This paper presents a novel fractional-order PID controller tuning strategy based on Bode’s optimal loop shaping which is commonly used for LTI feedback systems. Firstly, the controller parameters are achieved based on flat phase property and Bode’s optimal reference model, so that the controlled system is robust to gain variations and can achieve desirable transient performance according to various control requirements. Then, robustness analysis of the controlled system is carried out to support the results. Furthermore, the parameter setting is analyzed (...) to demonstrate the superiority of the proposed controller. At last, some simulation examples are shown to verify the accuracy and usefulness of the proposed control strategy. The proposed fractional-order PID controller does not have any restriction on the controlled plant, so it can be widely applied on both integer-order and fractional-order systems. (shrink)

This paper is concerned with the target tracking problem of an autonomous surface vehicle in the presence of a maneuvering target. The velocity information of target is totally unknown to the follower vehicle, and only the relative distance and angle between the target and follower are obtained. First, a reduced-order extended state observer is used to estimate the unknown relative dynamics due to the unavailable velocity of the target. Based on the reduced-order extended state observer, an antidisturbance guidance law for (...) target tracking is designed. The input-to-state stability of the closed-loop target tracking guidance system is analyzed via cascade theory. Furthermore, the above result is extended to the case that collisions between the target and leader are avoided during tracking, and a collision-free target tracking guidance law is developed. The main feature of the proposed guidance law is twofold. First, the target tracking can be achieved without using the velocity information of the target. Second, collision avoidance can be achieved during target tracking. Simulation results show the effectiveness of the proposed antidisturbance guidance law for tracking a maneuvering target with the arbitrary bounded velocity. (shrink)

In this paper, a normalized robust FOPID controller regulation algorithm is proposed. Only one parameter k is necessary to be tuned in the controller regulation process, so the proposed control algorithm is convenient to be applied on both fractional-order systems and integer-order systems. A robustness evaluation function is constructed based on the small gain theorem. Larger robustness evaluation function value will help the system achieve better robustness performance. Another parameter, β, is also available to serve as a tuning knob when (...) larger robust evaluation function value is needed. Therefore, the controlled systems can be stabilized and can achieve quite satisfactory robust control performance using the proposed algorithm. The corresponding robust analysis results are obtained according to different conditions in the discussion. For a special case of widely used fractional-order systems, the FOPI and FOID controllers are presented based on the same tuning scheme together with their robustness discussion. Some examples are shown to verify the robustness of systems controlled by the proposed algorithm. (shrink)

Epidemiological studies have confirmed that long-term exposure to road traffic noise can cause cardiovascular diseases, and when noise exposure reaches a certain level, the risk of related CDs significantly increases. Currently, a large number of Chinese residents are exposed to high noise exposure, which could greatly increase the risk of cardiovascular disease. On the other hand, relevant studies have found that people with high noise sensitivity are more susceptible to noise. And it is necessary to pay more attention to the (...) high noise-sensitive people. This study investigated the acute physiological effect of different noise-sensitive groups by indoor-level noise stimulus experiments under laboratory conditions, by observing heart rate variability indicators, including standard deviation of NN intervals, low frequency/high frequency, and heart rate. The results showed that there was no significant difference in HRV between the high-sensitive group and the low-sensitive group at the physiological baseline and the different stimulating noise levels. Then, based on the theory of cumulative effect of noise proposed by WHO Regional Office for Europe, non-significant but observable differences between groups were further discussed. By analyzing differences of the variation trends and the within-group significant changes of SDNN and HR between the two groups, the results tended to show that the high-sensitive group is more affected by road traffic noise. In addition, the values of SDNN and HR showed observable between-group differences at 55 dB and 65 dB which corresponding to the SPL associated with a significantly increased risk of cardiovascular disease concerned by epidemiological studies. According to the cumulative effect theory, these differences in HRV caused by short-term noise stimulation may have the potential to produce physiological response and lead to between-groups differences in prevalence after long-term recurrent effect, and deserve attention and further research. (shrink)

The thin set theorem for n-tuples and k colors states that every k-coloring of $[\mathbb {N}]^n$ admits an infinite set of integers H such that $[H]^n$ avoids at least one color. In this paper, we study the combinatorial weakness of the thin set theorem in reverse mathematics by proving neither $\operatorname {\mathrm {\sf {TS}}}^n_k$, nor the free set theorem imply the Erdős–Moser theorem whenever k is sufficiently large. Given a problem $\mathsf {P}$, a computable instance of $\mathsf {P}$ is universal (...) iff its solution computes a solution of any other computable $\mathsf {P}$ -instance. It has been established that most of Ramsey-type problems do not have a universal instance, but the case of Erdős–Moser theorem remained open so far. We prove that Erdős–Moser theorem does not admit a universal instance. (shrink)