Stability of Phase-Based Gain Modulation with Designer-Chosen Switch Functions

Abstract

Phase-Based Gain-Modulation (PBGM) control is realized by modulating controller gains in response to the phase of the system state or tracking error. PBGM controllers have been applied to robotic hands, parallel manipulators and flexible mechanisms to give increased damping, reduced tracking error and friction compensation.A novel method is presented to establish Lyapunov stability for PBGM control. Prior PBGM stability results incorporated a constraint which limited the range of provably stable systems. The present result removes this constraint, establishing Lyapunov stability for a substantially broader class of systems. Additionally, the new approach decouples the selection of the Lyapunov function from the controller design, permitting the controls designer to independently specify a switch function which determines the application of gain modulation.The present results are applied to analyze PBGM control of the Sarcos dextrous manipulator, illuminating the stability properties of control experiments previously reported in the literature. Numerical methods for design calculations are also presented.

Self-tuning of a switching controller for scanning motion systems

“…The experimental results (right part) are obtained under realistic scanning set-points, feedforward control design, and disturbances and yield error responses in the same order of magnitude as in the simulations. 1 This is in favor of the choice in (46). Nevertheless, the results obtained from simulation cannot be compared directly with the results obtained from measurement.…”

“…Given the linear feedback design with plant P and nominal (linear) controller C fb , the nonlinear (switching) controller consists of loop-shaping filters F 1 with inputũ, weighting filters F 2 with inputỹ, and switching function y´/(y) with input y and output u(y) = À/(y)y, see also (1). The plant output z, disturbances d, and reference r form the inputỹ viaỹ ¼ r þ dÀ z.…”

“…Small inputs that remain inside the deadzone length induce no extra gain and thus yield a favorable low-gain noise response. See for example [1] for an overview on both magnitude and phase-based switching functions.…”

Performance optimization of piecewise affine variable-gain controllers for linear motion systems

“…To balance this trade-off in a more desirable manner, it has been shown that variable-gain control (also called N-PID control) can be effective [6][7][8][9][10][11][12]. In these references, it has been shown that the variable-gain controllers have the capability of outperforming linear controllers.…”

Improved noise sensitivity under high-gain feedback in nano-positioning motion systems

“…In N-PID control, see also [4], [5], [6], the controller gain is adapted according to the (estimated) servo signals at hand. This generally gives more flexibility in dealing with position-dependent disturbances but the problem of noise amplification under high-gain feedback remains.…”