Nonlinear control with end-point acceleration feedback for a two-link flexible manipulator: Experimental results

Experimental results for end-point positioning of multi-link flexible manipulators through end-point acceleration feedback are presented in this article. The advocated controllers are implemented on a two-link flexible arm developed at the Control/Robotics Research Laboratory at Polytechnic University. The advocated approach in this article is based on a two-stage control design. The first stage is a nonlinear (1) feedback linearizing controller corresponding to the rigid body motion of the manipulator. Because this scheme does not utilize any feedback from the end-point motion, significant vibrations are induced at the end effector. To this effect, and to enhance the robustness of the closed-loop dynamics to parameter variations, the inner loop is augmented with an outer loop based on a linear output LQR design that utilizes an end-point acceleration feedback. The forearm of the manipulator is significantly more flexible as compared with the upper arm. Experimental and simulation results validate the fact that the end-effector performance is significantly better with the proposed (1) feedback linearizing control as compared with the linear independent joint PD control. In addition, the nonlinear control offers other advantages in terms of smaller and smoother actuator torques and reducing the effects of nonlinearities. Close conformation between simulation and experimental results validates the accuracy of the model.     

Control of flexible joint robots via external linearization approach

Based on the feedback linearization structure algorithm of differential geometric nonlinear control theory, an external linearization approach to the control of multilink flexible joint robots is considered in this article. The resulting externally linearized and input-output decoupled closed-loop system contains a linear subsystem and a nonlinear subsystem. The linear part describing the rigid motor motions is suitable for the design of nominal trajectory following control. However, the nonlinear joint deformation subsystem will cause perturbations in the nominal trajectory. To actively damp out the elastic vibrations and to render the complete closed-loop system robust to uncertainty in system parameters, a combined LQR stabilizer and servocompensator is used as the internal stabilization and error correcting control. The tracking errors of the end effector caused by the quasi-static joint deflections due to gravity can be compensated for by taking into account the nominal deflections in the trajectory planning and LQ regulation. A three-link PUMA type arm is tested via simulation.     

Robust control of mobile manipulators

A mobile manipulator is basically a manipulator mounted on a mobile vehicle. This arrangement has some advantages over stationary robots and mobile robots, such as the infinite workspace and the ability to avoid singularities. However, the control problem becomes a sophisticated one. This is due to the nonlinear and nonholonomic constraints governing the motion of the vehicle. Moreover, the dynamics of the manipulator and the vehicle are highly coupled; ground-surface irregularities, for example, affect the motion of the end effector kinematically and dynamically. A mobile manipulator is expected to pass through different environmental conditions, a fact which calls for a robust control scheme. Unfortunately, the robust control problem for nonholonomic systems is not well defined yet. Since the ultimate goal of control is to control the motion of the manipulator's end effector, it is proposed in this article to tackle the robustness issue by designing a manipulator decoupling controller. This controller aims at rejecting disturbances arising from the motion of the vehicle. © 1996 John Wiley & Sons, Inc.     

Inverse cartesian trajectory control and stabilization of a three-axis flexible manipulator

This article treats the question of end point trajectory control of a flexible manipulator based on the nonlinear inversion technique. The manipulator has two rigid links and the third link is elastic. A parameterization of the Cartesian coordinates of a point close to the end effector position is suggested. Using these coordinates as output variables, an inverse feedback control law is derived for tracking reference Cartesian trajectories. The stability of the zero dynamics associated with the end point motion control is examined. It is shown that inverse control of the end point causes divergent oscillatory flexible modes. In addition, for regulating the end point to a fixed position, a linear stabilizer is designed to damp the elastic vibration. Simulation results are presented to show that in the closed-loop system, reference end point trajectories can be accurately followed in spite of the parameter uncertainty in the arm dynamic model. © 1994 John Wiley & Sons, Inc.     

