Describing function

About: Describing function is a research topic. Over the lifetime, 1742 publications have been published within this topic receiving 26702 citations.

Design and Modeling of Anti Wind Up PID Controllers

Abstract: In this chapter several anti windup control strategies for SISO and MIMO systems are proposed to diminish or eliminate the unwanted effects produced by this phenomena, when it occurs in PI or PID controllers. Windup is a phenomena found in PI and PID controllers due to the increase in the integral action when the input of the system is saturated according to the actuator limits. As it is known, the actuators have physical limits, for this reason, the input of the controller must be saturated in order to avoid damages. When a PI or PID controller saturates, the integral part of the controller increases its magnitude producing performance deterioration or even instability. In this chapter several anti windup controllers are proposed to eliminate the effects yielded by this phenomena. The first part of the chapter is devoted to explain classical anti windup architectures implemented in SISO and MIMO systems. Then in the second part of the chapter, the development of an anti windup controller for SISO systems is shown based on the approximation of the saturation model. The derivation of PID SISO (single input single output) anti windup controllers for continuous and discrete time systems is implemented adding an anti windup compensator in the feedback loop, so the unwanted effects are eliminated and the system performance is improved. Some illustrative examples are shown to test and compare the performance of the proposed techniques. In the third part of this chapter, the derivation of a suitable anti windup PID control architecture is shown for MIMO (multiple input multiple output) continuous and discrete time systems. These strategies consist in finding the controller parameters by static output feedback (SOF) solving the necessary linear matrix inequalities (LMI’s) by an appropriate anti windup control scheme. In order to obtain the control gains and parameters, the saturation is modeled with describing functions for the continuous time case and a suitable model to deal with this nonlinearity in the discrete time case. Finally a discussion and conclusions sections are shown in this chapter to analyze the advantages and other characteristics of the proposed control algorithms explained in this work.

Observer-Based Control of LLC DC/DC Resonant Converter Using Extended Describing Functions

Abstract: This paper presents theoretical and practical results about dynamic analysis, frequency response, and control of a LLC resonant dc/dc converter operating under wide input voltage and load variations. A nonlinear model for the LLC resonant converter was developed using the extended describing function method; then, based on the derived model, a nonlinear observer-based controller was designed and implemented with a digital signal processor. Transient responses obtained under input voltage and output load variations show that the proposed controller is capable to stabilize the output effectively. Experimental results prove the superiority of the proposed observer-based controller over a conventional PID controller.

Justification of the Describing Function Method

Abstract: Explicit conditions are given under which the use of the describing function method to investigate the nature of oscillations in autonomous nonlinear feedback systems is justified. When these conditions are satisfied, bounds are given for the frequency, fundamental magnitude, and higher harmonics of the oscillation based on the describing function approximation.The feedback systems considered are those which can be decomposed into a linear time-invariant subsystem, not necessarily causal, stable, or finite-dimensional, and a nonlinear frequency independent subsystem, possibly containing hysteresis.The approach taken is to consider the describing function equation as an approximation to a determining equation for periodic solutions of the autonomous system’s operator equation, and to use local degree theory to guarantee the existence of a solution to the determining equation.

High-Bandwidth Secondary Voltage and Frequency Control of VSC-Based AC Microgrid

Abstract: This paper proposes a novel secondary control strategy for the power-electronic-based ac microgrid. This approach restores the voltage and frequency deviations by utilizing only local variables with very high bandwidth. This is realized with a finite control set model predictive control technique that is adopted in the inner level of the primary control of voltage source converters. In the outer level of the primary control, droop control and virtual impedance loops are exploited to adjust the power sharing among different distributed generation (DGs). As inner control level operates with a very high bandwidth, need for filtering of the calculated active and reactive powers in the outer level of the primary control is insignificant. Therefore, the secondary control can be operated with a far superior bandwidth compared to the case when the conventional cascaded linear control is used. Merits of the proposed approach are investigated analytically with the help of the describing function methodology that allows the quasi-linear approximation of the inner control level. Finally, simulation and experimental results are presented.