Direct adaptive control of a one-link flexible arm with tracking

A robust tracking controller for a one-link flexible arm based on a model reference adaptive control approach is proposed. In order to satisfy the model matching conditions, the reference model is chosen to be the optimally controlled linearized model of the system. The resulting controller overcomes the fundamental limitation in previously published research on direct adaptive control of flexible robots that required additional actuators solely to control the flexible degrees of freedom. The nominal trajectory is commanded by means of a tracking control. Simulation results for the prototype in the laboratory show improvements obtained with the outer adaptive feedback loop compared to a pure optimal regulator control. Robustness is tested by varying the payload mass.     

Force control and exponential stabilisation of one-link flexible arm

In this paper, we discuss a force control problem for a constrained one-link flexible arm. To solve the force control problem, we propose a simple boundary feedback controller that consists of the bending moment at the root of the flexible arm and its time derivative. The striking point is that information about the force and the rotational angle of the motor is not necessary for the implementation of the controller, and thus we do not need a force sensor or encoder in the construction of the controller. The exponential stability of the closed-loop system is then provided using the energy multiplier method. We describe several experiments carried out to investigate the performance of the proposed controller.     

Regulation of a one-link flexible robot arm using sliding-mode technique

This paper is concerned with the application of sliding control’ to the regulation of a one-link flexible robot arm, with an arbitrary number of flexible modes. Slidingmode technique is applied to achieve a robust feedback linearization of the highly non-linear dynamic equation of the arm. Pole placement is then used to attain good dynamic response. An example is given to demonstrate the potential of the sliding method. This work serves as a first step towards a practical solution in the feedback control of flexible arms using the sliding technique.     

Observer-based control of discrete-time Lipschitzian non-linear systems: application to one-link flexible joint robot

The problem of designing asymptotic observers along with observer-based feedbacks for a class of discrete-time non-linear systems is considered. We assume that the system non-linearity is globally Lipschitz and the system is supposed to be stabilizable by a linear controller. Sufficient linear matrix inequality condition is derived to ensure the stability of the considered system under the action of feedback control based on the reconstructed states. A numerical example of a single-link flexible joint robot is presented to illustrate the efficacy of the theoretical developments.     

Experiments in load-adaptive control of a very flexible one-link manipulator

An adaptive control algorithm based on the Self-Tuning Regulator concept has been experimentally demonstrated on a very flexible one-link robotic manipulator. The very lightly-damped structural resonances of the manipulator coupled with the use of a primary sensor separated from the actuator by flexible structure (non-collocated sensor and actuator) to give good accuracy in tip positioning make high-performance controllers very sensitive to modeling error. The adaptive controller is able to maintain precise tip position control despite wide variations in end effector load. An identification algorithm is employed which estimates the mass of the tip load. It makes use of a simple parameterization of system transfer functions which is a linear-fractional expression in the mass of the load. The Linear Quadratic Gaussian synthesis procedure is used for control design, a polynomial interpolation to a precalculated table of controller gains is made on-line to implement a controller appropriate to the identified value of load mass. Rate of convergence of the identification algorithm is such that the system is able to adapt to a 40% change in moment of inertia during a single commanded step change in position.     

Feedback control of one-link flexible manipulator with gear train

This article reports experimental results in control of a one-link flexible manipulator. A d.c. drive with gear train rotates the link with a tip-mass in the horizontal plane. A “stiff” hardware servo-system tracks the commanded drive velocity. We describe the experimental setup and develop a dynamic model for the one-mode flexible vibration control. We design and experimentally test controllers for active damping of the vibrations and stabilization of the link-tip position. Results for continuous control implemented with an analog computer and a sampled-data, digital-computer control are reported. A high control performance is achieved despite the gear-train friction influence. In addition, sampled-data digital controllers for tracking control of the link reference motion are designed and tested.     

Modeling and robust force control of constrained one-link flexible arms

In this article modeling and robust force control of constrained flexible one-link arms on the basis of a distributed parameter model are discussed. Since the tip of the flexible arm contacts a given constraint surface, a constraint condition should be satisfied. By using the Lagrange multiplier method and the Hamilton's principle, we derive dynamic equations of the joint angle, the vibration of the flexible arm, and the constraint force. The boundary condition of the derived distributed parameter system is related to the contact force and is nonhomogeneous. We introduce a change of variables to derive a homogeneous boundary condition. On the basis of a finite-dimensional modal model of the distributed parameter system, we analyze the stability of the force feedback by using the root locus technique and the compliance control. To compensate the spillover instability an optimal controller with low-pass property and a robust H_∞ controller are constructed. Experiments have been carried out and results confirm that the controllers perform remarkably well. © 1998 John Wiley & Sons, Inc.     

