ANALYSIS AND DESIGN OF FEEDBACK CONTROL SYSTEMS WITH TRACKING ERRORS SQUARE

In this study, a command tracking error square control scheme is first proposed for analysis and design of feedback control systems. One of the tracking errors is low‐pass filtered and used in the feedback loop for gain adaptation; the other is used in the forward loop for command tracking control. The overall systems are nonlinear feedback systems, and can be reconfigured to an automatic gain control (AGC) loop with command tracking error input. The stability and robustness of the controlled systems are verified by time response, frequency response, and large parameter variation testing with a simple illustrating example and are finally applied to a complicated electro‐hydraulic velocity servo system with large load disturbance.     

Parameterizing robust manipulator controllers under approximate inverse dynamics: A double‐Youla approach

We consider the goal of ensuring robust stability when a given manipulator feedback control law is modified online, for example, to safely improve the performance by a learning module. To this end, the factorization approach is applied to both the plant and controller models to characterize robustly stabilizing controllers for rigid‐body manipulators under approximate inverse dynamics control. Outer‐loop controllers to stabilize the nonlinear uncertain loop that results from approximate inverse dynamics are often derived by lumping uncertainty in a single term and subsequent analysis of the error system. Here, by contrast, the well‐known norm bounds of these uncertain dynamics are first recast into a generalized plant configuration that preserves the characteristic uncertainty structure. Then, the overall loop uncertainty is expressed with respect to the nominal outer‐loop feedback controller by means of an uncertain dual‐Youla operator. Therefore, using the dual‐Youla parameterization, we provide a novel way to rigorously quantify permissible perturbations of robot manipulator feedforward/feedback controllers. The method proposed in this paper does not constitute another robust control law for rigid‐body manipulators, but rather a characterization of a set of robustly stabilizing controllers. The resulting double‐Youla parameterization for the control of robot manipulators is amenable to numerous advanced design methods. The result is thoroughly discussed by a planar elbow manipulator and exemplified with a six‐degree‐of‐freedom robot scenario with varying payload.     

Experimental Control of a Two-Dof Flexible Robot Manipulator by Optimal and Sliding Methods

This paper presents an experimental study of a robust control scheme for flexible-link robotic manipulators. The design is based on a simple strategy for trajectory tracking which exploits the two-time scale nature of the flexible part and the rigid part of the dynamic equations of this kind of robotic arms: A slow subsystem associated with the rigid motion dynamics and a fast subsystem associated with the flexible link dynamics. Two experimental approaches are considered. In a first test an LQR optimal design strategy is used, while a second design is based on a sliding-mode scheme. Experimental results on a laboratory two-dof flexible manipulator show that this composite approach achieves good closed-loop tracking properties for both design philosophies, which compare favorably with conventional rigid robot control schemes.     

Bounded attitude control of rigid bodies: Real-time experimentation to a quadrotor mini-helicopter

A quaternion-based feedback is developed for the attitude stabilization of rigid bodies. The control design takes into account a priori input bounds and is based on nested saturation approach. It results in a very simple controller suitable for an embedded use with low computational resources available. The proposed method is generic not restricted to symmetric rigid bodies and does not require the knowledge of the inertia matrix of the body. The control law can be tuned to force closed-loop trajectories to enter in some a priori fixed neighborhood of the origin in a finite time and remain thereafter. The global stability is guaranteed in the case where angular velocity sensors have limited measurement range. The control law is experimentally applied to the attitude stabilization of a quadrotor mini-helicopter.     

非完整移动机器人的分段反馈稳定控制

研究一类具有非完整约束的移动机器人控制问题,首先采用一种分段连续状态反馈控制邮系统的渐近稳定,为了克服控制器在某些点出现奇异性以及由于控制器中所涉及的三角函数的周期性导致解的局部必 步利用输入／输出线化,线性近似等方法对控制算法进行了修正,数值仿真结果表明该算法是有效的。     

Decoupling and tracking control for elastic joint robots with coupled joint structure

The paper deals with the modeling, identification, and control of a flexible joint robot developed for medical applications at the German Aerospace Center (DLR). In order to design anthropomorphic kinematics, the robot uses a coupled joint structure realized by a differential gearbox, which however leads to strong mechanical couplings inside the coupled joints and must be taken into account. Therefore, a regulation MIMO state feedback controller based on modal analysis is developed for each coupled joint pair, which consists of full state feedback (motor position, link side torque, as well as their derivatives). Furthermore, in order to improve position accuracy and simultaneously keep good dynamic behavior of the MIMO state feedback controller, a cascaded tracking control scheme is proposed, based on the MIMO state feedback controller with additional feedforward terms (desired motor velocity, desired motor acceleration, derivative of the desired torque), which are computed in a computed torque controller and take the whole rigid body dynamics into account. Stability analysis is shown for the complete controlled robot. Finally, experimental results with the DLR medical robot are presented to validate the practical efficiency of the approaches.     