Feedback linearization families for nonlinear systems

Characterizations are developed for parameterized, linear, dynamic feedback control laws that can arise when linearizing a nonlinear, dynamic feedback control law for a specified nonlinear system about a family of constant operating points. Such characterizations are important in applying the recently-developed extended linearization design approach to various types of control problems. To illustrate, the input-output decoupling problem is considered.     

Recursive linearizing and decoupling control of robots

A control structure is considered for decoupling and linearizing the dynamic behavior of a robotic manipulator. Since computational efficiency is a crucial consideration in implementation of this control system, a fast recursive algorithm is presented for the necessary digital computations, and the computational requirements are studied in terms of the number of degrees of freedom of a general and open-chain robotic manipulator. An important feature of the algorithm is that decoupling is realized without employing matrix inversion. The sequential recursive algorithm is restructured into a parallel algorithm. A significant improvement in the computational speed is achieved in this manner. The computing requirements of the parallel algorithm are compared with those of the serial algorithm. For a six-degrees-of-freedom robot, the computational cost of the parallel algorithm is approximately 23 % of that of the original serial algorithm. Finally, the processor loads in some regions of the parallel algorithm are redistributed to achieve a balanced scheme. The resulting parallel algorithm requires approximately 17% of the computational effort of the serial algorithm, for a six-degrees-of-freedom robot.     

Control of a two-degree-of-freedom lightweight flexible arm with friction in the joints

This article describes the design and control of a two-joint, two-link flexible arm. This flexible arm was built with very light links, has most of its mass concentrated at the tip and uses a special mechanical configuration to approximately decouple radial tip motions from angular tip motions. The lightweight design and decoupling maximize the efficiency of power transmitted to the load. An important problem when controlling lightweight flexible arms is the large Coulomb friction of the motors. A two-nested-loop multivariable controller is used to control the lightweight flexible arm with friction in the joints. The inner loop controls the position of the motors while the outer loop controls the tip position. The resolved acceleration method is generalized to control this flexible arm. The compliance matrix is used to model the oscillations of the structure and is included in the decoupling/linearizing term of this controller. Experimental results are presented. © 1995 John Wiley & Sons, Inc.     

Multidimensional system of cascaded control of plasma form and current in tokamak with channel decoupling and <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript>-controller

Consideration was given to the development and numerical modeling of the multidimensional cascaded system with H _∞-controller in the external cascade for control of the plasma form and current in tokamak. For controller design, the problem of mixed sensitivity was solved by selecting the weight functions in the composite matrix of the performance criterion. The internal loop was intended for decoupling the current control channels in the magnetic coils of the tokamak poloidal fields and following the given scenario currents. Linearized models obtained from the nonlinear plasma-physical DINA code by linearizing the ITER scenario at different points were used to design the controllers. The robust stability margin was estimated in the frequency domain using singular numbers of the matrix transfer functions of the closed-loop control system. The designed cascaded system was modeled in the DINA code.     

Optimal directionality compensation in processes with input saturation non-linearities

A notion of process directionality in input-constrained processes is defined, and the class of processes that do not exhibit the process directionality is characterized. An optimal directionality compensator for non-linear processes with actuator saturation non-linearities is presented. Given an unconstrained controller output and the characteristic (decoupling) matrix of the process under consideration, the compensator calculates an optimal constrained (feasible) process input that results in a process response as 'close' as possible to the response of the same process to the unconstrained controller output. The compensator can be used for both linear and non-linear processes, irrespective of the type of controller being used. For processes whose non-singular characteristic matrix can be made diagonal by row or column rearrangements, the optimal directionality compensator is identical to a series of limiters (clippers); this class of processes does not exhibit the process directionality over a short time horizon. The performance of the optimal directionality compensator is shown and compared with those of clipping and direction preservation, by numerical simulation of a linear example under decentralized proportional-integral control, a linear example under model-based control, and a non-linear bioreactor under input-output linearizing control.     