Dynamic stability analysis of a one-link force-controlled flexible manipulator

This study analyzes the effects of link flexibility on the dynamic stability of a force-controlled flexible manipulator. The closed-loop dynamic equation for a l-link manipulator is first derived explicitly using the modal representation technique. Stability analysis is then carried out by computing the system eigenvalues. Results show that the link flexibility is one of the causes of dynamic instability of motion of the flexible robotic arm.     

Modeling and feedback control of a flexible arm

When a flexible arm is rotated by a motor about an axis through the arm's fixed end, transverse vibration may occur. The motor torque should be controlled in such a way that the motor rotates by a specified angle, while simultaneously stabilizing vibration of the flexible arm so that it is arrested as soon as possible at the end of rotation. In this paper, we first derive a partial differential equation and a set of boundary conditions governing the vibration. Then, a feedback control system which incorporates a dynamic compensator is designed using sensor outputs. A set of experiments has been constructed to demonstrate control strategies for a flexible arm, where a strain gage was used as a vibration sensor and a microcomputer was equipped as a controller. Several satisfactory experimental results are shown.     

Robust control of a hydraulically driven flexible arm

A new robust controller is proposed to regulate both flexural vibrations and rigid body motion of a hydraulically driven flexible ann. The controller combines backsteppmg control and sliding mode to arrive at a controller capable of dealing with a nonlinear system with uncertainties. The sliding mode technique is used to achieve an asymptotic joint angle and vibration regulation in the presence of payload uncertainty by providing a virtual torque input at the joint while the backstepping technique is used to regtthte the spool position of a hydraulic valve to provide the required torque. It is shown that there is no chatter in the hydraulic valve, which results in smoother operation of the system.     

Vibration control of a two-link flexible robot arm

Analysis and experimentation is described for a two-link apparatus in which both members are very flexible. Attention is focused on endpoint position control for point-to-point movements, assuming a fixed reference frame for the base, with two rotary joints. Each link is instrumented with acceleration sensing and is driven by a separate motor equipped with velocity and position sensing. The control perspective adopted is to implement a two-stage control strategy in which the vibration control problem for fine-motion endpoint positioning is considered separate from the gross-motion, large-angle slew problem. In the first stage the control law shapes the actuator inputsfor the large-angle movement in such a way that minimal energy is injected into the flexible modes, while in the second phase an endpoint acceleration feedback scheme is employed in independent joint controlfor vibration suppression at the link endpoints.     

A new controller design for a flexible one-link manipulator

A novel controller design for noncollocated flexible one-link manipulator arm tip position control based on variable structure sliding mode control is presented. Using the assumed-mode method, the plant model is derived. The discontinuous control law based on the variable structure system theory for the noncollocated manipulator tip position control is then designed. The position state variables are obtained directly from the inversion of the output submatrix multiplied by the sensor measurements. The velocity state variables are estimated through decoupled estimators-a separate first-order observer for each of the system's modes under consideration. Different sampling periods are used for the estimator and the controller. The performance of the controller is evaluated through a series of simulations, followed by an analysis of the designed control system     

Acceleration feedback for control of a flexible manipulator arm

Many studies to date have dealt with control and modeling strategies for endpoint positioning of flexible manipulator arm systems, and some actual experiments have been documented in verification of developed methods. This article describes laboratory results for a single-link flexible manipulator arm in which three separate control strategies are compared and contrasted. Namely, the control schemes compared are: compensation using classical root locus techniques with endpoint position feedback, a full state feedback, observer-based design, and compensation using endpoint acceleration feedback. The last technique, designs using accelerometer feedback, has received very little attention to date, and results here indicate great promise for use in flexible manipulator control.     

