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 recent decades, industry needs machines with higher speed and precision. Thus, an advanced industry-compatible control capable of a simultaneous increase in precision and speed is needed. Unfortunately, linear controllers, including integer and fractional order controllers, cannot satisfy this requirement of industry because of fundamental limitations such as the “water-bed" effect. In other words, precision and speed are conflicting demands in linear controllers, and designers should consider a proper trade-off between them when they tune these controllers. The reset control strategy which is one of the well-known non-linear controllers, has shown a great capacity to overcome the limitation of linear controllers. In our group, a newtype of reset compensator, which is termed “Constant in gain Lead in phase (CgLp)”, has been proposed as a potential solution for this significant challenge. Considering the first harmonic of the steady-state response of the CgLp compensator, which is called the Describing Function (DF) analysis, this compensator has a constant gain while providing a phase lead. As a result, this novel compensator can improve the precision of the control system, while simultaneously maintaining the high quality level of transient response (throughput of the system). As mentioned before, industry favours designing controllers in the frequency-domain because it provides an easy to use tool for performance analysis of control systems. Therefore, in order to interface this compensatorwell with the current control design in industry and broaden its applicability, it is important to study this type of reset compensator in the frequency-domain. So far, CgLp compensators have been studied in the frequency-domain using the DF method. However, there are some major drawbacks which have to be solved in order to make these compensators ready for industry utilization. Essentially, there is a lack of knowledge about the closed-loop steady-state performance of reset control systems. In addition, since the high order harmonics generated by CgLp compensators are neglected in the DF method, this method by itself is not an appropriate method for predicting open-loop and closed-loop steady-state performance, particularly for precision motion applications. Second, it is necessary to develop an intuitive frequency-domain stability method to assess the stability of CgLp compensators, similar to the Nyquist plot for linear controllers. Finally, to achieve a favourable dynamic performance, it is highly needed to propose a systematic frequency-domain tuning method for this type of reset compensators.