A globally convergent angular velocity observer for rigid bodymotion

The problem of obtaining the angular velocity of a rigid body from orientation and torque measurements only, without noisy numerical differentiation, is considered. A novel angular velocity/angular momentum observer for rigid body motion is presented. Using Euler quaternions and a mechanical energy function approach, it is shown that the observer estimates converge globally and that the convergence is eventually exponential. It is hoped that a mechanical energy function approach to rigid body control can be combined with the observer presented to lead to a globally stable, nonlinear, observer-based, rigid-body controller in which the observer and controller errors can be separated, in much the same way as one can separate controller and observer poles in the output feedback controllers of linear system theory     

3D Multi‐Agent Formation Control with Rigid Body Maneuvers

In this paper, we propose a control scheme for the formation maneuvering problem of multi‐agent systems where the team of agents can translate and rotate as a virtual rigid body in 3D. Using the single‐integrator model, we formulate the basic control law which is comprised of a formation acquisition term, function of the graph rigidity matrix, and a rigid body maneuvering term. The control is dependent on the relative position of agents that are connected in an infinitesimally and minimally rigid framework in addition to the desired rigid body motion of the formation. To facilitate the design of the rigid body maneuver, one agent in the convex hull of the formation serves as the reference point for the rotation component. A simulation study demonstrates the formation controller.     

Decentralized sliding mode control for flexible link robots

A technique using augmented sliding mode control for robust, real-time control of flexible multiple link robots is presented. For the purpose of controller design, the n-link, n-joint robot is subdivided into n single joint, single link subsystems. A sliding surface for each subsystem is specified so as to be globally, asymptotically stable. Each sliding surface contains rigid-body angular velocity, angular displacement and flexible body generalized velocities. The flexible body generalized accelerations are treated as disturbances during the controller design. This has the advantage of not requiring explicit equations for the flexible body motion. The result is n single input, single output controllers acting at the n joints of the robot, controlling rigid body angular displacement and providing damping for flexible body modes. Furthermore, the n controllers can be operated in parallel so that compute speed is independent of the number of links, affording real-time, robust, control.     

Robust control of robotic manipulators based on integral sliding mode

For rigid body robot manipulators, the computed torque approach provides asymptotic stability for tracking control tasks. However, the state dependent matrices needed to complete the computed torque algorithm are normally unknown and possibly too complex for a real-time implementation. This paper proposes a simple controller with computed-torque-like structure enhanced by integral sliding mode, having pole-placement capability. For the reduction of the chattering effect generated by the sliding mode part, the integral sliding mode is posed as a perturbation estimator with quasi-continuous control action provided by an additional low-pass filter. The time-constant of the latter tunes the controller functionality between the perturbation compensation and a pure integral sliding mode control, as well as between chattering reduction and system robustness. A comparative simulation study between conventional sliding mode control, integral sliding mode control, and integral sliding mode in form of a perturbation estimator for a two-link robot arm validates the proposed design.     

Anti‐windup synthesis for nonlinear dynamic inversion control schemes

A general anti‐windup (AW) compensation scheme is provided for a class of input constrained feedback‐linearizable nonlinear systems. The controller considered is an inner‐loop nonlinear dynamic inversion controller, augmented with an outer‐loop linear controller, of arbitrary structure. For open‐loop globally exponentially stable plants, it is shown that (i) there always exists a globally stabilizing AW compensator corresponding to a nonlinear generalization of the Internal‐Model‐Control (IMC) AW solution; (ii) important operator theoretic parallels exist between the AW design scheme for linear control and the suggested AW design scheme for nonlinear affine plants and (iii) a more attractive AW compensator may be obtained by using a nonlinear state‐feedback term, which plays a role similar to the linear state‐feedback term in linear coprime factor‐based AW compensation. The results are demonstrated on a dual‐tank simulation example. Copyright © 2009 John Wiley & Sons, Ltd.     

A general co-ordinate transformation framework for multi-axis motion control with applications in the testing industry

Transforming feedback variables into a different co-ordinate system is a practical and effective way of simplifying controller design for multi-axis motion systems. A general transformation framework is presented in this paper for parallel-actuator systems, including those with overconstraint (i.e. with more actuators than rigid body degrees-of-freedom). Force control for the extra axes is considered, and appropriate transformations from measured actuator positions and forces to position and force variables used for control are given, although solutions are not unique. A number of heuristic techniques which are already used in the structural testing industry can be formalised as part of the new framework; examples are given in the paper. The framework also allows these techniques to be extended to new applications, particularly those with overconstraint.     

