Brian J. Driessen

Globally Asymptotic and Locally Exponential Tracking Observer/Controller for a Relatively Large Class of Systems with Hysteresis

In this work, we present an observer and controller for a class of plants with a relatively large class of hysteresis. For these considered classes of hysteretic systems, we propose and present an observer/controller that estimates or observes the hysteresis state and drives the position tracking error to zero. We prove that the combined tracking error and observer errors converge to zero both globally asymptotically and locally exponentially.

Tracking observer/controller for a relatively large class of systems with hysteresis and without velocity measurement

Abstract In this work, we present an observer and controller for a class of plants with a relatively large class of hysteresis and without velocity measurement. For these considered classes of hysteretic systems, we propose and present an observer/controller that estimates or observes both the hysteresis state and the velocity and drives the position tracking error to zero. We prove that the combined tracking error and observer errors converge to zero, non-globally. Additionally, in the process, we verify that the convergence in [B.J. Driessen, V.M. Duggirala, Globally asymptotic and locally exponential tracking observer/controller for a relatively large class of systems with hysteresis, Journal of Intelligent and Robotic Systems 50 (2) (2007) 207–215] is actually semi-globally exponential (here meaning: exponential on any arbitrarily large compact set, for a fixed set of gains), while [B.J. Driessen, V.M. Duggirala, Globally asymptotic and locally exponential tracking observer/controller for a relatively large class of systems with hysteresis, Journal of Intelligent and Robotic Systems 50 (2) (2007) 207–215] claimed only globally asymptotic and locally exponential. The method, in the present paper, of combining asymptotic bound relations to prove that the observer error converges to zero appears to be a new alternative to the often difficult approach of trying to find a single Lyapunov function that simultaneously covers all of the error variables.

Globally exponential continuous controller/observer for position tracking in robot manipulators with hysteretic joint friction

In this work, we present a continuous observer and continuous controller for a multiple degree of freedom robot manipulator with hysteretic joint friction. The fictitious hysteresis state is of course unknown to the controller and must be estimated. The joint velocities are assumed measured here. For this considered plant, we propose and present a continuous observer/controller that estimates or observes the hysteresis state and drives the position tracking error to zero. We prove that the combined tracking error and observer error converges to zero globally exponentially.

Globally exponential controller/observer for tracking in robots with DC motor dynamics and only link position measurement

We consider the tracking problem of a multi-degree of freedom rigid-link, revolutejointed robotic manipulator with actuator (DC brush motor) dynamics and only link position measurement. No velocities are measured; no currents are measured. The control voltage is discontinuous, however only at isolated times, not in sliding modes. We prove the time-isolation and the global-exponential convergence. This is the first global-exponential result for this plant; it is also the first global-asymptotic result for this plant.

Semi-globally Exponential Tracking Observer/Controller for Robots with Joint Hysteresis and Without Velocity Measurement

In this work, we consider a multiple degree of freedom robotic plant with joint hysteresis and without velocity measurement. We show, by construction, how a semi-globally exponential hysteresis observer/controller that assumes velocity measurement, a number of which we point out from the literature, can be combined/modified with a velocity observer to yield a combined semi-globally exponential tracking observer/controller. The resulting observer/controller estimates both the hysteresis state and the joint velocity. We prove that the combined estimation error and tracking error converges to zero semi-globally exponentially. One deemed contribution as compared to previous work for this same type of plant is that the usual requirement of velocity measurement has been removed; another is the proved semi-globally exponential result.

Overlapping-multi-layer deadzone for alleviating over conservativeness in robot adaptive tracking

Abstract We present an overlapping-multi-layer deadzone approach to the adaptive tracking control of robotic manipulators in the presence of an unknown mass matrix and completely unmodeled disturbance torques. Even in the unrealistic case of a known mass matrix, over conservative bounds on the disturbance size lead to an unnecessarily large single-level deadzone and hence an unnecessarily large asymptotic tracking error. Additionally, a single-level deadzone is not assured to prevent the “bursting” phenomenon if the mass matrix is not known. The approach we propose herein is proved to cause convergence of the generalized tracking error to within a user-specified tolerance above the level of the smallest “valid” deadzone size (times a known bound on the square root of the ratio of the largest-possible eigenvalue of the mass matrix to the smallest-possible eigenvalue of the mass matrix), even though this size is not known a priori. The result is that we obtain provable convergence to a tracking error size that is much smaller than we would have with a single-level conservative deadzone. The reason deadzones of sufficient size are needed in the first place is as follows (and this applies even if sigma-modification or e1-modification are used). Even if the mass matrix were unrealistically known, without any deadzone, the following can happen, to the best of our knowledge. We can incur indefinite cycling between (i) and (ii): (i) time periods of Lyapunov function increase, due to a parameter error increase, while the generalized tracking error remains small, (ii) time periods of Lyapunov function decrease due to large reductions in the parameter error while the generalized tracking error simultaneously increases to large peak values before returning back to a small value. With indefinite cycling between (i) and (ii), there is no convergence of the generalized tracking error to small values. This phenomenon has been termed “bursting” by authors such as [P. Ioannou, J. Sun, Robust Adaptive Control, Prentice-Hall, Englewood Cliffs, NJ, 1996.] and is described as “one of the most annoying phenomena in adaptive control.” To the best of our knowledge, this paper, once published, will represent the first presentation of an overlapping-multi-layer deadzone method for adaptive tracking control of robotic manipulators with unknown mass matrix and disturbance torque.

Global convergence for two-pulse rest-to-rest learning for single-degree-of-freedom systems with stick-slip Coulomb friction

In this paper, we consider the problem of rest-to-rest maneu-ver learning, via iterative learning control (ILC), for single-degree-of-freedom systems with stick-slip Coulomb friction and input bounds. The static coefficient of friction is allowed to be as large as three times the kinetic coefficient of friction. The input is restricted to be a two-pulse one. The desired inputs first pulse magnitude is required to be five times the largest possible kinetic (sliding) friction force. The theory therefore allows the stiction force to be as large as the desired second input pulse. Under these conditions, we prove global convergence of a simple iterative learning controller. To the best of our knowledge, such a global-convergence proof has not been presented previously in the literature for the rest-to-rest problem with stick-slip Coulomb friction.