Document Type : Research article


1 Faculty of Electrical and Computer Engineering, Babol Noshirvani University of Technology, Babol 47148 - 71167, Iran

2 Research Fellow in Autonomous Vehicles, Department of Mechanical Engineering Science, University of Surrey, Guildford, GU2 7XH, UK


This work represents a new method for robustness analysis of the model reference adaptive controller (MRAC) in the presence of input saturation. Saturation is one of the nonlinear factors affecting the stability of control systems which must be considered in controller design and stability analysis experiments. Various methods are presented for the stability and robustness analysis of adaptive control systems, and employment of describing function (DF) can be attractive and practical, due to the appropriate effectiveness of DF in estimating limit cycles and also the application of quasi-linearization theory. In this work, the stability analysis and a limit cycle estimation of a saturated system in the frequency domain is performed. The controller parameters are adjusted in a way that the system achieves its stable limit cycle in the presence of the initial conditions for the states. Moreover, the efficiency of the proposed method for second-order systems is reported in the presence of symmetric saturation and uncertainty model in Rohrs counterexample as the unmodeled dynamics. The results demonstrate the proposed method provides a proper analysis of system stability during the changes in the control parameters and the saturation amplitude.


  • The describing function (DF) technique for the first time is proposed to analyze the MRAC with input saturation.
  • The main objective is to propose a tool to estimate the system’s limit cycle and determine the approximate initial conditions for the adaptive system with nonlinearity
  • The frequency analysis and simulation in the time domain of a second-order system represent the appropriate accuracy of the proposed method in estimating the limit cycle


Main Subjects