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...

Frequency-domain stability methods for reset control systems

Reset controllers have the potential to enhance the performance of high-precision industrial motion systems. However, similar to other non-linear controllers, the stability analysis for these controllers is complex and often requires parametric model of the system, which may hinder their applicability. In this paper a frequency-domain...

Frequency-Domain Analysis of "Constant in Gain Lead in Phase (Cglp)" Reset Compensators: Application to precision motion systems

Proportional Integral Derivative (PID) controllers dominate the industry and are used in more than 90 percent of machines in this era. One of the reason for the popularity of these controllers is the existence of easy to use frequency-domain analysis tools such as loop-shaping for this type of controller. Due to the advancement of technology in...

A Frequency-Domain Tuning Method For a Class of Reset Control Systems

Constant in gain Lead in phase (CgLp) compensators, which are a type of reset elements, have shown high potential to overcome limitations of linear control systems. There are few works which investigate the tuning of these compensators. However, there are some significant drawbacks which make those methods unreliable. First, their analyses...

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...

A Frequency-Domain Stability Method for Reset Systems

The potential of reset controllers to enhance the performance of control systems has been extensively demonstrated in the literature. However, similarly to other non-linear controllers, the stability analysis for these controllers is complex and relies on parametric models of the systems which may hinder the applicability of these controllers...

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...

Linear fractional order controllers: A survey in the frequency domain

Today, there is a great tendency toward using fractional calculus to solve engineering problems. The control is one of the fields in which fractional calculus has attracted a lot of attention. On the one hand, fractional order dynamic models simulate characteristics of real dynamic systems better than integer order models. On the other hand,...

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...