Design of a variable gain integrator with reset

This paper studies the properties of a variable gain integrator with reset, i.e. a nonlinear lag filter that is obtained by a) saturating the input, b) filtering the saturated input with a Clegg integrator, and c) add the filtered output to the unsaturated input before applying it to a PID-based controller. Depending on the amount of saturation, the corner frequency of the lag filter is reduced along with the associated phase lag. This follows from a describing function analysis in which at low frequencies a minus 20 dB/decade amplitude decay is realized with a phase lag of only 32.48 degrees. Conditions to assess global asymptotic stability of the closed-loop nonlinear control system are provided that are based on a circle criterion-like argument for the flow condition, which applies to the intervals without resets, combined with a jump condition at reset. The reset integrator design is demonstrated on a piezo-actuated motion system where its favorable phase and amplitude properties induce overshoot and settling times comparable to a single (linear) integrator, but with the disturbance rejection properties of a double integrator

Hybrid integral reset control with application to a lens motion system

\u3cp\u3eA hybrid integral controller with reset is proposed. This hybrid controller ensures improved low-frequency disturbance rejection properties under double integrator (PI\u3csup\u3e2\u3c/sup\u3eD) control without inducing the undesired increase of overshoot otherwise resulting from adding an extra linear integrator to a PID controller. The controller is applied to an optical lens motion system that requires PID control in one operating mode and PI\u3csup\u3e2\u3c/sup\u3eD control in the other, therewith motivating a hybrid integral control strategy. The reset element in the controller is included to improve transient performance. To guarantee closed-loop stability, a conditional (and partial) reset rule is introduced that restricts the input-output behavior of the dynamic reset element, i.e., the hybrid integrator with reset, to a bounded sector. As a result, stability can be guaranteed on the basis of a circle criterion-like argument and checked by (measured) frequency response data. Stability and performance of the hybrid integral control design with conditional (and partial) reset are investigated by application to a piezo-actuated lens system that is part of an industrial wafer scanner.\u3c/p\u3

Hybrid integral reset control with application to a lens motion system

A hybrid integral controller with reset is proposed. This hybrid controller ensures improved low-frequency disturbance rejection properties under double integrator (PI2D) control without inducing the undesired increase of overshoot otherwise resulting from adding an extra linear integrator to a PID controller. The controller is applied to an optical lens motion system that requires PID control in one operating mode and PI2D control in the other, therewith motivating a hybrid integral control strategy. The reset element in the controller is included to improve transient performance. To guarantee closed-loop stability, a conditional (and partial) reset rule is introduced that restricts the input-output behavior of the dynamic reset element, i.e., the hybrid integrator with reset, to a bounded sector. As a result, stability can be guaranteed on the basis of a circle criterion-like argument and checked by (measured) frequency response data. Stability and performance of the hybrid integral control design with conditional (and partial) reset are investigated by application to a piezo-actuated lens system that is part of an industrial wafer scanner

Frequency-domain tools for stability analysis of reset control systems

\u3cp\u3eThe potential of reset controllers to improve the transient performance of linear (motion) systems has been extensively demonstrated in the literature. The design and stability analysis of these reset controllers generally rely on the availability of parametric models and on the numerical solution of linear matrix inequalities. Both these aspects may hamper the application of reset control in industrial settings. To remove these hurdles and stimulate broader application of reset control techniques in practice, we present new sufficient conditions, based on measured frequency response data of the system to be controlled, to guarantee the stability of closed-loop reset control systems. The effectiveness of these conditions is demonstrated through experiments on an industrial piezo-actuated motion system.\u3c/p\u3

Experimental evaluation of reset control for improved stage performance

\u3cp\u3eA reset integral controller is discussed that induces improved low-frequency disturbance rejection properties under double integrator control without giving the unwanted increase of overshoot otherwise resulting from adding an extra linear integrator. To guarantee closed-loop stability, a (conditional) reset condition is used that restricts the input-output behavior of the dynamic reset element to a [0,α]-sector with α a positive (finite) gain. As a result, stability can be guaranteed on the basis of a circle criterion-like argument and checked through (measured) frequency response data. Both stability and performance of the control design will be discussed via measurement results obtained from a wafer stage system of an industrial wafer scanner.\u3c/p\u3