Blackbody Temperature Control Based on Adaptive Double Output Function of PID Self-tuning
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摘要: 首先, 通過分析黑體溫度控制系統的物理模型, 推演出黑體傳遞函數的表達式.推演過程中得知黑體易受環境溫度和空氣散熱的影響, 所以黑體溫度控制系統是個非線性時變系統.結合實驗黑體的階躍響應數據, 采用階躍響應法對傳遞函數進行近似計算, 得出黑體溫控系統的傳遞函數是極點在左半軸的二階系統, 該系統等效于二階低通濾波器.經過低通濾波器的信號, 會濾除高頻部分, 當用繼電器法進行參數自整定時, 僅需計算能量較大的基波信號.通過對基波信號進行比較, 得出繼電器法的整定公式, 并參照Ziegler-Nichols整定法則計算出PID參數.同時, 本文針對黑體加熱器具有雙路輸出的特點, 提出了一種雙路動態輸出法, 通過理論分析了該方法可以消除環境對黑體溫度的影響.對于環境溫度變化較大的, 采用繼電器法PID參數自整定的方式來消除; 對于黑體運行過程中環境溫度變化較小的, 采用雙路動態輸出法來減少影響.最后, 結合實驗數據, 引入性能指標, 驗證了本文所述方法對黑體的溫度控制性能有一定的提升.Abstract: Firstly, the expression of blackbody transfer function is deduced by analyzing the physical model of blackbody temperature control system. The blackbody temperature control system is a non-linear time-varying system. Based on the step response data of the experimental blackbody, the transfer function of the blackbody temperature control system is approximated by the step response method. It is concluded that the transfer function of the blackbody temperature control system is a second-order system with a left half axis, and the system is equivalent to a second-order low-pass filter. After low-pass filter, the high-frequency part will be filtered. When relay method is applied to parameter self-tuning, only the fundamental wave signal with large energy needs to be calculated. By comparing the fundamental wave signals, the setting formula of relay method is obtained, and the PID parameters are calculated according to Ziegler-Nichols setting rule. At the same time, aiming at the characteristics of double output of blackbody heater, a double dynamic output method is proposed, and the influence of environment on blackbody temperature can be eliminated by theoretical analysis. For the large change of ambient temperature, relay PID parameter self-tuning method can be used to eliminate; for the small change of ambient temperature during blackbody operation, dual dynamic output method can be used to reduce the impact. Finally, combined with the experimental data, the introduction of performance indicators verifies that the method described in this paper has a certain improvement in the control performance of blackbody temperature.
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Key words:
- Parameter self-tuning /
- blackbody /
- two-way dynamic /
- second-order hysteresis system /
- PID
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表 1 Ziegler-Nichols整定法則
Table 1 Ziegler-Nichols setting rule
控制器類型 Kp Tn Tv Ki Kd P 0.5· Kpcrit — — — — PD 0.8· Kpcrit — 0.12 Tcrit — Kp × Tv PI 0.45· Kpcrit 0.85 Tcrit — Kp/Tn — PID 0.6· Kpcrit 0.5 Tcrit 0.12 Tcrit Kp/Tn Kp × Tv 
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表 2 比例積分微分模糊規則
Table 2 Proportional integral differential fuzzy rule
P, I, D NB(EC) NM(EC) NS(EC) ZO(EC) PS(EC) PM(EC) PB(EC) NB(E) PB, NB, PS PB, NB, NS PM, NM, NB PM, NM, NB PS, NS, NB ZO, ZO, NM ZO, ZO, PS NM(E) PB, NB, PS PB, NB, NS PM, NM, NB PS, NS, NM PS, NS, NM ZO, ZO, NS NS, ZO, ZO NS(E) PM, NB, ZO PM, NM, NS PM, NS, NM PS, NS, NM ZO, ZO, NS NS, PS, PS NS, PS, ZO ZO(E) PM, NM, ZO PM, NM, NS PS, NS, PS ZO, ZO, NS NS, NS, NS NM, NM, NS NM, NM, ZO PS(E) PS, NM, ZO PS, NS, ZO ZO, ZO, ZO NS, PS, ZO NS, PS, ZO NM, PM, ZO NM, PB, ZO PM(E) PS, ZO, PB ZO, ZO, NS NS, PS, PS NM, PS, PS NM, PM, PS NM, PB, PS NB, PB, PB PB(E) ZO, ZO, PB ZO, ZO, PM NM, PS, PM NM, PM, PM NM, PM, PS NB, PB, PS NB, PB, PB
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表 3 階躍響應(抗干擾)性能指標
Table 3 Step response (anti-interference) performance index
條件 IAE ITAE PV TV 綜合1 (綜合2) S 1.000000 (1.000000) 1.000000 (1.000000) 1.000000 (1.000000) 1.000000 (1.000000) 1.000000 (1.000000) D 0.847483 (0.723668) 0.562693 (0.678478) 0.442698 (0.805442) 0.762998 (0.907009) 0.653968 (0.778649) SF 0.943743 (0.992518) 0.807751 (1.004470) 0.633536 (0.944839) 0.851171 (1.013720) 0.809050 (0.988887) DF 0.843329 (0.520340) 0.525302 (0.432016) 0.042592 (0.806038) 0.642354 (0.805883) 0.513394 (0.641069)
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表 4 穩定精度測試(55 ℃)
Table 4 Stability accuracy testing (55 ℃)
條件 絕對誤差 (℃) 絕對精度 均方差 TV 綜合3 S 0.003979 0.0000723455 0.00163144 1.000000 1.000000 D 0.002308 0.0000419636 0.000764468 0.846146 0.844462 SF 0.003132 0.0000569455 0.00125763 0.954824 0.953850 DF 0.002628 0.0000477818 0.000786771 0.885582 0.884021
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表 5 性能指標
Table 5 Performance index
條件 綜合1 綜合2 綜合3 性能指標 S 1.000000 1.000000 1.000000 1.000000 D 0.653968 0.778649 0.844462 0.759026 SF 0.809050 0.988887 0.953850 0.917262 DF 0.513394 0.641069 0.884021 0.679495
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