INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL Int. J. Robust. Nonlinear Control 2011; 21:1994–2008 Published online 3 December 2010 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/rnc.1674 Design of UDE-based controllers from their two-degree-of-freedom nature ‡ Qing-Chang Zhong 1,3, ∗, † , Alon Kuperman 2,3 and R. K. Stobart 1 1 Department of Aeronautical and Automotive Engineering, Loughborough University, U.K. 2 Department of Electrical Engineering and Electronics, Ariel University Center of Samaria, Israel 3 Department of Electrical Engineering and Electronics, The University of Liverpool, U.K. SUMMARY The control algorithm based on the uncertainty and disturbance estimator (UDE) is a robust control strategy and has received wide attention in recent years. In this paper, the two-degree-of-freedom nature of UDE-based controllers is revealed. The set-point tracking response is determined by the reference model, whereas the disturbance response and robustness are determined by the error feedback gain and the filter introduced to estimate the uncertainty and disturbances. It is also revealed that the error dynamics of the system is determined by two filters, of which one is determined by the error feedback gain and the other is determined by the filter introduced to estimate the uncertainty and disturbances. The design of these two filters are decoupled in the frequency domain. Moreover, after introducing the UDE-based control, the Laplace transform can be applied to some time-varying systems for analysis and design because all the time-varying parts are lumped into a signal. It has been shown that, in addition to the known advantages over the time-delay control, the UDE-based control also brings better performance than the time-delay control under the same conditions. Design examples and simulation results are given to demonstrate the findings. Copyright  2010 John Wiley & Sons, Ltd. Received 19 May 2010; Revised 22 September 2010; Accepted 8 October 2010 KEY WORDS: uncertainty and disturbance estimator (UDE); robust control; time-delay control; two- degree-of-freedom 1. INTRODUCTION The modern control theory focuses on developing various robust control algorithms to achieve good performance in tracking and disturbance rejection. For example, H ∞ control [1], genetic algorithm- based control [2], predictive control [3], adaptive control [4], sliding-mode cascaded control [5] and multirate control [6] approaches have been proposed and widely used. Quantitative feedback control [7] is another method to design robust controllers that are able to deal with parametric uncertainty in a non-conservative way while minimizing the cost of feedback. The uncertainty and disturbance estimator (UDE)-based control approach, proposed in [8] as a replacement of the time-delay control (TDC) [9], is also a promising candidate for the next generation robust control systems. ∗ Correspondence to: Qing-Chang Zhong, Department of Aeronautical and Automotive Engineering, Loughborough University, U.K. † E-mail: Q.Zhong@lboro.ac.uk ‡ A preliminary version of this paper was presented at the UKACC International Conference on CONTROL 2010, Coventry, U.K., September 2010. Copyright  2010 John Wiley & Sons, Ltd.