Adaptive force and position control of manipulators

The article presents simple methods for the design of adaptive force and position controllers for robot manipulators within the hybrid control architecture. The force controller is composed of an adaptive PID feedback controller, an auxiliary signal, and a force feedforward term, and achieves tracking of desired force setpoints in the constraint directions. The position controller consists of adaptive feedback and feedforward controllers as well as an auxiliary signal, and accomplishes tracking of desired position trajectories in the free directions. The controllers are capable of compensating for dynamic cross-couplings that exist between the position and force control loops in the hybrid control architecture. The adaptive controllers do not require knowledge of the complex dynamic model or parameter values of the manipulator or the environment. The proposed control schemes are computationally fast and suitable for implementation in online control with high sampling rates. The methods are applied to a two-link manipulator for simultaneous force and position control. Simulation results confirm that the adaptive controllers perform remarkably well under different conditions.     

Adaptive backstepping control of a class of uncertain nonlinear systems with unknown backlash-like hysteresis

In this note, we consider the same class of systems as in a previous paper, i.e., a class of uncertain dynamic nonlinear systems preceded by unknown backlash-like hysteresis nonlinearities, where the hysteresis is modeled by a differential equation, in the presence of bounded external disturbances. By using backstepping technique, robust adaptive backstepping control algorithms are developed. Unlike some existing control schemes for systems with hysteresis, the developed backstepping controllers do not require the uncertain parameters within known intervals. Also, no knowledge is assumed on the bound of the "disturbance-like" term, a combination of the external disturbances and a term separated from the hysteresis model. It is shown that the proposed controllers not only can guarantee global stability, but also transient performance.     

Model-free robot joint position regulation and tracking with prescribed performance guarantees

The problem of robot joint position control with prescribed performance guarantees is considered; the control objective is the error evolution within prescribed performance bounds in both problems of regulation and tracking. The proposed controllers do not utilize either the robot dynamic model or any approximation structures and are composed by simple PID or PD controllers enhanced by a proportional term of a transformed error through a transformation related gain. Under a sufficient condition for the damping gain, the proposed controllers are able to guarantee (i) predefined minimum speed of convergence, maximum steady state error and overshoot concerning the position error and (ii) uniformly ultimate boundedness (UUB) of the velocity error. The use of the integral term reduces residual errors allowing the proof of asymptotic convergence of both velocity and position errors to zero for the regulation problem under constant disturbances. Performance is a priori guaranteed irrespective of the selection of the control gain values. Simulation results of a three dof spatial robotic manipulator and experimental results of one dof manipulator are given to confirm the theoretical findings.     

Variable structure control of robotic manipulator with PID sliding surfaces

Dynamic behaviour of a system in sliding mode is entirely defined by the sliding surface. Customarily, the surface is selected as a hyperplane in the system's state-space resulting in a PD-type sliding surface. This is not the only possible structure, and other designs with more complex or time-varying surfaces may provide definite advantages. Slotine and Spong included an integral term in the sliding surface expression that resulted in a type of PID sliding surface. However, the advantages of such a design were not elaborated in following publications of these or other researchers. In this paper we present a new design procedure and stability analysis for robotic variable structure controllers with PID-like sliding surfaces. Two versions of the controller are presented: regular and adaptive. The former is very simple and can operate with an unknown dynamic model; the only information required is a bound on one parameter. The latter provides an on-line estimation for this bound. Both controllers are robust with respect to bounded external disturbances and some unmodelled dynamic effects. The simulation results have demonstrated stability, with minimum transient responses that may be significantly faster than responses of traditional PD-manifold controllers under the same conditions. © 1998 John Wiley & Sons, Ltd.     

Energy- and Entropy-Based Stabilization for Lossless Dynamical Systems via Hybrid Controllers

A novel class of dynamic, energy-based hybrid controllers is proposed as a means for achieving enhanced energy dissipation in lossless dynamical systems. These dynamic controllers combine a logical switching architecture with continuous dynamics to guarantee that the system plant energy is strictly decreasing across switchings. The general framework leads to closed-loop systems described by impulsive differential equations. In addition, we construct hybrid dynamic controllers that guarantee that the closed-loop system is consistent with basic thermodynamic principles. In particular, the existence of an entropy function for the closed-loop system is established that satisfies a hybrid Clausius-type inequality. Special cases of energy-based and entropy-based hybrid controllers involving state-dependent switching are described.     