Design of a torque controller for the adept-2 robot

The ability to command actuator torque is necessary to perform research into robot control. Commercial manipulators using direct-drive actuators offer high performance, but do not allow specification of actuator torque. We experimentally characterize the motors in an Adept-2 manipulator, and develop a linearizing and decoupling controller which allows torque specification. Torque ripple is 13%.     

线性定常系统的Petri网解耦控制

将Petri网与现代控制理论相结合,应用于连续系统的性能分析如可控性、可观性和稳定性等已日益普遍,但Petri网应用于系统的解耦控制研究很少.提出了广义连续自控网系统的形式化定义,描述了线性定常系统的广义连续自控网系统模型并分析了广义连续自控网系统模型与状态空间描述的等效性.基于状态反馈动态解耦的基本原理,探讨了利用Petri网模型结构实现线性定常系统解耦控制的新方法.该方法采用图的遍历算法,可有效的判断系统的可解耦性以及实现解耦控制律,避免了传统解耦控制方法中计算所需的大量矩阵运算.最后给出了两个具体的应用实例.     

Attraction domain estimate for single-input affine systems with constrained control

Nonlinear single-input affine systems represented in a canonical (normal) form are considered. The control resource is assumed to be constrained. For a closed-loop system obtained by applying a linearizing feedback, the problem of finding an estimate of the attraction domain is set. A method for constructing an ellipsoidal estimate that is based on results of absolute stability theory is suggested. Construction of the estimate reduces to solving a system of linear matrix inequalities. The discussion is illustrated by numerical examples.     

感应电动机定子磁链与转矩的逆解耦及存在性

对于具有多变量、非线性、强耦合特征的异步电动机调速系统,实现定子磁链与电磁转矩的动态解祸控制足提高系统性能的关键.本文从异步电动机的5阶模犁及其固有的电磁特性出发,证明了其系数矩阵的非奇异性,进而结合逆系统理论证明定子磁链与电磁转矩的逆解耦在任何状态下都是存在的.在此基础上设计了一种通过非线性状态反馈的逆解耦控制方案,将复杂系统解耦成电磁转矩与定子磁链的两个独立线性回路,然后利用线性系统理论分别对转矩与磁链调节器进行综合设计.仿真实验结果验证逆解耦的存在性与解耦控制方案的有效性.     

Intelligent fault-tolerant system of vibration control for flexible structures

This paper describes an intelligent fault-tolerant control method for vibration control of flexible structures. We consider a case where the fault phenomena of the control system for flexible structures can be treated as a change of system parameters. Therefore, the adaptive control method can be applied to a vibration control system for flexible structures with a fault. In this paper, a neural network (NN) adaptive control system is used to compensate for the change in the parameters of a plant with a fault. When the characteristics of the plant and of a nominal model have been agreed by a NN adaptive control system, the control method designed for the nominal model, such as decoupling feedback control or linearizing feedback control, can be used even if the change in the system parameters has been caused by a fault. To confirm the effectiveness of the proposed fault-tolerant control method, the simulational results from a 5-link robotic arm are shown at the end of the paper. This work was presented, in part, at the Fourth International Symposium on Artificial Life and Robotics, Oita, Japan, January 19–22, 1999     

Analytical decoupling control strategy using a unity feedback control structure for MIMO processes with time delays

An analytical decoupling control method is proposed for multiple-input–multiple-output (MIMO) processes with multiple time delays. The desired diagonal system transfer matrix is proposed first in terms of the H₂ optimal performance specification, resulting in the ideal desired decoupling controller matrix derived within the framework of a unity feedback control structure. It is demonstrated that dead-time compensators must be enclosed in the decoupling controller matrix to realize absolute decoupling for MIMO processes with multiple time delays. To alleviate the difficulties associated with the implementation, the ideal desired decoupling controller matrix is transformed into a practical form using an analytical approximation approach. Correspondingly, the stability of the resultant control system is assessed, together with its robust stability in the presence of process uncertainties. An on-line tuning rule for the single adjustable parameter of each column controllers in the decoupling controller matrix is given to cope with the process unmodeled dynamics. Finally, illustrative examples are given to show the superiority of the proposed method over the recently improved decoupling control methods.     

