控制器的作用是将摆角控制在零的一个邻域内,在此邻域内首先采用近似的线性化模型来描述倒立摆系统,然后采用基于极点配置的方法设计系统的线性状态反馈控制器以使系统的状态稳定在给定值,两个控制器的输出通过加权求和作为倒立摆的控制作用.仿真结果证实了该方法的有效性.     

植保机钟摆式喷杆主动悬架自适应模糊控制

针对具有不确定性与参数时变性的钟摆式喷杆主动悬架系统的运动控制问题,设计出一种基于间接型自适应模糊控制方法的喷杆位姿主动控制器。为一种结构简单、成本低廉且应用广泛的钟摆式喷杆主动悬架系统建立了数学模型,并在此基础上,为了不失一般性,对系统模型进行了输入输出线性化变换。应用间接自适应模糊控制方法克服由于系统不确定性以及外部干扰带来的一些负面影响。此外,应用Lyapunov综合法设计控制器中调整参数的自适应律。仿真结果表明,所提出的控制方法具有快速响应性以及较强的自适应性和鲁棒性。所设计的控制器有利于提高植保机的喷雾均匀性及喷杆的稳定性。     

具有控制约束的网络控制系统的鲁棒H_∞控制

针对具有控制约束的网络控制系统(Networked Control Systems,NCS)的特点,建立了具有外部扰动的网络控制系统模型,对其H∞性能加以分析和研究,并验证所取得的理论成果.假设具有控制约束的网络控制系统的H∞控制器与执行器均为事件驱动,传感器为时间驱动,且网络诱导时延小于传感器的采样周期,然后将此类网络控制系统的广义被控对象建模为一类线性离散系统,运用Lyapunov函数和线性矩阵不等式(LMI),导出闭环系统渐近稳定且满足给定H∞性能指标的充分条件,并给出了控制器的具体求法.得到了系统的H∞控制器存在条件及具体方法,通过设计该控制器,使具有外部扰动的网络控制系统的性能有很大的改善,通过Matlab仿真证明该控制器行之有效.     

Asynchronous switching output feedback control of discrete-time switched linear systems

In this paper, the problem of dynamic output-feedback control synthesis is addressed for discrete-time switched linear systems under asynchronous switching. The proposed hybrid controller consists of a standard dynamic output-feedback switching control law and an impulsive reset law induced by controller state jumps. Using the average dwell time technique incorporating with multiple quadratic Lyapunov functions, the switching control synthesis conditions for asymptotic stability with guaranteed weighted ?₂-gain performance are derived as a set of linear matrix inequalities (LMIs). The proposed hybrid synthesis scheme advances existing design methods for output-feedback asynchronous switching control of switched linear systems in two important aspects: LMI formulation of the synthesis problem; and arbitrary order of the controller state. A numerical example is used to illustrate the effectiveness and advantages of the proposed design technique.     

双摆机器人摆杆平衡态任意转换运动控制的实现

双摆机器人两摆杆具有一个自稳定(Down-down)和三个自不稳定(Down-up, up-down, up-up)的平衡状态, 4个平衡状态之间可以构成12个相互转换的运动动作和8个自旋动作. 本文运用基于动觉智能图式的仿人智能控制理论, 设计具有基于特征辨识多控制模态结构的控制器; 采用``类等效'的系统建模方法和改进型遗传算法, 实现双摆机器人模型的精确辨识和其多模态控制器多参数的整定与优化, 并解决了多控制模态之间的平滑切换, 以及从仿真研究到实时控制成功的快速过渡等关键问题. 以(Down-up)向(Up-down)状态的转换为例, 说明了如何实现四个平衡状态之间的任意相互转换的运动控制, 并介绍了仿人智能控制器设计的详细过程. 仿真与实时控制的实例证明了设计理论与方法的有效性.     

Fluctuations of a stochastic approximation procedure with diffusion perturbation

A stochastic approximation procedure with a singularly perturbed regression function is considered. The form of the limit process is obtained that corresponds to the fluctuation of the stochastic approximation procedure in the neighborhood of an equilibrium point. A generator for the limit process is also constructed. The solution of the singular perturbation problem is given for the asymptotic representation of the generator of a Markov renewal process. The results obtained allow one to extend the possibilities of investigation of the asymptotic behavior of the procedure itself.     

A real-time optimal energy-saving walking pattern generator based on gradient descent method and linear quadratic control

Many recent approaches have successfully generated a stable walking pattern for biped robots, but discussions about its optimization are relatively few. In this paper, a Center of Gravity (COG) trajectory optimization method is proposed to minimize the cost function of joint torque, joint limit, and joint speed limit. The linear quadratic control-based inverted pendulum controller optimizes the COG trajectories in sagittal and lateral directions with the COG height trajectory. The COG height trajectory is optimized by finding the derivative of the cost function with respect to the COG height offline. Then the proposed walking pattern generator builds the COG height trajectory database of different walking steps for online connection of a walking pattern. The walking pattern generator is verified by experiments and simulations of different step cycles with our humanoid robot, NINO, and it can clearly reduce the required joint torque of the robot while walking. In addition, compared with the fixed COG height trajectory, the energy consumption is reduced by 14% from the experimental results. Thus, the method succeeds in generating a more energy-saving walking pattern.