A DIALOG-ORIENTED AND GRADIENT-BASED STABILITY MARGIN IN UNCERTAIN SYSTEMS

ABSTRACT

Gradients and matricial gradients for optimally increasing the stability margin and the admissible uncertainty of a dynamic system are the targets of this presented article. To design a dynamic system, the gradients are used in a dialog between a system scientist and gradient-based computer support. The stability margin is derived for output state controllers, including regular state controllers. The resonant frequency and the damping factors are investigated as a direct function of the maximum admissible uncertainty. The resulting gradients are extended to observer-assisted controllers, to minimum-order observers, and to dynamic-output state controllers.     

On Adaptive Output Feedback Controf Robotic Manipulators with Online Disturbance Estimation

The problem of disturbance estimation and compensation for adaptive output feedback type controllers are investigated. Specifically two adaptive output feedback controllers designed for robotic manipulators are extended to compensate external disturbances which are common in robotic applications with repetitive task. The uncertain disturbance term in the robot dynamics is modeled as a fixed term plus a combination of sinusoidal signals. The overall stability and convergence of the tracking error for both controllers is ensured via Lyapunov based analysis. Extensive simulation studies are presented to illustrate the feasibility of the proposed method.     

时滞切换系统动态反馈H∞控制

对于由若干线性时滞子系统构成的切换系统,考虑了动态反馈控制与切换策略的设计,以实现H∞性能的优化．利用其连续性不受切换行为影响的Lyapunov-Krasovskii泛函构造方式,并结合闭环子系统的适当变换,导出了与时滞相关的控制器及切换策略的存在性判据．通过参数代换与矩阵相似变换,将此判据等价地转化为线性矩阵不等式,从而解得泛函与控制器参数．仿真结果验证了方法的有效性．     

时滞切换系统动态反馈H∞控制

对于由若干线性时滞子系统构成的切换系统, 考虑了动态反馈控制与切换策略的设计, 以实 现H-infinity性能的优化. 利用其连续性不受切换行为影响的Lyapunov-Krasovskii泛函构造方式, 并结合闭环子系统的适当变换, 导出了与时滞相关的控制器及切换策略的存在性判据.通过参数代换与矩阵 相似变换, 将此判据等价地转化为线性矩阵不等式, 从而解得泛函与控制器参数. 仿真结果验证了方法的有 效性.     

基于自优化的SDN交换机动态迁移机制

为提高SDN控制器的使用效率以及多控制器之间的负载均衡度,对多控制器的部署问题进行了研究,并提出了一种交换机动态迁移机制.该动态迁移机制基于周期性运行的自优化的算法实现,按照控制器的部署情况,将网络划分成多个域,通过分析各域内相关参数,分别找出负载最高和最低的控制器节点,并根据控制器负载和交换机请求率快速选择出最佳的迁移交换机和迁移目的地.控制器的负载均衡度、交换机请求的处理时延和算法的复杂度是算法设计中所考虑的主要因素.该算法的优点在于通过局部的动态调整实现了对SDN控制层的灵活管理.仿真结果表明,基于自优化的交换机动态迁移方案能够有效提高多控制器间的负载均衡度,减小流请求的处理时延,同时将运算复杂度保持在一个相对合理的水平.     

Global position regulation of friction manipulators via switched chattering control

Switched position control algorithms are developed to globally stabilize friction mechanical manipulators around a desired position. Both static and dynamic position feedback designs are presented. The controllers constructed, referred to as chattering controllers, do not rely on the generation of sliding motions while providing robustness features similar to those possessed by their sliding mode counterparts. Stability analysis is given within the Lyapunov vector functions framework extended to discontinuous dynamic systems. Performance issues of the chattering controllers are evaluated in an experimental study of a three degrees-of-freedom robot manipulator.     

