In this paper, a practical PI-PD controller parameter tuning method is proposed, which uses the incenter of the triangle and the Fermat point of the convex polygon to optimize the PI-PD controller. Combined with the stability boundary locus method, the PI-PD controller parameters that can ensure stability for the unstable fractional-order system with time delay are obtained. Firstly, the parameters of the inner-loop PD controller are determined by the centre coordinates of the CSR in the kd−kf plane. Secondly, a new graphical method is used to calculate the parameters of the PI controller, in which Fermat points in the CSR of (kp−ki) plane are selected. Furthermore, the method is extended to uncertain systems, and the PI-PD controller parameters are obtained by using the proposed method through common stable region of all stable regions. The proposed graphical method not only ensures the stability of the closed-loop system but also avoids the complicated optimization calculations. The superior control performance of this method is illustrated by simulation.
In order to guarantee the passivity of a kind of conservative system, the port Hamiltonian framework combined with a new energy tank is proposed in this paper. A time-varying impedance controller is designed based on this new framework. The time-varying impedance control method is an extension of conventional impedance control and overcomes the singularity problem that existed in the traditional form of energy tank. The validity of the controller designed in this paper is shown by numerical examples. The simulation results show that the proposed controller can not only eliminate the singularity problem but can also improve the control performance.
For the speed control of direct current motor, a fractional complex‐order controller (FCOC) is proposed in this paper. The FCOC is an extension of the fractional‐order controller. It is known that fractional‐order controllers exhibit strong robustness to open‐loop gain variations. However, in actual situations, due to external interference, the phase angle and gain of the system may change at the same time. The FCOC proposed in this paper adds an additional parameter, which makes the system show strong robustness when the phase angle and gain change simultaneously. Existing methods for parameter tuning of FCOCs only consider the preset gain crossover frequency and the expected phase margin. This may not allow the system to exhibit good dynamic and stable performance. In this paper, based on the frequency domain analysis, the parameters of the FCOC are tuned by integrating the gain crossover frequency, cutoff frequency, phase margin, and amplitude margin. The optimal solution satisfying a set of constraint equations is obtained by optimization algorithm. Finally, the simulation results are compared with those of the fractional‐order controller and the integer‐order controller. At the same time, the robustness of the system under disturbance is analyzed. The results show that the complex fractional‐order control presented in this paper has better dynamic performance and robustness.
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