【正文】 s two levels of The scaling gains (Ke, Kd, K0, and K1) are at the lower level. The tuning of these scaling gains will affect the gains of fuzzy PID The fuzzy PID control actually has two levels of The scaling gains (Ke, Kd, K0, and K1) are at the lower level. The tuning of these scaling gains will affect the gains of fuzzy PID controllers, resulting in the changing of the control performance. As the control actions are fuzzily coupled, the contribution of each Ke, Kd, K0, and K1 to different control actions is still not very clear, which makes the practical design and tuning process rather difficult. 3 Tuning Fuzzy PID Based on the IMC To tune the fuzzy PID controller based on the IMC method,an analytical model of the fuzzy PID controller is obtained first by simple derivation. Then, the parameters of the fuzzy PID controller can be determined on the basis of the IMC principle. Suppose that an industrial process can be modeled by a first order plus delay time (FOPDT) structure that has the transfer function as follows: ? ? LST KP ??? e1ss~ (7) where K, T, and L are the steadystate gain, the time constant, and the time delay, respectively. The estimation of these parameters using the step response method, frequency response, and closedloop relay feedback, etc., is welldescribed. The FOPDT model is one of the most mon and adequate ones used, especially in the process control One obtains from(6): ? ? ???????? ??? 10 1 KpKsABU P ID ? （ 8） ? ? ? ? ? ?sususU NP IDP ID ?? （ 9） ? ? ? ?ssABKsu N ?? ?????? ?? 10 （ 10） with δ(s) being a nonlinear term without an explicit analytical expression. Obviously, the fuzzy PID control can be considered as a conventional PID with a nonlinear pensation. The conventional PID control term is uPID(s) and the nonlinear pensation is uN(s). 11 Tuning of Fuzzy PID Controller Based on IMC. If we consider the nonlinear pensation uN as a process disturbance and set Gf(s) )=CIMC(s), which is shown in Figure 3, the IMCbased tuning for fuzzy PID controllers can be simplified as follows. By the firstorder Pade180。 otherwise, it gives a low bandwidthand sluggish response. To improve the rise time, the value of R should be small. Therefore, the two parameters ? and? can be determined. Remark: The fuzzyPID control (11) is actually a conventional PID control uPID plus a pseudosliding mode control δ. Because the sliding mode control is a robust control, the fuzzy PID control is more robust than a conventional PID control. 4 Control Simulations In this section, the control performance of fuzzy PID tuned by the proposed method is pared with that of conventional PID control. Quantitative criteria for measuring the performance are chosen as IAE and ITAE. Smaller numbers imply better performance. dtetdte ?? ?? IT AEIE A ， (14) In all control simulations, parameters of conventional PID control are determined by IMCbased method and the parameters of fuzzy PID control are determined by the proposed tuning method. Example an industrial process that is approximately described by a firstorder rational transfer function model with a delay time as follows: ? ? 1s ???P (15) The linear part is the dominant process. The small delay time implies weak nonlinear features. As shown in Figure 5, little difference is observed between the conventional PID control and fuzzy PID control due to the small delay time. However, when the delay time is increased to L=, there will be large model error caused by approximating the delay time with a firstorder Pade180。 Elsevier: Amsterdam, The Netherlands, 1985. (2) Manel, A.。 Jordi, A.。 Sheikhzadeh, M.。 Hu, B. G.。 Gatland, H. Conventional Fuzzy Logic Control and Its Enhancement. IEEE Trans. Syst., Man, Cyberics 1996, 26 (10), 791–797. (7) Gee, K. I. M.。 Raymond, G. G. TwoLevel Tuning of Fuzzy PID Cotrollers. IEEE Trans. Syst., Man, Cyberics, Part B 2020, 31 (2), 263–269. (8) Woo, Z. W.。 Lin, J. J. A PID Type Fuzzy Controller with SelfTuning Scaling Factors. Fuzzy Sets Syst. 2020, 115, 321–326. (9) Vega, P.。 Aleixander, V. SelfTuning Predictive PID Controller. IEE Pro. D 1991, 138 (3), 303–311. (10) Rajani, K. M.。 Nikhil, R. P. A SelfTuning Fuzzy PI Controller. Fuzzy Sets Syst. 2020, 115, 327–338. (12) Yesil, E.。 Eksin, I. Self Tuning Fuzzy PID Type Load and Frequency Controller. Energy ConVers. Manage. 2020, 45, 377–390. (13) Xu, J. X.。 Liu, C.。 Hang, C. C.。 Kiam, H. A.。 Chun, D. W.。 Gatland, H. B.。s Shaanxi province pass through a stop on the ancient Silk Road, Gansu39。80s. We sat on the back of pickup trucks for hours. The sky was blue, and we couldn39。t have a formal stage. The audience just sat on the grass. Usually, the performances became a big party with local people joining in. For him, the rewarding part about touring isn39。s performers of the troupe still tour the region39。s Poly Theater. Their show, titled Ulan Muqir on the Grassland, depicted the history and development of the art troupe. Being from the region allowed me to embrace the culture of Inner Mongolia and being a member of the troupe showed me where I belonged, Nasun, the art troupe39。s Liaoning province, decades ago. The solider gave the old man a handmade saddle when they bid farewell. The story inspired Nasun to write Carved Saddle, a song that later became one of his most popular numbers. Now, every year, Nasun recruits young singers and dancers for the troupe. The troupe has also designed a new repertoire, which is mostly based on the daily lives of Mongolian people, especially the lives of nomadic families, and has bined contemporary musical elements with folk songs of the region. Haimu, a 25yearold kho