Uniformly ultimately bounded fuzzy adaptive tracking controllers for uncertain systems

Fuzzy adaptive tracking controllers for a class of uncertain nonlinear dynamical systems are proposed and analyzed. The controllers consist of adaptive and robustifying components whose role is to ify the effects of uncertainties and to achieve a desired tracking performance. The interactions between the two components have been investigated. The closed-loop system driven by the proposed controllers is shown to be stable with all the adaptation parameters being bounded. In particular, the proposed controllers guarantee uniform ultimate boundedness of the tracking error and the time bound of the uniform ultimate boundedness is obtained. An upper bound on the steady-state tracking error is obtained as a function of the gain of the robustifying term and the parameters of the adaptive component. The controllers are tested on an inverted pendulum and simulation results are included. A comparison of the proposed controllers with the ones in the literature is conducted.     

From Nonlinear to Fuzzy Approaches in Trajectory Tracking Control of Wheeled Mobile Robots

In this paper, two knowledge based controllers are proposed to overcome the difficulties of a computed torque nonlinear controller (NC) in perfect trajectory tracking of nonholonomic wheeled mobile robots (WMRs). First, the effects of different dynamic models developed in angular and Cartesian coordinate systems are fully examined on the persistent excitation condition and consequently on the trajectory tracking performance of WMRs. Using the dynamic model coordinated in the Cartesian frame as the base of the NC results in perfect compensation of large position off‐tracks and unbiased estimation of the plant's unknown parameters. However, using the WMR's dynamic model with rotation angles of driving wheels as the base of nonlinear and fuzzy controllers leads to accurate orientation tracking. Through replacing the proportional and differential terms of the NC by fuzzy functions, a fuzzy nonlinear controller (FNC) is generated. Due to the complicated dynamics of the WMR in which the center of mass does not coincide with the center of rotation, the expert knowledge of fuzzy controllers is extracted considering the rotation angles and rates of driving wheels as input variables. Fuzzy tuning of the NC results in a superior tracking performance against measurement noises, though the control torques are decreased and smoothed significantly. Second, a complete fuzzy controller (FC) is generated to make perfect tracking of the WMR's position and orientation. The local stability analysis of fuzzy controllers is examined considering the corresponding analytical structures as nonlinear controllers. The superior performances of the proposed fuzzy controllers compared to those of the NCs are evaluated through simulations.     

Nonlinear variable structure excitation and steam valving controllers for power system stability

A set of novel nonlinear variable structure excitation and steam-valving controllers are proposed in this paper. On the basis of the classical dynamic equations of a generator, excitation control and steam valving control are simultaneously considered. Design of these controllers combines the differential geometry theory with the variable structure controlling theory. The mathematical model in the form of ＂an affine nonlinear system＂ is set up for the control design of a large-scale power plant. The dynamic performance of the nonlinear variable structure controllers proposed for a single machine connected to an infinite bus power system is simulated. Simulation results show that the nonlinear variable structure excitation and steam-valving controllers give satisfactory dynamic performance and good robustness.     

Rational stabilising commutative controllers: parameterisation and characterisation of degrees of freedom

The Characteristic Locus Method constitutes a generalisation of the classical frequency response approach and as such provides a natural platform for design aimed at meeting specifications such as closed-loop stability and dynamic performance. However, to overcome problems of sensitivity to uncertainty, it is necessary to precondition the plant transfer function matrix (TFM) with the view to improving the orthogonality of the eigenvector functions. All that remains then is to use controllers which adjust the frequency response of the eigenfunctions of the TFM while leaving the eigenvectors unaltered. This implies the need for commutative controllers which may be irrational and may not be internally stabilising. The present paper gives a complete characterisation of the class of stabilising rational commutative controllers and derived necessary and sufficient conditions for the existence of this class. These ideas are illustrated by means of case study in which the degrees of freedom contained within the class of commutative controllers are deployed for the meeting design specifications on dynamic performance as well as tolerance to uncertainty.     

Output deadbeat controllers with stability for discrete-time multivariable linear systems

This short paper Treats the problem of designing output deadbeat controllers having the property that the control input to the system converges to zero as time goes to infinity, for discrete-time multivariable linear systems. Two configurations of controllers are considered: one is of state feedback; the other is a dynamic controller using an observer. The existence of such controllers is examined, and the methods are presented for designing such controllers when they exist. The controller using a state feedback obtained in this paper is optimal in the sense that the controller settles the output in zero for any initial state in the minimum number of steps. On the other hand, the dynamic controller is not optimal in that sense, but it minimizest, wheretis defined as an integer such that the controller drives the output to zero in no more thantsteps for any set of initial conditions of the system and the observer.     

