Abstract
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 are performed in the open-loop configuration which do not guarantee the existence of steady-state response of the closed-loop. If it is guaranteed, unlike linear control systems, open-loop analyses cannot precisely predict the closed-loop steady-state performance. In addition, the stability condition could not be assessed during the tuning process. These significant challenges have been separately solved in our recent works by proposing frequency-domain frameworks for analyzing the closed-loop performance and stability of reset control systems. However, they are not formulated and implemented for tuning CgLp compensators. In this paper, based on the loop-shaping approach, the recent frequency-domain framework and the frequency-domain stability method are utilized to provide a reliable frequency-domain tuning method for CgLp compensators. Finally, different performance metrics of a CgLp compensator, tuned by the proposed method, are compared with those of a PID controller on a precision positioning stage. The results show that this method is effective, and the tuned CgLp can achieve more favorable dynamic performance than the PID controller.
Highlights
Proportional Integral Derivative (PID) controllers have been used in the industry for several decades
This paper has proposed a frequency-domain tuning method for Constant in gain Lead in phase (CgLp) compensators based on the defined pseudosensitivities for reset control systems
A PID.CgLp structure was considered, and its parameters were tuned such that the pseudo-sensitivity was minimized under several loop-shaping and stability constraints
Summary
Proportional Integral Derivative (PID) controllers have been used in the industry for several decades. Considering only the first harmonic of the steady-state output of reset elements (Describing Function (DF) analysis [30]) reveals that reset elements provide less lag phase in comparison with their base linear structures Based on this phase advantage, several new phase compensators have been proposed [11], [23], [31]–[33]. The DF method cannot precisely predict the closed-loop performance even considering the open-loop high order harmonics of reset control systems [36]–[45], which results in the differences between the obtained results and the expected performance. In that work, pseudo-sensitivities for reset control systems are defined which combine high order harmonics to precisely predict the closed-loop steady-state performance of these systems.
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