An improved analytical tuning rule of a Proportional-Integral-Derivative (PID) controller for integrating systems with time delay is proposed using the direct synthesis method and multiple dominant pole-placement approach. Different from the traditional multiple dominant pole-placement method, the desired characteristic equation is obtained by placing the third-order dominant poles at −1/λ and placing the second-order non-dominant poles at −5/λ (λ is the tuning parameter). According to root locus theory, the third-order dominant poles and the second-order non-dominant poles are nearly symmetrically located at the two sides of the fifth-order dominant poles. This makes the third-order dominant poles closer to the imaginary axis than the fifth-order dominant poles, which means that, possibly, better performances can be achieved. Analytical formulas of a PID controller with a lead-lag filter are derived. Simple tuning rules are also given to achieve the desired robustness, which is measured by the maximum sensitivity (Ms) value. The proposed method can achieve better performances and maintain better performances when there exist parameters’ perturbation compared with other methods. Simulations for various integrating processes as well as the nonlinear continuous stirred tank reactor (CSTR) model illustrate the applicability and effectiveness of the proposed method.
Traditional walkers are commonly used for the elderly in social life, which solves the basic problem of walking, but it is difficult to ensure safety when a fall occurs, and the human-computer interaction is poor. The image recognition method or the IMU sensor method fixed on the user, such as a wearable watch, is used by most of the current fall detection methods. Wearable sensors require the user's wearing operation, which is a little troublesome, and the detection accuracy is related to the way of wearing. The image recognition method requires a high-priced camera and a fixed installation position, which is unable to adapt to outdoor activities. We investigated a low-cost method of mounting the sensor on the body of the walker. We propose in this paper an improved fall detection method, namely Precondition and Limit Threshold SPRT (PLT-SPRT), and a novel fall detection system on the smart walker based on PLT-SPRT. The signals of the upper and lower limb sensors are fused based on the Kalman filter algorithm, and the admittance control parameters are obtained through the system identification method. In this study, the improved sequential probability ratio test algorithm is used to set the null hypothesis and the alternative hypothesis, construct the likelihood ratio and optimize the decision function, which is used to judge whether falls occur. The system is simulated by Matlab software, the user intention after fusion is more accurate, and the optimized decision function is judged accurately. Verified by the embedded system based on STM32 of the smart walker equipment in the real world, it can accurately identify the fallen state, with low detection delay, and the fallen state is detected about 160ms earlier than the traditional threshold-based detection algorithm, at the same time, the accuracy is higher than 94.9%, which meets the high real-time requirements of fall detection and is the ideal solution for smart walkers.
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