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
Practical performances of controller design methods strongly depend on relevancy of identified models.Fractional order system models promise advantage of more accurate modeling of real systems.This study presents a di...Practical performances of controller design methods strongly depend on relevancy of identified models.Fractional order system models promise advantage of more accurate modeling of real systems.This study presents a discussion on utilization of two fundamental numerical solution methods of fractional calculus in identification problems of One Noninteger Order Plus Time Delay with one pole(NOPTD-I)models.The identification process is carried out by estimating parameters of a NOPTD-I type transfer function template so that the step response of the NOPTD-I model can sufficiently fit experimental step response data.In the study,step responses of NOPTD-I models are numerically calculated according to two fundamental methods,which are Mittag-Leffler(ML)function and Grunwald-Letnikov(GL)definition.Particle swarm optimization(PSO)algorithm is used to perform data fitting.Illustrative examples are presented to evaluate model parameter estimation performances of these two methods for synthetically generated noisy test data.An experimental study is conducted for modeling pitch rotor of TRMS to compare experimental performances.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Practical performances of controller design methods strongly depend on relevancy of identified models.Fractional order system models promise advantage of more accurate modeling of real systems.This study presents a discussion on utilization of two fundamental numerical solution methods of fractional calculus in identification problems of One Noninteger Order Plus Time Delay with one pole(NOPTD-I)models.The identification process is carried out by estimating parameters of a NOPTD-I type transfer function template so that the step response of the NOPTD-I model can sufficiently fit experimental step response data.In the study,step responses of NOPTD-I models are numerically calculated according to two fundamental methods,which are Mittag-Leffler(ML)function and Grunwald-Letnikov(GL)definition.Particle swarm optimization(PSO)algorithm is used to perform data fitting.Illustrative examples are presented to evaluate model parameter estimation performances of these two methods for synthetically generated noisy test data.An experimental study is conducted for modeling pitch rotor of TRMS to compare experimental performances.
