Lih-Chang Lin

Feedback linearization and fuzzy control for conical magnetic bearings

Conical magnetic bearings with radial and thrust (axial) control using the input-output feedback linearization method are considered. By suitable selection of nine output variables, the nonlinear magnetic bearing system is transformed to nine linear decoupled subsystems with no internal dynamics using feedback linearization control. Furthermore, a hybrid approach integrating feedback linearization and fuzzy control is proposed for improving the transient performance and robustness of the nonlinear magnetic bearings. Computer simulations are shown to illustrate the effectiveness of the proposed control strategy for simultaneous rotor-shaft speed tracking control and gap deviations regulation.

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.

Fuzzy dynamic output feedback control with adaptive rotor imbalance compensation for magnetic bearing systems

This paper presents a dynamic output feedback control with adaptive rotor-imbalance compensation based on an analytical Takagi-Sugeno fuzzy model for complex nonlinear magnetic bearing systems with rotor eccentricity. The rotor mass-imbalance effect is considered with a linear in the parameter approximator. Through the robust analysis for disturbance rejection, the control law can be synthesized in terms of linear matrix inequalities. Based on the suggested fuzzy output feedback design, the controller may be much easier to implement than conventional nonlinear controllers. Simulation validations show that the proposed robust fuzzy control law can suppress the rotor imbalance-induced vibration and has excellent capability for high-speed tracking and levitation control.

Rigid model-based neural network control of flexible-link manipulators

Applications of neural networks to the identification and control of flexible manipulators are considered. Usually, neural networks need a large number of neurons and a great amount of computation for learning, and the error is not easy to reduce. This study tries to combine the a priori knowledge of the corresponding rigid manipulators model with two multilayered neural networks for the identification and control of a flexible-link manipulator. The suggested approach can use fewer neurons and needs shorter learning time for reducing the error. A planar (in the vertical plane) two-link flexible arm with the first link rigid and the second link flexible is tested via simulation. The mathematical model of the flexible arm for simulation is derived by the finite element method using Lagranges equation.

A Lagrange‐Euler‐assumed modes approach to modeling flexible robotic manipulators

Abstract This paper presents a general Lagrange‐Euler‐assumed modes dynamics formulation for lightweight flexible manipulators. The proposed explicit form formulation, not yet available in the existing literature, can be viewed as an extended version of the Lagrange‐Euler formulation for rigid manipulators. The deformation of a link from its rigid body position is modeled by a homogeneous 4×4 transformation matrix composed of summations of assumed link modes. The number of modes can be arbitrarily selected. The joint flexibility is modeled by a linear torsionai spring with known characteristics. The methodology presented can be easily used to derive the full nonlinear dynamic equations of flexible manipulators by computing only the dynamic coefficients using computer algebra such as MACSYMA. The resulting nonlinear dynamic equations are in a closed form and are especially suitable for advanced nonlinear control strategy synthesis. Taken as an illustrative example, a two‐link flexible manipulator is studie...

Fuzzy Modeling and Control for Conical Magnetic Bearings Using Linear Matrix Inequality

A general nonlinear model with six degree-of-freedom rotor dynamics and electromagnetic force equations for conical magnetic bearings is developed. For simplicity, a T–S (Takagi–Sugeno) fuzzy model for the nonlinear magnetic bearings assumed no rotor eccentricity is first derived, and a fuzzy control design based on the T–S fuzzy model is then proposed for the high speed and high accuracy control of the complex magnetic bearing systems. The suggested fuzzy control design approach for nonlinear magnetic bearings can be cast into a linear matrix inequality (LMI) problem via robust performance analysis, and the LMI problem can be solved efficiently using the convex optimization techniques. Computer simulations are presented for illustrating the performance of the control strategy considering simultaneous rotor rotation tracking and gap deviations regulation.

Motor-based control of manipulators with flexible joints and links

A motor-based decoupling and partial (input-output) linearization approach to the control of multilink robots with joint and link flexibilities is studied. The control strategy consists of two parts; nominal tracking control and perturbed stabilization control. The nominal tracking control derived by the differential geometric structure algorithm is an input-output decoupling and partial linearization feedback law capable of precise motor-based trajectory tracking, but the zero dynamics of the unobservable nonlinear elastic subsystem remains unstable. In order to actively suppress the elastic vibrations, a perturbation control is introduced in the vicinity of a desired trajectory. The perturbed stabilization control synthesized by the combined LQR (linear quadratic regulator) and servocompensator is used to achieve active damping of elastic vibration and robust tracking of motor dynamics. To offset the tracking errors of the end effector caused by joint and link deflections due to gravity, the quasi-static deflections can be taken into account in the trajectory planning and LQR. A two-link arm is tested by simulation.<<ETX>>

A composite adaptive control with flexible quantity feedback for flexible‐link manipulators

This article presents a mixture of joint subsystem-based adaptive control and simple flexible quantity feedback for flexible-link manipulators. The complex full flexible-arm system is composed of two severely coupling subsystems called the joint subsystem and flexible subsystem. Linear parametrization is first used to design an adaptive law for identifying the unknown parameters of a flexible manipulator based only on the joint subsystem. Joint-angle trajectory tracking can thus be achieved using the derived stable nonlinear adaptive control with the estimates of unknown parameters. To stabilize the flexible subsystem, we can simply add the feedback of transversal acceleration or deflection at the end point and/or along the flexible beam. The suggested approach is much simpler than those based on the full dynamics model of a flexible arm in required computations. Computer simulations on a single-link and a two-link flexible arm are tested to illustrate the validity of the strategy for both trajectory tracking and active damping.

Fuzzy-enhanced Adaptive Control for Flexible Drive System with Friction Using Genetic Algorithms

When a mechatronic system is in slow speed motion, serious effect of nonlinear friction plays a key role in its control design. In this paper, a stable adaptive control for drive systems including transmission flexibility and friction, based on the Lyapunov stability theory, is first proposed. For ease of design, the friction is fictitiously assumed as an unknown disturbance in the derivation of the adaptive control law. Genetic algorithms are then suggested for learning the structure and parameters of the fuzzy-enhancing strategy for the adaptive control to improve systems transient performance and robustness with respect to uncertainty. The integrated fuzzy-enhanced adaptive control is well tested via computer simulations using the new complete dynamic friction model recently suggested by Canudas de Wit et al. for modeling the real friction phenomena. Much lower critical velocity of a flexible drive system that determines systems low-speed performance bound can be obtained using the proposed hybrid control strategy.

Integrated PID-type Learning and Fuzzy Control for Flexible-joint Manipulators

The increased complexity of the dynamics of robots considering joint elasticity makes conventional model-based control strategies complex and difficult to synthesize. In this paper, a model-free control using integrated PID-type learning and fuzzy control for flexible-joint manipulators is proposed. Optimal PID gains can be learned by a neural network learning algorithm and then a simple standard fuzzy control could be incorporated in the overall control strategy, if needed, for enhancing the system responses. A modified recursive least squares algorithm is suggested for faster learning of the connection weights representing the PID-like gains. Simulation results show that the suggested simple model-free approach can control a complex flexible-joint manipulator to meet stringent requirements for both transient and steady-state performances.