Abstract
This paper devotes to the robust stability problem for an uncertain linear time invariant (LTI) feedback system with actuator saturation nonlinearity. Based on a three degree of freedom (DOF) non-interfering control structure, the robust stability is enforced with the describing function (DF) approach for an uncertain LTI system to avoid the limit cycle. A new type of anti-windup (AW) compensator is designed using the quantitative feedback theory (QFT) graphical method, which results in a simple design procedure and low-order AW control system. One of the most significant benefits of the proposed method is free of the non-convexity (intractable) drawback of the linear matrix inequality (LMI)-based approach. The analysis conducted on the benchmark problem clearly reveals that the proposed QFT-based anti-windup design is able to handle both saturation and uncertainty in a very effective manner.
Highlights
Unwanted oscillatory behavior is the most common reason for instability in many applications, especially electrical circuits
The robust stability problem of uncertain linear systems with input amplitude saturation has been considered in this article
A quantitative feedback theory (QFT)-based design method is proposed for an AW controller that guarantees the robust stability of the uncertain linear time invariant (LTI) system during its nonlinear mode and avoids the problem of limit cycle using the describing function technique
Summary
Unwanted oscillatory behavior is the most common reason for instability in many applications, especially electrical circuits. A stable oscillatory motion (limit cycle) has been observed in many practical systems, for instance, in electrical circuits and systems such as buck converters [1], Chua’s circuits [2], power systems [3], bang-bang clocks and data recovery circuits [4], and Micro-electro mechanical systems (MEMS) oscillators [5]. The intense research on the limit cycle behaviors focuses on establishing their existence, investigating their stability and bifurcations analysis [2], and so on. For single-input single-output (SISO) systems, the existence problem was investigated by the well-known describing function (DF) method from the classical control techniques [6]. The actuator input saturation is the main reason for the limit cycle development
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