Shaping Nonlinearity in Reset Control Systems to Realize Complex-Order Controllers: Application in Precision Motion Control

This dissertation addresses the demand for faster, more precise, and robust controllers in the precision motion industry. Traditional linear controllers have limitations due to the waterbed effect and Bode’s phase-gain relationship. To overcome these limitations, complex-order controllers are explored in this study. The dissertation focuses on...

Closed-Loop Frequency Analysis of Reset Control Systems

This article introduces a closed-loop frequency analysis tool for reset control systems. To begin with sufficient conditions for the existence of the steady-state response for a closed-loop system with a reset element and driven by periodic references are provided. It is then shown that, under specific conditions, such a steady-state response...

Band-Passing Nonlinearity in Reset Elements

This article addresses nonlinearity in reset elements and its effects. Reset elements are known for having less phase lag based on describing function (DF) analysis compared to their linear counterparts; however, they are nonlinear elements and produce higher-order harmonics. This article investigates the steady-state higher-order harmonics for...

Continuous reset element: Transient and steady-state analysis for precision motion systems

This paper addresses the main goal of using reset control in precision motion control systems, breaking of the well-known “Waterbed effect”. A new architecture for reset elements will be introduced which has a continuous output signal as opposed to conventional reset elements. A steady-state precision study is presented, showing the steady...

Complex-order Reset Control System

According to the well-known loop shaping method for the design of controllers, the performance of the controllers in terms of step response, steady-state disturbance rejection and noise attenuation and robustness can be improved by increasing the gain at lower frequencies and decreasing it at higher frequencies and increasing the phase margin as...

Stacking Integrators Without Sacrificing the Overshoot in Reset Control Systems

According to the well-known loop-shaping control design approach, the steady-state precision of control systems can be improved by stacking integrators. However, due to the waterbed effect in linear control systems, such an action will worsen the transient response by increasing overshoot and creating wind-up problems. This paper presents a new...

Fractional-order single state reset element

This paper proposes a fractional-order reset element whose architecture allows for the suppression of nonlinear effects for a range of frequencies. Suppressing the nonlinear effects of a reset element for the desired frequency range while maintaining it for the rest is beneficial, especially when it is used in the framework of a “Constant in...

Augmented fractional-order reset control: Application in precision mechatronics

Linear control such as PID possesses fundamental limitations, seen through the Waterbed effect. Reset control has been found to be able to overcome these limitations, while still maintaining the simplicity and ease of use of PID control due to its compatibility with the loop shaping method. However, the resetting action also gives rise to...

Tuning of CgLp based reset controllers: Application in precision positioning systems

This paper presents the tuning of a reset-based element called “Constant in gain and Lead in phase” (CgLp) in order to achieve desired precision performance in tracking and steady state. CgLp has been recently introduced to overcome the inherent linear control limitation - the waterbed effect. The analysis of reset controllers including ones...

Benefiting from linear behaviour of a nonlinear reset-based element at certain frequencies

This paper addresses a phenomenon caused by resetting only one of the two states of a so-called second order 'Constant in gain Lead in phase' (CgLp) element. CgLp is a recently introduced reset-based nonlinear element, bound to circumvent the well-known linear control limitation - the waterbed effect. The ideal behaviour of such a filter in...

Reset control approximates complex order transfer functions

A controller with the frequency response of a complex order derivative may have a gain that decreases with frequency, while the phase increases. This behaviour may be desirable to ensure simultaneous rejection of high-frequency noise and robustness to variations of the open-loop gain. Implementations of such complex order controllers found in...