Adaptive fuzzy output feedback control for a single-link flexible robot manipulator driven DC motor via backstepping

In this paper, an adaptive fuzzy output feedback approach is proposed for a single-link robotic manipulator coupled to a brushed direct current (DC) motor with a nonrigid joint. The controller is designed to compensate for the nonlinear dynamics associated with the mechanical subsystem and the electrical subsystems while only requiring the measurements of link position. Using fuzzy logic systems to approximate the unknown nonlinearities, an adaptive fuzzy filter observer is designed to estimate the immeasurable states. By combining the adaptive backstepping and dynamic surface control (DSC) techniques, an adaptive fuzzy output feedback control approach is developed. Stability proof of the overall closed-loop system is given via the Lyapunov direct method. Three key advantages of our scheme are as follows: (i) the proposed adaptive fuzzy control approach does not require that all the states of the system be measured directly, (ii) the proposed control approach can solve the control problem of robotic manipulators with unknown nonlinear uncertainties, and (iii) the problem of “explosion of complexity” existing in the conventional backstepping control methods is avoided. The detailed simulation results are provided to demonstrate the effectiveness of the proposed controller.     

Stability analysis of controlled multiple-link robotic manipulator systems with time delays

Controlled robotic manipulator systems, normally operating in an acceptable manner, may become unstable, when time delays exist in the feedback loop. This instability may cause oscillations and thus deteriorate the system performance. In this paper we introduce a method to analyze the performance of robotic manipulators with small time delays in the feedback loop. Specifically, we may predict the limits of a stable system Operation, i.e., the robustness and expected system error bounds, as a function of the time delay and system parameters. The analysis method uses nonlinear control theory concepts, such as Lyapunov's second method, and takes advantage of norms to establish operational bounds. Previous research of time-delay systems analysis is also reviewed, in general, and pertaining to robotic controls, in particular. The results of the analysis can be displayed graphically and may be used to adjust the controller gains and trajectories to ensure satisfactory operation. Predictably, the system response is slowed as the time delay increases. The validity of the analysis is demonstrated with a numerical example of a two-link manipulator using a computed-torque controller. The time responses of the example, run on a computer-generated model, supports the analysis results and predicted performance.     

Dynamical behavior in a stage-structured differential-algebraic prey-predator model with discrete time delay and harvesting

A differential-algebraic model system which considers a prey-predator system with stage structure for prey and harvest effort on predator is proposed. By using the differential-algebraic system theory and bifurcation theory, dynamic behavior of the proposed model system with and without discrete time delay is investigated. Local stability analysis of the model system without discrete time delay reveals that there is a phenomenon of singularity induced bifurcation due to variation of the economic interest of harvesting, and a state feedback controller is designed to stabilize the proposed model system at the interior equilibrium; Furthermore, local stability of the model system with discrete time delay is studied. It reveals that the discrete time delay has a destabilizing effect in the population dynamics, and a phenomenon of Hopf bifurcation occurs as the discrete time delay increases through a certain threshold. Finally, numerical simulations are carried out to show the consistency with theoretical analysis obtained in this paper.     

Full forward kinematics of redundant kinematic hybrid manipulator

A unified recursive mathematic model is established for full forward kinematics analysis of various redundant kinematic hybrid manipulators which are formed by several different parallel manipulators connected in series. In the established model, the relationships between the general input velocity/acceleration and the general output velocity/acceleration are discovered. The Jacobian matrices for mapping the general output velocities to the general input velocity and the Hessian matrices for mapping the general output velocities to the general input acceleration are derived. The unified iteration recursive formulae are derived for solving the general output velocity/acceleration of the end moving platform of the redundant kinematic hybrid manipulator by only giving the general input velocity/acceleration of every parallel manipulator. A 3D model of a novel (4SPS + SPR )+ (4SPS/SP) + 3SPR type hybrid manipulator is constructed and its full forward velocity/acceleration formulae are derived from the established unified recursive mathematic model and are proved to be correct by utilizing a simulation solution of the novel redundant kinematic hybrid manipulator.     

Adaptive Predictor-Based Output Feedback Control for a Class of Unknown MIMO Linear Systems

In this paper, the problem of characterizing adaptive output feedback control laws for a general class of unknown MIMO linear systems is considered. Specifically, the presented control approach relies on three components, i.e., a predictor, a reference model and a controller. The predictor is designed to predict the system’s output with arbitrary accuracy, for any admissible control input. Subsequently, a full state feedback control law is designed to control the predictor output to approach the reference system, while the reference system tracks the desired trajectory. Ultimately, the control objective of driving the actual system output to track the desired trajectories is achieved by showing that the system output, the predictor output and the reference system trajectories all converge to each other.     