A sufficient condition for the stability of optimizing controllers with saturating actuators

The quadratic programme that must be solved with certain output–feedback model predictive controllers can be expressed as a continuous sector‐bounded nonlinearity together with two linear transformations. Thus, the multivariable circle criterion gives a simple test for stability, with or without model mismatch. In particular, it may be applied if the open‐loop plant is stable and the actuators are subject to simple saturation constraints. In the case of single horizon model predictive control, it suffices to check for positive realness a transfer function matrix whose dimension corresponds to the number of inputs. For an arbitrary length receding horizon it suffices to check the poles of a low dimension transfer function matrix and the eigenvalues (over an appropriate range of operator values) of a matrix whose dimension is independent of the horizon length. Copyright © 2005 John Wiley & Sons, Ltd.     

一种基于双闭环控制的高频逆变器

为了提高逆变器的动态性能,改善输出电压波形质量,应用了具有电流反馈内环和电压反馈外环相结合的双闭环控制技术。内环用于改善系统的动态性能,迅速地消除负载扰动的影响;而外环则用于改善系统的稳态性能。本文通过Matlab／Simulink对系统进行了建模,验证了双闭环控制结构的可行性。     

A New Control Scheme of Single-link Flexible Manipulators Robust to Payload Changes

A new scheme is presented in this paper to control single-link flexiblemanipulators. The objective is to control the tip position of the flexiblearm in the presence of joint friction and payload changes. The controlscheme is based on two nested loops: an inner feedback loop to control themotor position which is robust to joint friction, and an outer loop tocontrol the tip position which is robust to payload changes. This outer loopis composed of a feedforward term and a feedback term. This results in asimple control law that needs minimal computing effort and, thus, can beused for real time control of flexible arms. The proposed method is generalin the sense that it can be applied to very different arm structures anddiverse sensor systems configurations. Results corresponding to twodifferent arm setups are presented.     

基于PID算法的直流电机PWM调速控制器设计

为提高对直流伺服电机转速的控制精度,将控制器硬件电路设计成闭环控制系统,通过位置传感器采样获取伺服电机转速并反馈给单片机系统,引入基于PID控制的算法对单片机进行编程控制,设计了一款能通过反馈控制自动修正直流电机转速的调速控制器,文中给出了控制器的硬件电路设计方法和系统软件的编程算法。该控制器具有成本低、控制精度高、调速范围宽、响应速度快等特点,通过简单硬件接口就能将其嵌入到的各种小功率直流电机控制产品中加以应用。     

空间多刚体系统姿态的协同控制

将一种针对多个一般非线性系统的基于输出反馈的协同控制方法应用在采用四元数法描述的空间多个刚体姿态的协同控制系统中去，给出了空间多刚体系统姿态协同控制问题有解的充分条件，并设计了多刚体系统姿态的协同控制律．算例仿真结果表明，此法设计的协同控制器能够稳定控制描述各个刚体系统的姿态四元数，使其渐近稳定．     

Tracking in nonlinear differential-algebraic control systems with applications to constrained robot systems

We consider the design of a feedback control law for control systems described by a class of nonlinear differential-algebraic equations so that certain desired outputs track given reference inputs. The nonlinear differential-algebraic control system being considered is not in state variable form. Assumptions are introduced and a procedure is developed such that an equivalent state realization of the control system described by nonlinear differential-algebraic equations is expressed in a familiar normal form. A nonlinear feedback control law is then proposed which ensures, under appropriate assumptions, that the tracking error in the closed loop differential-algebraic system approaches zero exponentially. Applications to simultaneous contact force and position tracking in constrained robot systems with rigid joints, constrained robot systems with joint flexibility, and constrained robot systems with significant actuator dynamics are discussed.     

Contribution to the indirect decentralized adaptive control of manipulation robots

In this paper, efficient approaches to the synthesis of indirect decentralized adaptive control for manipulation robots are presented. The first part of control synthesis consists of the estimation of unknown dynamic robot parameters using the methods of recursive identification and fast dynamic as well as identification models in a symbolic form. The second part of synthesis includes the self-tuning control strategy which is a basis for adaptive control synthesis according to the estimates of the unknown dynamic parameters. Using the theory of decentralized systems, a new robust algorithm for adaptive control with the ability of adaptation in the feedforward or feedback loop are proposed. A complete stability and convergence analysis is presented. A special part of the paper represents an analysis of practical implementation of the proposed control algorithms on modern microprocessor-based robot controllers. Based on this analysis, an efficient application of indirect adaptive algorithms in real time with high-quality system performance is shown. Adaptive algorithms are verified through simulation of trajectory tracking for an industrial robot with unknown dynamic parameters of payload.     

