Proportional-Integral-Derivative control system has been widely used in industrial applications.For uncertain and unstable systems,tuning controller parameters to satisfy the process requirements is very challenging.I...Proportional-Integral-Derivative control system has been widely used in industrial applications.For uncertain and unstable systems,tuning controller parameters to satisfy the process requirements is very challenging.In general,the whole system’s performance strongly depends on the controller’s efficiency and hence the tuning process plays a key role in the system’s response.This paper presents a robust optimal Proportional-Integral-Derivative controller design methodology for the control of unstable delay system with parametric uncertainty using a combination of Kharitonov theorem and genetic algorithm optimization based approaches.In this study,the Generalized Kharitonov Theorem(GKT)for quasi-polynomials is employed for the purpose of designing a robust controller that can simultaneously stabilize a given unstable second-order interval plant family with time delay.Using a constructive procedure based on the Hermite-Biehler theorem,we obtain all the Proportional-Integral-Derivative gains that stabilize the uncertain and unstable second-order delay system.Genetic Algorithms(GAs)are utilized to optimize the three parameters of the PID controllers and the three parameters of the system which provide the best control that makes the system robust stable under uncertainties.Specifically,the method uses genetic algorithms to determine the optimum parameters by minimizing the integral of time-weighted absolute error ITAE,the Integral-Square-Error ISE,the integral of absolute error IAE and the integral of time-weighted Square-Error ITSE.The validity and relatively effortless application of presented theoretical concepts are demonstrated through a computation and simulation example.展开更多
In this paper, it is shown that for low-order uncertain systems, there is no need to calculate all the minimum and maximum values of the coefficients for a perturbed system which is expressed in terms of polynomials a...In this paper, it is shown that for low-order uncertain systems, there is no need to calculate all the minimum and maximum values of the coefficients for a perturbed system which is expressed in terms of polynomials and hence no need to formulate and test all the four Kharitonov＇s polynomials. Furthermore, for higher-order systems such as n ≥ 5, the usual four Kharitonov＇s polynomials need not be tested initially for sufficient condition of perturbed systems; rather, the necessary condition can be checked before going for sufficient condition. In order to show the effectiveness of the proposed method, numerical examples are shown and computational efficiency is highlighted.展开更多
Complex polynomials are of significance in engineering applications.This paper addresses the robust stability of such polynomials.We first system-atically discuss the alternative pair of polynomials and obtain some fu...Complex polynomials are of significance in engineering applications.This paper addresses the robust stability of such polynomials.We first system-atically discuss the alternative pair of polynomials and obtain some fundamentalresults.The geometric characterizations of the family of stable complex polyno-mials are investigated.Some connections with Sturm chains and conditions for theconvex combination of polynomials to be aperiodic are established.展开更多
In this paper, an analytical technique is presented for time domain analysis （transient and steady-state response） of perturbed PWM push-pull DC-DC converter using interesting corollary on Kharitonov＇s theorem. The...In this paper, an analytical technique is presented for time domain analysis （transient and steady-state response） of perturbed PWM push-pull DC-DC converter using interesting corollary on Kharitonov＇s theorem. The main advantage of the proposed analysis is that even though the transfer function model of a PWM push-pull DC-DC converter is perturbed, the complete analysis has been done on a linear transfer function model of a PWM push-pull DC-DC converter. The proposed analysis is verified using MATLAB simulation. This analysis will be very much useful to power electronics engineers, since the technique is very simple and computationally efficient and easily applicable in precise applications such as aerospace applications.展开更多
文摘Proportional-Integral-Derivative control system has been widely used in industrial applications.For uncertain and unstable systems,tuning controller parameters to satisfy the process requirements is very challenging.In general,the whole system’s performance strongly depends on the controller’s efficiency and hence the tuning process plays a key role in the system’s response.This paper presents a robust optimal Proportional-Integral-Derivative controller design methodology for the control of unstable delay system with parametric uncertainty using a combination of Kharitonov theorem and genetic algorithm optimization based approaches.In this study,the Generalized Kharitonov Theorem(GKT)for quasi-polynomials is employed for the purpose of designing a robust controller that can simultaneously stabilize a given unstable second-order interval plant family with time delay.Using a constructive procedure based on the Hermite-Biehler theorem,we obtain all the Proportional-Integral-Derivative gains that stabilize the uncertain and unstable second-order delay system.Genetic Algorithms(GAs)are utilized to optimize the three parameters of the PID controllers and the three parameters of the system which provide the best control that makes the system robust stable under uncertainties.Specifically,the method uses genetic algorithms to determine the optimum parameters by minimizing the integral of time-weighted absolute error ITAE,the Integral-Square-Error ISE,the integral of absolute error IAE and the integral of time-weighted Square-Error ITSE.The validity and relatively effortless application of presented theoretical concepts are demonstrated through a computation and simulation example.
文摘In this paper, it is shown that for low-order uncertain systems, there is no need to calculate all the minimum and maximum values of the coefficients for a perturbed system which is expressed in terms of polynomials and hence no need to formulate and test all the four Kharitonov＇s polynomials. Furthermore, for higher-order systems such as n ≥ 5, the usual four Kharitonov＇s polynomials need not be tested initially for sufficient condition of perturbed systems; rather, the necessary condition can be checked before going for sufficient condition. In order to show the effectiveness of the proposed method, numerical examples are shown and computational efficiency is highlighted.
基金A project supported by the National Natural Science Foundation of China
文摘Complex polynomials are of significance in engineering applications.This paper addresses the robust stability of such polynomials.We first system-atically discuss the alternative pair of polynomials and obtain some fundamentalresults.The geometric characterizations of the family of stable complex polyno-mials are investigated.Some connections with Sturm chains and conditions for theconvex combination of polynomials to be aperiodic are established.
文摘In this paper, an analytical technique is presented for time domain analysis （transient and steady-state response） of perturbed PWM push-pull DC-DC converter using interesting corollary on Kharitonov＇s theorem. The main advantage of the proposed analysis is that even though the transfer function model of a PWM push-pull DC-DC converter is perturbed, the complete analysis has been done on a linear transfer function model of a PWM push-pull DC-DC converter. The proposed analysis is verified using MATLAB simulation. This analysis will be very much useful to power electronics engineers, since the technique is very simple and computationally efficient and easily applicable in precise applications such as aerospace applications.