Dynamics and stability of a hybrid serial-parallel mobile robot

Kinematics, dynamics, and stability analysis of a hybrid serial-parallel wheeled mobile robot is detailed in this paper. Privileging the advantages of both serial and parallel robots, the suggested structure will provide higher stability for heavy object manipulation by a mobile robotic system. The proposed system is made of a differentially-driven wheeled platform, a planar parallel manipulator, which is called here as star-triangle (ST) mechanism, and a serial Puma-type manipulator arm. In order to develop a comprehensive kinematics model of the robot; first it is divided into three modules, i.e. a mobile platform, a parallel ST mechanism, and a serial robot. Next, a closed-form dynamics model is derived for the whole hybrid system based on a combined Newton–Euler and Lagrange formulation. Then, a careful validation procedure is presented to verify the obtained dynamics model. Finally, using the new postural stability metric named as moment-height stability (MHS), the important role of the parallel ST mechanism for stabilizing the mobile robotic system is demonstrated. The obtained results show that the proposed hybrid serial–parallel arrangement effectively enhances the tip-over stability of the overall mobile robotic system. Hence, it can be successfully exploited to prevent tip-over instability particularly during heavy object manipulation tasks.     

飞艇姿态跟踪系统的研究

研究了具有参数不确定和外部干扰的飞艇姿态跟踪控制问题．飞艇姿态运动的数学模型为一个多输入/多输出不确定非线性系统,根据该系统的特点,采用了一个基于不确定项上界的鲁棒输出跟踪控制器设计方法,应用输入/输出反馈线性化法和李雅普诺夫方法,设计了飞艇姿态鲁棒控制律,它可确保系统输出按指数规律跟踪期望输出．该控制器设计简单,易于实现．仿真结果表明:即使系统存在不确定性和外界干扰,仍可在闭环系统中实现精确的姿态控制．     

Funnel Control for Linear DAEs

We study funnel control for linear differential-algebraic multi-input multi-output systems which are not necessarily regular. We show that the funnel controller (that is a static nonlinear output error feedback) achieves - for a special class of right-invertible systems with asymptotically stable zero dynamics - tracking of a reference signal by the output signal within a pre-specified performance funnel. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Natural gradient algorithm for stochastic distribution systems with output feedback

In this paper, we use natural gradient algorithm to control the shape of the conditional output probability density function for the stochastic distribution systems from the viewpoint of information geometry. The considered system here is of multi-input and single output with an output feedback and a stochastic noise. Based on the assumption that the probability density function of the stochastic noise is known, we obtain the conditional output probability density function whose shape is only determined by the control input vector under the condition that the output feedback is known at any sample time. The set of all the conditional output probability density functions forms a statistical manifold (M), and the control input vector and the output feedback are considered as the coordinate system. The Kullback divergence acts as the distance between the conditional output probability density function and the target probability density function. Thus, an iterative formula for the control input vector is proposed in the sense of information geometry. Meanwhile, we consider the convergence of the presented algorithm. At last, an illustrative example is utilized to demonstrate the effectiveness of the algorithm.     

Tracking control of high-performance robots via stabilizing controllers for uncertain systems

The development of flexible manufacturing systems calls for industrial robots characterized by robustness of performance with regard to the variations of the loads and real time specification of the trajectory in the work space. In this paper, the design of a feedback controller guaranteeing such performance is considered. At first, the manipulator dynamics are embedded into a larger class of uncertain dynamical systems and a class of feedback controls is proposed that guarantees uniform ultimate boundedness of the tracking error. Successively, the methodology is specialized for the case of robotic manipulators to track trajectories described in task-oriented coordinates; the proposed control algorithm operates without requiring any explicit coordinate transformation.     

Stabilization and tracking controller for a class of nonlinear discrete-time systems

In this paper, stabilization and tracking control problem for parametric strict feedback class of discrete time systems is addressed. Recursive design of control function based on contraction theory framework is proposed instead of traditional Lyapunov based method. Explicit structure of controller is derived for the addressed class of nonlinear discrete-time systems. Conditions for exponential stability of system states are derived in terms of controller parameters. At each stage of recursive procedure a specific structure of Jacobian matrix is ensured so as to satisfy conditions of stability. The closed loop dynamics in this case remains nonlinear in nature. The proposed algorithm establishes global stability results in quite a simple manner as it does not require formulation of error dynamics. Problem of stabilization and output tracking control in case of single link manipulator system with actuator dynamics is analyzed using the proposed strategy. The proposed results are further extended to stabilization of discrete time chaotic systems. Numerical simulations presented in the end show the effectiveness of the proposed approach.     

Model reference control and identification of robotic manipulators under uncertainty

The robotic manipulator is considered in terms of an open kinetic chain with n-degrees of freedom, with nonlinear and nonlinearizable characteristics and couplings, and with uncertain but bounded values of system parameters. The chain is powered by n-actuators and effected by a pay-load which is unknown but within a known band.The objective is to reach for a moving target and avoid moving obstacle. It is specified in terms of a dynamic model to be followed. The well known linear model-reference adaptive control technique is extended to the nonlinear case at hand and used to stabilize the manipulator about the model, at the same time on-line identifying the uncertain parameters and the payload. The method is similar to the self-tuning control which is used in manufacturing when high speed must be combined with high accuracy and not-too-high requirements on sensors (reducing the number of transducers and reading time) as well as broadening the functional abilities of the actuators.The identification uses nonlinear identifier (predictor) system which also stabilizes the resultant response of the manipulator and itself about the desired dynamic model.Algorithms for the adaptive laws in both control and identification are provided. Numerical simulation illustrates the results.     