Robust tracking control for rigid robotic manipulators

The problem of robust tracking control using a nominal feedback controller and a variable structure compensator for a rigid robotic manipulator with uncertain dynamics is addressed in this note. It is shown that the effects of large system uncertainties can be eliminated and asymptotic convergence of the output tracking error can be guaranteed by using a variable structure compensator in the closed loop feedback control system for the rigid robotic manipulator     

基于非线性L1自适应动态逆的飞行器姿态角控制

钊对常规动态逆控制器不能有效抵消系统中的不确定性这一缺点,提出了一种非线性L_1自适应动态逆控制方法.该方法能够克服常规动态逆的不足,在保证系统鲁棒性的前提下,提升飞行器姿态角控制效果.首先,采用时标分离原理,将姿态角控制系统分为内外两个回路:外回路采用常规动态逆控制器,用于姿态角的跟踪控制;内回路采用非线性L_1自适应控制器,用于角速率的控制.其中,L_1自适应控制器由静态反馈控制器和自适应控制器组成:静态反馈控制器通过状态反馈实现,用于保证内回路的稳定和具有期望的闭环特性;自适应控制器由状态观测器、自适应律和控制律组成,用于抵消系统中的不确定性.其次,对所提控制方法的稳定性进行了分析,结果证明了该控制方法能够保证内回路的稳定和外回路的误差有界.最后,在综合考虑多种不确定性的情况下,将本文提出的非线性L_1自适应动态逆控制方法用于某无人飞行器姿态角控制,仿真结果验证了该控制方法的有效性和鲁棒性.     

Stability and Control of Collective Systems

In this paper, decentralized, distributed feedback control laws are presented for cooperative robotic systems whose task is to localize unknown sources. The control laws follow from a second order representation of the source field. The stability of the proposed feedback control laws for the individual robots, and for the entire robot collective, is demonstrated using Lyapunov's direct method and a vector Lyapunov approach. Additional feedback control laws are proposed to achieve an additional level of coordination. In particular, control laws that achieve desired formations surrounding a localized source are developed.     

A design method for indirect iterative learning control based on two-dimensional generalized predictive control algorithm

Indirect iterative learning control (ILC) facilitates the application of learning-type control strategies to the repetitive/batch/periodic processes with local feedback control already. Based on the two-dimensional generalized predictive control (2D-GPC) algorithm, a new design method is proposed in this paper for an indirect ILC system which consists of a model predictive control (MPC) in the inner loop and a simple ILC in the outer loop. The major advantage of the proposed design method is realizing an integrated optimization for the parameters of existing feedback controller and design of a simple iterative learning controller, and then ensuring the optimal control performance of the whole system in sense of 2D-GPC. From the analysis of the control law, it is found that the proposed indirect ILC law can be directly obtained from a standard GPC law and the stability and convergence of the closed-loop control system can be analyzed by a simple criterion. It is an applicable and effective solution for the application of ILC scheme to the industry processes, which can be seen clearly from the numerical simulations as well as the comparisons with the other solutions.     

Decoupling force and motion control in industrial robots

A theoretical approach to force control design for industrial robots involved in surface-following tasks is described in this paper, assuming an infinitely stiff environment. Independent Joint Control techniques, based on standard (PID) algorithms, are adopted for position control. Force control acts as an outer loop, by adding a bias to the position set points in the joint space. A simple model and compensation of the joint flexibility effects, that play an important role in determining the dynamic behavior of the system, are also presented, leading to a force control decoupled from motion control. Some experimental results are discussed, with reference to the industrial robot SMART.     

Central pattern generator based reflexive control of quadruped walking robots using a recurrent neural network

This paper presents a novel Central Pattern Generator (CPG) model for controlling quadruped walking robots. The improvement of this model focuses on generating any desired waveforms along with accurate online modulation. In detail, a well-analyzed Recurrent Neural Network is used as the oscillators to generate simple harmonic periodic signals that exhibit limit cycle effects. Then, an approximate Fourier series is employed to transform those mentioned simple signals into arbitrary desired outputs under the phase constraints of several primary quadruped gaits. With comprehensive closed-form equations, the model also allows the user to modulate the waveform, the frequency and the phase constraint of the outputs online by directly setting the inner parameters without the need for any manual tuning. In addition, an associated controller is designed using leg coordination Cartesian position as the control state space based on which stiffness control is performed at sub-controller level. In addition, several reflex modules are embedded to transform the feedback of all sensors into the CPG space. This helps the CPG recognize external disturbances and utilize inner limit cycle effect to stabilize the robot motion. Finally, experiments with a real quadruped robot named AiDIN III performing several dynamic trotting tasks on several unknown natural terrains are presented to validate the effectiveness of the proposed CPG model and controller.     

指数稳定的机器人鲁棒跟踪控制

本文提出了一种用于控制具有参数不确性机器人轨迹踊跃的鲁棒控制策略，该控制器的设计根据Ｌｙａｐｕｎｏｖ理论，由一个基于Ｓｌｏｔｉｎｅ方法的标称控制器和一个非线性连续反馈补偿器组成。