The robust stability study of the classic Smith predictor-based control system for uncertain fractional-order plants with interval time delays and interval coefficients is the emphasis of this work.Interval uncertaint...The robust stability study of the classic Smith predictor-based control system for uncertain fractional-order plants with interval time delays and interval coefficients is the emphasis of this work.Interval uncertainties are a type of parametric uncertainties that cannot be avoided when modeling real-world plants.Also,in the considered Smith predictor control structure it is supposed that the controller is a fractional-order proportional integral derivative(FOPID)controller.To the best of the authors'knowledge,no method has been developed until now to analyze the robust stability of a Smith predictor based fractional-order control system in the presence of the simultaneous uncertainties in gain,time-constants,and time delay.The three primary contributions of this study are as follows:ⅰ)a set of necessary and sufficient conditions is constructed using a graphical method to examine the robust stability of a Smith predictor-based fractionalorder control system—the proposed method explicitly determines whether or not the FOPID controller can robustly stabilize the Smith predictor-based fractional-order control system;ⅱ)an auxiliary function as a robust stability testing function is presented to reduce the computational complexity of the robust stability analysis;andⅲ)two auxiliary functions are proposed to achieve the control requirements on the disturbance rejection and the noise reduction.Finally,four numerical examples and an experimental verification are presented in this study to demonstrate the efficacy and significance of the suggested technique.展开更多
Time-delayed state feedback is an easy realizable control method that generates control force by differencing the current and the delayed versions of the system states.In this paper,a new form of the time-delayed stat...Time-delayed state feedback is an easy realizable control method that generates control force by differencing the current and the delayed versions of the system states.In this paper,a new form of the time-delayed state feedback structure is introduced.Based on the proposed time-delayed state feedback method,a new robust tracking system is designed.This tracking system improves the conventional state feedback with integral action disturbance rejection characteristics in the presence of the disturbance signals imposed on the system dynamics or on the sensors that measure the system states.Also,the proposed tracking system tracks the ramp-shaped reference input signal,which is not achievable through conventional state feedback.Moreover,since the proposed method adds delays to the closed-loop system dynamics,the ordinary differential equation of the system changes to a delay differential equation with an infinite number of characteristic roots.Thus,conventional pole placement techniques cannot be used to design the time-delayed state feedback controller parameters.In this paper,the simulated annealing algorithm is used to determine the proposed control system parameters and move the unstable roots of the delay differential equation to the left half-plane.Finally,the efficiency of the proposed reference input tracker is demonstrated by presenting two numerical examples.展开更多
基金supported by the Estonian Research Council(PRG658)。
文摘The robust stability study of the classic Smith predictor-based control system for uncertain fractional-order plants with interval time delays and interval coefficients is the emphasis of this work.Interval uncertainties are a type of parametric uncertainties that cannot be avoided when modeling real-world plants.Also,in the considered Smith predictor control structure it is supposed that the controller is a fractional-order proportional integral derivative(FOPID)controller.To the best of the authors'knowledge,no method has been developed until now to analyze the robust stability of a Smith predictor based fractional-order control system in the presence of the simultaneous uncertainties in gain,time-constants,and time delay.The three primary contributions of this study are as follows:ⅰ)a set of necessary and sufficient conditions is constructed using a graphical method to examine the robust stability of a Smith predictor-based fractionalorder control system—the proposed method explicitly determines whether or not the FOPID controller can robustly stabilize the Smith predictor-based fractional-order control system;ⅱ)an auxiliary function as a robust stability testing function is presented to reduce the computational complexity of the robust stability analysis;andⅲ)two auxiliary functions are proposed to achieve the control requirements on the disturbance rejection and the noise reduction.Finally,four numerical examples and an experimental verification are presented in this study to demonstrate the efficacy and significance of the suggested technique.
文摘Time-delayed state feedback is an easy realizable control method that generates control force by differencing the current and the delayed versions of the system states.In this paper,a new form of the time-delayed state feedback structure is introduced.Based on the proposed time-delayed state feedback method,a new robust tracking system is designed.This tracking system improves the conventional state feedback with integral action disturbance rejection characteristics in the presence of the disturbance signals imposed on the system dynamics or on the sensors that measure the system states.Also,the proposed tracking system tracks the ramp-shaped reference input signal,which is not achievable through conventional state feedback.Moreover,since the proposed method adds delays to the closed-loop system dynamics,the ordinary differential equation of the system changes to a delay differential equation with an infinite number of characteristic roots.Thus,conventional pole placement techniques cannot be used to design the time-delayed state feedback controller parameters.In this paper,the simulated annealing algorithm is used to determine the proposed control system parameters and move the unstable roots of the delay differential equation to the left half-plane.Finally,the efficiency of the proposed reference input tracker is demonstrated by presenting two numerical examples.