Solving a Local Boundary Value Problem for a Nonlinear Nonstationary System in the Class of Feedback Controls

An algorithm convenient for numerical implementation is proposed for constructing differentiable control functions that transfer a wide class of nonlinear nonstationary systems of ordinary differential equations from an initial state to a given point of the phase space. Constructive sufficient conditions imposed on the right-hand side of the controlled system are obtained under which this transfer is possible. The control of a robotic manipulator is considered, and its numerical simulation is performed.     

Modeling of the Crosstalk Phenomenon by Bilateral Coupling of the Non-Stationary Maxwell Equations and the Circuit Equations

In this paper, we introduce a general modeling approach for the crosstalk phenomenon within electro-magnetic systems. We model the phenomenon by bilateral coupling of two sets of differential equations, namely non-stationary Maxwell equations and circuit equations. Considering these two sets of equations as input-output systems, the bilateral coupling approach connects the output of one system to the input of the other system and conversely, via coupling and re-coupling relations. The coupling of these two sets leads to a set of partial differential-algebraic equations modeling the crosstalk phenomenon. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

输入通道有干扰多变量MRAC系统的全局稳定化控制

对具有未建模动态并且输入通道存在干扰的动态不确定多输入多输出(MIMO)模型参考自适应控制(MRAC)系统,应用输出反馈给出了一种变结构模型跟踪控制器设计．系统的已建模部分有大于1的任意相对阶且已建模部分阶的上界是未知的．通过引入辅助信号和带有记忆功能的正规化信号,以及适当选择控制器参数,保证了闭环系统的全局稳定性,且跟踪误差可调整到任意小．     

Sliding Mode Control of an Underactuated Two-Link Manipulator

We consider a horizontally mounted two-link manipulator of which only the first joint is actuated and the friction in the second joint is neglected. As a consequence, predefined equilibrium points are difficult to reach and point-to-point control is a challenging task. Starting from a partially feedback linearized model, a transformation to Byrnes-Isidori normal form is presented. Based on this decomposition, the projection into a two-dimensional subspace reveals certain similarities to a double integrator. Modifying an existing sliding mode approach for that system, a control law which steers the manipulator to an equilibrium point can be deduced. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Output Regulation in Differential Variational Inequalities using Internal Model Principle and Passivity-Based Approach

We consider the problem of designing state feedback control laws for output regulation in a class of dynamical systems where state trajectories are constrained to evolve within time-varying, closed, and convex sets. The first main result states sufficient conditions for existence and uniqueness of solutions in such systems. We then design a static state feedback control law using the internal model principle, which results in a well-posed closed-loop system and solves the regulation problem. As an application, we demonstrate how control input resulting from the solution of a variational inequality results in regulating the output of the system while maintaining polyhedral state constraints. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Soft-Computing Algorithm-based Cognitive Observer for an Elastic Robotic Arm

This paper proposes the use of Support Vector Machine (SVM) algorithm for modeling and states estimation of an elastic robotic arm. Due to the complexity of the elastic robotic arm, an accurate mathematical model and large number of sensors are needed to achieve accurate estimation. Initially, it is assumed that all system states are measurable for a short period of time. Additionally, the system output and input signals are being continuously measured. The modeling module builds two models, the internal model which will capture the dynamics of the elastic robotic arm and the data-driven observer model which will estimate the system states. The internal model and data-driven observer are obtained based on the experimental measurements using SVM algorithm in contrast to classical methods that uses the mathematical system model to drive an observer. The internal model is able to make multi-steps ahead predictions of all system states; therefore it can be used to generate a suitable control strategy. Once the models are ready, the main sensors can be removed or turned off. The proposed modeling module will eliminate the need for mathematical modeling and reduces the number of permanent sensors needed. If the main sensors are removed completely, the hardware price can be radically reduced. The simulation result demonstrates the efficiency and high performance of the modeling module. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Multivariable fuzzy control applied to the physical–chemical treatment facility of a Cellulose factory

Feedback linearization is a well-known technique in nonlinear control in which known system nonlinearities are canceled by the control input leaving a linear control problem. Feedback linearization requires an exact model for the system. Fundamental and advanced developments in neuro-fuzzy synergy for modeling and control are used to apply the feedback linearization control law on second-order plants. In the models that are used, the nonlinear plant is decomposed on six fuzzy systems necessary to apply the control signal to allow the following of a reference value. A practical application is also presented using a waste water plant. This method can be extended to multiple input–multiple output (MIMO) plants based on input–output data pairs collected directly from the plant.