Adaptive control of rigid body satellite

The minimal controller synthesis （MCS） is an extension of the hyperstable model reference adaptive control algorithm. The aim of minimal controller synthesis is to achieve excellent closed-loop control despite the presence of plant parameter variations, external disturbances, dynamic coupling within the plant and plant nonlinearities. The minimal controller synthesis algorithm was successfully applied to the problem of decentralized adaptive schemes. The decentralized minimal controller synthesis adaptive control strategy for controlling the attitude of a rigid body satellite is adopted in this paper. A model reference adaptive control strategy which uses one single three-axis slew is proposed for the purpose of controlling the attitude of a rigid body satellite. The simulation results are excellent and show that the controlled system is robust against disturbances.     

On controller tuning for a flexible-link manipulator with varying payload

In this article experimental results are presented for system identification and control of a single-link flexible manipulator carrying an unknown, varying payload. The control objective is to maintain endpoint position accuracy in the presence of flexure effects after rapid movement due to a rigid body slew-angle commanded position. Various time-domain parameter estimation techniques are used to identify ARMA model representations to be employed in controller tuning schemes for vibration compensation. Only endpoint acceleration measurements and motor shaft angle measurements are utilized in relatively simple PID control schemes, which are tuned as dictated by a varying, unknown payload.     

Finite-time stabilization for a class of more general p-normal nonlinear systems with input and output nonlinearities

This study investigates the global finite-time state feedback stabilization for a class of more general p-normal nonlinear systems subjects to input time-delay and uncertain output function under rational powers. A novel control input compensation signal comprising a finite integral of previous control values is presented, and an equivalent system with control input dependent-free time delay is obtained by introducing a variable transformation technique that includes the compensation signal. A suitable controller is designed in line with the homogeneous domination method to ensure the globally finite-time stability of the closed-loop system. Finally, the effectiveness of the proposed control scheme is verified through a numerical simulation and an induction heater circuit system.     

Global asymptotic stability of a tracking sectorial fuzzy controller for robot manipulators.

This paper shows that fuzzy control systems satisfying sectorial properties are effective for motion tracking control of robot manipulators. We propose a controller whose structure is composed by a sectorial fuzzy controller plus a full nonlinear robot dynamics compensation, in such a way that this structure leads to a very simple closed-loop system represented by an autonomous nonlinear differential equation. We demonstrate via Lyapunov theory, that the closed-loop system is globally asymptotically stable. Experimental results show the feasibility of the proposed controller.     

Active vibration control of a flexible beam,based on flow source control

This paper presents a new method of actively controlling the vibration of a flexible beam by using a rigid body motion actuator based on flow source control. The proposed flow source controller generates a control input of a rotating angle instead of a torque that acts as an effort source control input. It is shown that the proposed flow source control improves the vibration suppression performance when disturbance forces such as friction forces are involved in the rigid body motion dynamics. The stability and the robustness to disturbance of the flow source controller are compared with an effort source controller. An optimal control theory is used to design the flow source vibration controller and a conventional PD controller is used for the motor position controller. Computer simulations and experimental results on a rotating beam system show that the vibration control performance achieved by the proposed flow source control method is superior to that of an effort source control method.     

机械手的全局稳定自适应控制方案

本文针对机械手一类复杂的非线性系统,综合非线性补偿和模型参考自适应控制两种方法的基本思想,提出一种有效的全局渐近稳定自适应控制方案.此方案没有对机械手模型做任何线性近似,控制算法中只用到了容易测量的关节角位移和角速度信号,而且保证控制量平滑.最后给出了满意的仿真结果.     

Multirate parallel distributed compensation of a cluster in wireless sensor and actor networks

The stabilisation problem for one of the clusters with bounded multiple random time delays and packet dropouts in wireless sensor and actor networks is investigated in this paper. A new multirate switching model is constructed to describe the feature of this single input multiple output linear system. According to the difficulty of controller design under multi-constraints in multirate switching model, this model can be converted to a Takagi–Sugeno fuzzy model. By designing a multirate parallel distributed compensation, a sufficient condition is established to ensure this closed-loop fuzzy control system to be globally exponentially stable. The solution of the multirate parallel distributed compensation gains can be obtained by solving an auxiliary convex optimisation problem. Finally, two numerical examples are given to show, compared with solving switching controller, multirate parallel distributed compensation can be obtained easily. Furthermore, it has stronger robust stability than arbitrary switching controller and single-rate parallel distributed compensation under the same conditions.     