多自由度伺服系统的非线性解耦控制

多自由度伺服系统各轴之间存在的非线性耦合,是影响系统控制性能的一个重要因素,为了提高系统控制性能,本文研究了多自由度伺服系统的解耦控制．首先建立了多自由度伺服系统的一般化耦合数学模型;然后根据Singh法求出逆系统;最后结合期望的标称线性传递函数,算出解耦控制规律．本算法避开微分几何理论,直接对矩阵进行运算,易于理解．文章给出了应用此方法对3轴仿真转台进行解耦控制的例子．     

Variable structure trajectory control of an elastic robotic arm

This article introduces a variable structure system scheme to control the end effector trajectory of a two-link flexible robotic arm. Because control of the actual tip position leads to unstable zero dynamics, control of points in the neighborhood of the tip is considered. An output is chosen as the sum of the joint angle and tip elastic deformation times a constant factor for each link. For the chosen output, a discontinuous output control law is derived based on the variable structure theory. The control law thus derived accomplishes the desired trajectory tracking of the output. A linear stabilizer is designed using the pole assignment technique for the final capture of the terminal state and stabilization of the elastic modes. Simulation results are presented to show that in the closed-loop system large maneuvers can be performed in the presence of payload uncertainty, thereby exhibiting the robustness of the controller.     

Flexible fixturing and automatic drilling of sheet metal parts using a robot manipulator

The design of robotic system for sheet metal drilling is presented. The machining of sheet metal aerospace parts is currently done manually with the aid of precision drill templates. The drilling template serves two purposes: it locates the drill bit relative to the work surface, and bears the dynamic loads of the drilling process. In the developed system, the template is eliminated by decoupling these tasks. First, an end effector is designed for the drilling task and is positioned using a six degree of freedom robot. Second, the accuracy is improved through the use of active end point recalibration. Dynamic loading of the arm is reduced by making the drilling end effector a jig hand that is preloaded against the workpiece. The developed system is presented and the resultant performance is evaluated through analysis and experiments.     

Reinforcement learning to adaptive control of nonlinear systems

Based on the feedback linearization theory, this paper presents how a reinforcement learning scheme that is adopted to construct artificial neural networks (ANNs) can linearize a nonlinear system effectively. The proposed reinforcement linearization learning system (RLLS) consists of two sub-systems: The evaluation predictor (EP) is a long-term policy selector, and the other is a short-term action selector composed of linearizing control (LC) and reinforce predictor (RP) elements. In addition, a reference model plays the role of the environment, which provides the reinforcement signal to the linearizing process. The RLLS thus receives reinforcement signals to accomplish the linearizing behavior to control a nonlinear system such that it can behave similarly to the reference model. Eventually, the RLLS performs identification and linearization concurrently. Simulation results demonstrate that the proposed learning scheme, which is applied to linearizing a pendulum system, provides better control reliability and robustness than conventional ANN schemes. Furthermore, a PI controller is used to control the linearized plant where the affine system behaves like a linear system.     

解耦控制的现状及发展

通过对多变量系统解耦设计的必要性分析,介绍了传统解耦、自适应解耦、鲁棒解耦、智能解耦等各种解耦方法,并叙述了各种方法的研究现状和应用情况,同时分析了各种方法局限性。指出解耦控制领域的研究已成为控制理论和控制工程界共同关注的热点。自适应解耦与智能解耦,侧重于控制器的研究,它们更多采用试探、优化方法来设计控制器．理论研究还尚待完善。因此,寻求一种有效的、简单易行的控制方法,即寻求理论与实际结合点,是今后研究的方向。