Multi-rate digital redesign of cascaded and dynamic output feedback systems

In this paper, a new indirect digital redesign method is presented for multi-rate sampled-data control systems with cascaded and dynamic output feedback controllers. These analogue controllers are often pre-designed based on desirable frequency specifications, such as bandwidth, natural angular frequency, etc. To take advantage of the digital controller over the analogue controller, digital implementation of these analogue controllers are often desirable. As only measured input-output signals are available, an ideal state reconstructing algorithm is utilised to obtain the multi-rate discrete-time states of the original continuous-time system. Based on the Chebyshev quadrature method, the gains of the multi-rate cascaded and the output feedback digital controllers are determined from their continuous-time counterparts according to the different sampling rates employed in the different parts of the closed-loop system. As a result, the respective analogue controllers with the high-frequency and low-frequency characteristics can be implemented using the respective fast-rate sampling and slow-rate sampling digital controllers. Unlike the classical direct bilinear transform method, which is an open-loop direct digital redesign method, the proposed digital controllers take into account the state-matching of the original continuous-time closed-loop system and the digitally redesigned sampled-data closed-loop system. To further improve the state-matching performance, an improved digital redesign approach is also developed to construct the multi-rate cascaded and dynamic output feedback digital controllers. Illustrative examples are given to demonstrate the effectiveness of the developed methods.     

Stability analysis and optimal tuning of EWMA controllers – Gain adaptation vs. intercept adaptation

Exponentially weighted moving average (EWMA) controllers are the most commonly used run-to-run controllers in semiconductor manufacturing industry. An EWMA controller can be implemented in two different ways. One way is to keep the process gain as its off-line estimate and update the intercept term at each run, which is termed EWMA with intercept adaptation; the other is to keep the intercept term as its off-line estimate and update the process gain at each run, which is termed EWMA with gain adaptation. Despite the fact that gain variation and adaptation is typical in semiconductor industry, most EWMA formulations are for intercept adaptation and few results exist on the stability and sensitivity of EWMA with gain adaptation. In this paper, we propose a general formulation to analyze the stability of both EWMA controllers. The proposed state-space representation not only reveals the similarities and differences between two types of EWMA controllers, but also explains why the stability conditions for both types of EWMA controllers are independent of process disturbances. In addition, we propose a general framework that unifies the analysis of the optimal control performance for both types of EWMA controllers. The proposed framework is different from existing approaches in that it decouples the state estimation from the control law, and derives the optimal weighting based on the state estimation performance. The proposed framework significantly simplifies the analysis procedure, especially for EWMA with gain adaptation. Using this framework, we derive the optimal EWMA weighting through solving the discrete-time algebraic Riccati equation (DARE) for various process disturbances that are encountered in semiconductor manufacturing industry. Simulation examples are given to illustrate the optimality of the EWMA weighting derived using the framework. Some practical aspects of controller tuning are also discussed based on the simulation results.     

广义系统输出反馈严格正实控制器设计

研究连续广义系统的正实控制问题。目的是设计静态输出反馈和动态输出反馈严格正实控制器使得闭环系统容许且扩展严格正实。基于广义系统严格正实引理，利用线性矩阵不等式和广义代数Riccati不等式，给出了广义系统静态输出反馈和动态输出反馈严格正实控制器存在的充要条件及设计方法。对动态输出反馈情形，给出了一个数值算例说明控制器设计方法的有效性及可行性。     

Tuning and robustness analysis of event-based PID controllers under different event-generation strategies

In this article, we propose practical rules for tuning event-based PID controllers with two sampling strategies: symmetric send-on-delta (SSOD) and regular quantification (RQ). We present a detailed analysis about the effect of the derivative term of the controller when using SSOD or RQ and some guide lines are given to select the derivative filter coefficient. The two sampling strategies are compared, showing that, even when both of them lead to similar controlled output response, systems with RQ have better robustness properties than those with SSOD. The study is based on the describing function and the results are applicable to process with dynamic responses of different types: with time delays, non-minimum phase, under-damped response, etc. The rules presented here are given in terms of phase and gain margins that are measures of robustness used in the design of continuous PID controllers. This allows the application of conventional PID tuning methods to the case of event-based PID. The tuning rules are very simple and can be used for tuning PID, PI, PD and other controller structures.