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Abstract
The existing model-free adaptive control encounters problems, such as too many parameters that need to be determined, some of which with unclear physical significance and whose selection depend entirely on trial and error. Aiming at this problem, a new dynamic linearized model is established by using Taylor series expansion of discrete-time nonlinear systems and the differential mean value theorem. Then, a new data-driven model-free adaptive control is proposed, which reduces the required parameters from six in the existing model-free adaptive control to four in the new model-free adaptive control. All the parameters have clear physical significance, and the selections of the initial values of the parameters are based on the stability conditions of the closed-loop system. Therefore, the selection of the parameters in the new model-free adaptive control does not depend entirely on trial and error but on regularity. By introducing the idea of internal model control in the new model-free adaptive control, the anti-disturbance performance of the closed-loop system is enhanced. Finally, simulation results for three complicated nonlinear systems show that the proposed model-free adaptive control is superior to the existing model-free adaptive control.
Highlights
Obtaining the accurate mathematical model of actual systems is usually difficult because of their complexity [1]–[3], which limits the applications of the model-based control methods and their control performance [4]
The root mean square (RMS) and integral time absolute (ITAE) indexes of new model-free adaptive control (MFAC) as listed in Table 1 are smaller than those of the existing MFAC [5], no matter whether the unknown nonlinear system is of time-varying structure, or of non-minimum-phase
All parameters in the new MFAC have clear physical significance, and the selection of the parameters is based on the stability conditions of the closed-loop system
Summary
Obtaining the accurate mathematical model of actual systems is usually difficult because of their complexity [1]–[3], which limits the applications of the model-based control methods and their control performance [4]. Based on the compact form dynamic linearization [5], a mode-free adaptive controller is designed by using local dynamic linearization and adding a time-varying parameter to share some part of the nonlinearity that needs to be estimated online [20] These problems have not been solved completely, even though uncertainty and disturbance in the system are considered to some extent. By introducing the concept of internal model control [23], a new data-driven model-free adaptive control method is proposed This method can effectively reduce the number of controller parameters designed, and the selection of parameters is based on the stability conditions of closed-loop system, which does not depend entirely on trial and error. The simulation results show the effectiveness and superiority of the proposed method
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