基于飞轮的欠驱动航天器姿态控制器设计

在以飞轮作为姿态控制执行机构的航天器中,如果部分飞轮发生故障而使得航天器欠驱动时,姿态控制性能会急剧下降.本文对两个匕轮的刚性航天器,研究了姿态控制问题.在零动量的假设下,利用Backstepping方法,为欠驱动姿态控制系统设计了一个新型的姿态控制器.设计过程分两步进行:首先,根据姿态运动学模型,设计出可使航天器姿态全局渐近稳定的控制角速率;然后,根据姿态动力学模型,得到使航天器姿态全局渐近稳定的控制力矩.该控制器为非连续控制器,可使航天器姿态误差全局一致渐近收敛为零,并使系统具有良好的动态性能.计算机仿真表明,本文所设计出的控制器是可行的.     

Robust Adaptive Control of Robots Using Neural Network: Global Stability

A desired compensation adaptive law‐based neural network (DCAL‐NN) controller is proposed for the robust position control of rigid‐link robots. The NN is used to approximate a highly nonlinear function. The controller can guarantee the global asymptotic stability of tracking errors and boundedness of NN weights. In addition, the NN weights here are tuned on‐line, with no offline learning phase required. When compared with standard adaptive robot controllers, we do not require linearity in the parameters, or lengthy and tedious preliminary analysis to determine a regression matrix. The controller can be regarded as a universal reusable controller because the same controller can be applied to any type of rigid robots without any modifications. A comparative simulation study with different robust and adaptive controllers is included.     

Finite‐time angular velocity observers for rigid‐body attitude tracking with bounded inputs

The attitude tracking of a rigid body without angular velocity measurements is addressed. A continuous angular velocity observer with fractional power functions is proposed to estimate the angular velocity via quaternion attitude information. The fractional power gains can be properly tuned according to a homogeneous method such that the estimation error system is uniformly almost globally finite‐time stable, irrespective of control inputs. To achieve output feedback attitude tracking control, a quaternion‐based nonlinear proportional‐derivative controller using full‐state feedback is designed first, yielding uniformly almost globally finite‐time stable of the attitude tracking system as well as bounded control torques a priori. It is then shown that the certainty equivalent combination of the observer and nonlinear proportional‐derivative controller ensures finite‐time convergence of the attitude tracking error for almost all initial conditions. The proposed methods not only avoid high‐gain injection, as opposed to the semi‐global results, but also overcome the unwinding problem associated with some quaternion‐based observers and/or controllers. Numerical simulations are presented to verify the effectiveness of the proposed methods. Copyright © 2016 John Wiley & Sons, Ltd.     

A simple PD controller for robots with elastic joints

The point-to-point control of manipulators having elastic joints is considered. It is shown that a simple PD (proportional plus derivative) controller, similar to that used for rigid robots, suffices to globally stabilize the elastic joint robots about a reference position. A robustness analysis is also given with respect to uncertainties on the robot parameters. The results of numerical simulation tests of a manipulator with three revolute elastic joints are presented     

基本积分型李亚普诺夫函数的直接自适应神经网络控制

针对一类具有下三角形函数控制增益矩阵的非线性系统,基于滑模控制原理,并利用 多层神经网络的逼近能力,提出了一种直接自适应神经网络控制器设计的新方案.通过引入积 分型李亚普诺夫函数及残差与逼近误差和的上界函数的自适应补偿项,证明了闭环系统是全局 稳定的,跟踪误差收敛到零.     

基于积分型切换函数的自适应神经网络控制

针对一类具有未知函数控制增益的非线性系统,利用RBF神经网络的逼近能力,依据滑模控制原理,提出了一种直接自适应神经网络控制器设计新方案。通过引入积分型切换函数及逼近误差自适应补偿项,监督控制用饱和函数代替符号函数,根据李雅普诺夫稳定性理论,证明了闭环系统是全局稳定的,跟踪误差收敛到零。该算法应用于连续搅拌型化学反应器CSTR（Continuous Stirred Tank Reactor）,仿真结果显示,该算法能很好地使CSTR跟踪给定的温度信号,表明了该控制策略的有效性。     

具有模糊监督控制器的积分变结构间接自适应控制

针对一类不确定非线性系统, 基于变结构控制原理, 并利用具有非线性可调参数的模糊系统去逼近过程未知函数, 提出一种具有模糊监督控制器的积分变结构间接自适应控制方案. 该方案通过监督控制器保证闭环系统所有信号有界. 进一步, 通过引入最优逼近误差的自适应补偿项来消除建模误差的影响. 理论分析证明了跟踪误差收敛到零. 仿真结果表明了该方法的有效性.