King Yuan

Output tracking of a non-linear non-minimum phase PVTOL aircraft based on non-linear state feedback control

In this paper, a special class of square multi-input multi-output (MIMO) non-linear non-minimum phase systems is considered whereby the internal dynamics does not depend explicitly on the inputs. For such systems, a new output tracking control aproach is proposed and applied to a planar vertical takeoff and landing (PVTOL) aircraft. This control approach first generates input-output linearization of the original non-linear system. Then the internal dynamics is rewritten by separating its linear part from its non-linear part. Finally, a non-linear auxiliary input is introduced to stabilize the overall closed-loop system by a Lyapunov-based technique and a minimum-norm strategy. The effectiveness and excellent performance of the resulting non-linear state feedback controller are demonstrated by using the simulation results.

Noncollocated passivity-based PD control of a single-link flexible manipulator

The passivity property of a noncollocated single-link flexible manipulator with a parameterized output is studied. The system can be characterized by either the irrational transfer function of an infinite-dimensional model or its truncated rational transfer functions. Necessary and sufficient conditions for these transfer functions to be passive are found. It is also shown that a non-passive, marginal minimum-phase, truncated transfer function can be rendered passive by using either the root strain feedback or the joint angular acceleration feedback. For the noncollocated truncated passive transfer function, a PD controller suffices to stabilize the overall system. Numerical results are given to show the efficacy of the proposed approaches.

Robust nonlinear control of robotic manipulators

Abstract A robust nonlinear control strategy is proposed to deal with the control problem of robotic manipulators with second order nonlinear actuator dynamics. The control scheme is composed of two stages: the nominal dynamics stage and the perturbed dynamics stage. The control at the nominal dynamics stage and the perturbed dynamics stage. The control at the nominal dynamics stage is aimed at exact linearization and input/output decoupling of the nonlinear actuator‐manipulator system in the task space by nonlinear feedback and nonlinear state space diffeomorphic transformations. The resulting closed‐loop nominal system is capable of precise trajectory following in a desired second‐order linear behavior. To compensate uncertainties in a practical situation, an optimal error correcting compensator is designed to achieve some robustness at the perturbed dynamics stage. Simulation study of a cylindrical robot is given to illustrate the effectiveness of the proposed scheme.

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.

On the Stability of Zero Dynamics of a Single-Link Flexible Manipulator for a Class of Parametrized Outputs

In order to correct the misinterpretation which has occurred in two recent works concerning the stability of infinite-dimensional zero dynamics, the stability of zero dynamics of a noncollocated single-link flexible manipulator is considered in this article for a class of outputs containing a constant parameter. The characteristic equation governing the eigenvalues of zero dynamics is derived. The distribution of these eigenvalues on the complex plane (which depends on the values of the constant parameter) can be found analytically by using the methods of infinite product expansion and root locus. The equivalence of the eigenvalues of zero dynamics and the zeros of the transfer function is also verified.

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...

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>>

On tracking control for affine nonlinear systems by sliding mode

Abstract The stability problem of output tracking of a bounded time-varying reference by decouplable affine nonlinear systems using sliding mode control is investigated. It is shown that when the error dynamics on the sliding surface is chosen to be linear time-invariant, closed loop stability of systems under the presented sliding mode control can be guaranteed only if the systems are minimum phase.

On minimum-fuel control of affine nonlinear systems

The minimum-fuel control problem is investigated for a class of multiinput affine nonlinear systems whose associated Lie algebra is nilpotent. After preliminary notions and definitions are presented, emphasis is on the solution to the optimal control problem of the Lie algebra generated by certain system vector fields is nilpotent. Consequences of the maximum principle are deduced for such systems. >

Characterization of allowable perturbations for robust decoupling of affine non-linear systems

For affine non-linear systems, we study the effects of uncertainties in systems vector fields on decoupled linear input-output behaviour. A characterization of an allowable class of perturbations which preserve the decoupling properties of the nominal system is given. An immediate consequence of this characterization indicates that decoupling position control of rigid robotic manipulators is not robust under any perturbations in robot dynamics. The result is applied to simple hamiltonian control systems to characterize the allowable perturbation of total energy function.