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This paper proposes a design method for a robust fractional-order PID (FOPID) controller for time-delay systems. A new Bode's ideal transfer function is introduced to tolerance the time-delay in loop. Robust stability is analyzed for the Bode's model in terms of gain and phase margins to help the parameter tuning. To simplify FOPID design from solving nonlinear equations, five unknown parameters are reduced to one in the Bode shaping by data fitting between a parametric model and the real plant. Then, the problem is simply solved by one-dimensional searching. Furthermore, the proposed FOPID controller design is extended to multi-input and multi-output (MIMO) systems by using disturbance observer (DOB). Finally, simulation results are presented to show the effectiveness of the proposed method.

Recently, a typical recurrent neural network termed the zeroing neural network (ZNN) with prominent properties (e.g., finite-time convergence and noise suppression) has been studied to solve the time-variant linear equation. However, these ZNN models may not perform well when being affected by harmonic noise. In this paper, for completeness, a new ZNN model that is tolerant to harmonic noise is proposed and investigated for solving the time-variant linear equation. Such a model is then theoretically analyzed to converge the computational error to zero, thereby ensuring the model convergence property. Simulation results with three examples are illustrated to further validate the efficacy of the proposed harmonic-noise-tolerance ZNN model.

An improved disturbance rejection control based on the combination of an extended-state observer (ESO) and Q-filter is presented for piezoelectric actuators. Analysis using the standard disturbance observer framework is performed to verify that the new method can improve the accuracy of disturbance estimation even under measurement noise. An advantage of the proposed method is that the bandwidth of the ESO can be reduced without the degradation of disturbance rejection performance. An experiment is performed to validate the effectiveness of the proposed method.

Recently, based on different error functions, a series of continuous-time Zhang dynamics (CTZD) models have been developed by Zhang et al to solve for time-varying square root. For completeness and also for potential digital hardware implementation, this paper further investigates the discrete-time forms of these CTZD models, which are termed as the discrete-time ZD (DTZD) algorithms. Specifically, in this paper, by utilizing the Taylor-type difference rule, different DTZD algorithms are proposed for time-varying square root finding. Then, theoretical results are provided to show the computational properties of these DTZD algorithms. Numerical results with two illustrative examples are presented to further substantiate the effectiveness of the proposed DTZD algorithms on finding time-varying square root.

Control of fractional-order systems has attracted more and more attention in many fields. Time delay is an inherent phenomenon in the real process, but the control techniques available for fractional-order system with time delay cannot guarantee the robustness and the control performance. In this paper, stabilizing and optimal PID controller tuning methods are proposed for delay fractional-order systems. The requirements on both robust stability in frequency domain and transient performance in time domain are met. Comparisons are made among four stabilizing and optimal controllers to reveal the relationship between the tuning parameters and control performance via simulation tests.

This paper deals with the disturbance rejection problem in a repetitive control system (RCS) with time-varying uncertainties. The RCS is first described in the two-dimensional (2D) form. Next, an equivalent-input-disturbance (EID)-based estimator is incorporated into the 2D RCS to solve the problem of aperiodic disturbance rejection. Under this configuration of the system, while a periodic reference input is tracked by the repetitive controller, both unknown periodic and aperiodic disturbances are compensated for by the EID estimator. A robust stability condition of the RCS is presented in the form of a linear matrix inequality, and the condition is further employed to design the parameters in the RCS. This design method enables preferential adjustment of control and learning actions. Simulations are illustrated to demonstrate the validity of this method.