主从式柔性机械臂计算机控制系统

本文详细分析了一个主从式柔性机械臂计算机控制系统的硬件组成，功能、及软件实现。该控制系统运行可靠，可以实现多种控制算法，用它4作为柔性机械臂振动主动控制的实验装置是合适的。     

Motion control and shape optimization of a suitlike flexible arm

A method of motion control as well as shape optimization is proposed for the preliminary design of a suitlike flexible arm, which is composed of some variable-length and fixed-length beams. The large deformation, variable geometry and motion of the flexible structure are calculated by dynamic finite element analysis (FEA) using the step by step time integration method. A neural-networks-inverse-model, which learns nonlinear behaviour of the flexible structure, has been applied for the motion control as an inverse model of the flexible arm. For this geometrically nonlinear structure and time response problem, the optimum shape of the cross-section has been calculated under constraints of stress, stiffness and minimum weight with FEA and sensitivity analysis combined with fuzzy rules. This method has been applied for the design of a flexible arm, which simulates a process of lifting a human body and moving it. The calculated optimum shape has a much higher stiffness with decrease in weight in comparison with the initial shape. Moreover, the calculated motion agrees well with the one aimed for and the flexible arm reduces the impact force.     

Trajectory control of a PUMA robot arm by inversion and servocompensation

Based on invertibility and functional reproducibility, an approach to the control of the PUMA arm with six rotational degrees of freedom is presented. The control system has two important features: (i) the ability for fast, precise trajectory tracking; and (ii) robustness to uncertainty in the system, such as variable payload, inertia, etc. The control law derived using invertibility gives decoupled, independently controlled responses in each joint angle using torquers. For robustness, a first-order servocompensator is designed for each decoupled inner loop driven by the joint angle error. For smooth joint angle responses, a command generator is constructed that produces the reference trajectories to be tracked. Simulation results are presented to show that rapid, accurate trajectory following is achieved in the closed-loop system in spite of large payload uncertainty.     

Experimental two-axis vibration suppression and control of a flexible robot arm

This article focuses on the implementation of a dual-mode controller for the maneuver of a two-axis flexible robotic arm. The joint angle trajectory tracking is accomplished by proportional and derivative and feedforward controllers. Based on the pole placement technique, a linear stabilizer is designed for elastic mode stabilization in the plane perpendicular to each joint axis. The stabilizer is switched on when the trajectory reaches the vicinity of the terminal state. The effect of switching time of the stabilizer and varying payload on arm vibration are investigated. With the proposed control system, accurate joint angle tracking and elastic mode stabilization can be accomplished. © 1993 John Wiley & Sons, Inc.     

Experimental control of a single-link flexible robot arm using energy shaping

Flexible-link robotic manipulators are mechanical devices whose control can be rather challenging, among other reasons because of their intrinsic under-actuated nature. This paper presents the application of an energy-based control design methodology (the so-called IDA-PBC, interconnection and damping assignment passivity-based control) to a single-link flexible robotic arm. It is shown that the method is well suited to handle this kind of under-actuated device not only from a theoretical viewpoint but also in practice. A Lyapunov analysis of the closed-loop system stability is given and the design performance is illustrated by means of a set of simulations and laboratory control experiments, comparing the results with those obtained using conventional control schemes for mechanical manipulators.     

Nonlinear ultimate boundedness control and stabilization of a flexible robotic arm

We treat the question of control of an elastic robotic arm of two links. Of course, this approach can be extended to other elastic arms. A nonlinear ultimate boundedness controller (UBC) is synthesized such that in the closed-loop system the joint angle tracking error is uniformly bounded and tends to a certain small neighborhood of the origin. The controller includes a reference joint angle trajectory generator and integral error feedback. Although the joint angles are controlled using the UBC, elastic modes are excited. A feedback stabilizer is designed for the linearized model including the UBC about the terminal state that is switched only in the vicinity of the equilibrium state for stabilization. Simulation results are presented to show that in the closed-loop system including the UBC and the stabilizer accurate joint angle trajectory following and elastic mode stabilization are accomplished in the presence of uncertainty.     

Robust force control of a flexible arm with a nonsymmetric rigid tip body

In this article, we discuss modeling and robust control of bending and torsional vibrations and contact force of a flexible arm with a nonsymmetric rigid tip body. By using Hamilton's principle and the Lagrange multiplier method, dynamic equations of the constrained flexible arm are derived. Since the flexible arm has the nonsymmetric tip body, the bending and torsional vibrations are coupled. As the obtained boundary conditions of the distributed parameter system are nonhomogeneous, we introduce a change of variables to derive homogeneous boundary conditions. By using the eigenvalues and the correpsonding eigenfunctions related to the distributed parameter system, we derive a finite‐dimensional modal model. To compensate for the spillover instability, we construct robust controllers of an optimal controller with a low‐pass property and an H_∞ controller. Some experiments have been carried out to show the effectiveness of the proposed robust controllers. © 2001 John Wiley & Sons, Inc.