Degang Chen

Nonlinear inversion-based output tracking

An inversion procedure is introduced for nonlinear systems which constructs a bounded input trajectory in the preimage of a desired output trajectory. In the case of minimum phase systems, the trajectory produced agrees with that generated by Hirschorns inverse dynamic system; however, the preimage trajectory is noncausal (rather than unstable) in the nonminimum phase case. In addition, the analysis leads to a simple geometric connection between the unstable manifold of the system zero dynamics and noncausality in the nonminimum phase case. With the addition of stabilizing feedback to the preimage trajectory, asymptotically exact output tracking is achieved. Tracking is demonstrated with a numerical example and compared to the well-known Byrnes-Isidori regulator. Rather than solving a partial differential equation to construct a regulator, the inverse is calculated using a Picard-like interaction. When preactuation is not possible, noncausal inverse trajectories can be truncated resulting in the tracking-error transients found in other control schemes.

Adaptive linearization of hybrid step motors: stability analysis

An adaptive linearization scheme for torque-ripple cancellation is presented, and the stability and robustness are established. By taking a new approach in parameterizing the motor dynamics, the number of adapted parameters is reduced by a factor of two relative to the standard approach. This parameterization and the unique periodic property of the motor enable the authors to find conditions on exogenous signals which guarantee persistency of excitation. The authors develop a robustness result which, roughly speaking, shows that the allowable model perturbation does not decrease in size as the adaptation rate is slowed. This is accomplished with a unique dual-Lyapunov-function technique. The kinds of perturbation considered include nonlinear dependence on state and parameter error. This nonlinear adaptive control scheme has been successfully implemented. Experimental results demonstrate over 30 db reduction in torque ripple. >

Nonlinear adaptive torque-ripple cancellation for step motors

The modeling of torque-ripple in hybrid step motors and its cancellation using adaptive linearization control are discussed. Although the nonlinear adaptive control of this problem can fit into a general framework, a representation of the torque-ripple which reduces the number of adapted parameters per torque-ripple harmonic by half is used. By doing so, it is possible to prove conditions on exogenous signals to guarantee the persistency of excitation of the regressor, and hence the exponential stability of the unperturbed system. It is shown that the adaptive system is robust to a class of state- and parameter-dependent modeling errors and disturbances even when the adaptation gain and convergence rate of the unperturbed system become small. The adapted parameter errors are proved to converge to a neighborhood of zero whose radius can be made small by slow adaptation. The proposed control scheme is verified in an experiment in which a 32-dB reduction in torque-ripple component at the rotor pole frequency is observed.<<ETX>>

Application of Kharitonov's theorem to mechanical systems

Kharitonovs theorem is used to derive a robust stability condition for proportional-integral-derivative (PID)-controlled multi-degree-of-freedom mechanical systems. The characteristic equation of such a system is given as a determinant of a third-order polynomial with matrix coefficients from which a scalar interval polynomial is obtained. A simple procedure for designing PID controllers for these mechanical systems is described, and a new Kharitonov-like result which states roughly that a controller designed for an upper bounding inertia matrix results in stable set-point regulation for all other inertias is proved. >

Multiloop PI/PID controller design based on Gershgorin bands

A new definition of the ultimate point is proposed for diagonally dominant, MIMO systems. Analytical formulas are developed for the new ultimate gains and ultimate frequencies based on the system frequency response and Gershgorin bands. Decentralized PI and PID controllers with set-point weighting factors can be tuned by using a modified version of the Ziegler-Nichols (ZN) relations. The proposed design method is simple and easy to implement. Two simulation examples compare the performance of the proposed multiloop design method with alternative techniques.

Stabilization of Free-Flying Under-Actuated Mechanisms in Space

Under-actuated mechanisms provide low cost automation and can overcome actuator failures. These mechanisms are particularly useful for space applications mainly because of their less weight and lower power consumption. In space under-actuation could be effectively introduced in large space structures and robot manipulators. Such mechanisms would however be difficult to control because of the fewer number of actuators in the system. In this paper, we formulate the dynamics of open chain under-actuated mechanisms in space using Hamiltons canonical equations. Next, we develop a theorem that provides us with sufficient conditions for the asymptotic stabilty of autonomous systems. We use this asymptotic stability theorem to verify the efficacy of control strategies that we develop to stabilize our under-actuated system to equilibrium manifolds. Simulation results provide support to our theoretical claims.