Blackbody Temperature Control Based on Adaptive Double Output Function of PID Self-tuning
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摘要: 首先, 通过分析黑体温度控制系统的物理模型, 推演出黑体传递函数的表达式.推演过程中得知黑体易受环境温度和空气散热的影响, 所以黑体温度控制系统是个非线性时变系统.结合实验黑体的阶跃响应数据, 采用阶跃响应法对传递函数进行近似计算, 得出黑体温控系统的传递函数是极点在左半轴的二阶系统, 该系统等效于二阶低通滤波器.经过低通滤波器的信号, 会滤除高频部分, 当用继电器法进行参数自整定时, 仅需计算能量较大的基波信号.通过对基波信号进行比较, 得出继电器法的整定公式, 并参照Ziegler-Nichols整定法则计算出PID参数.同时, 本文针对黑体加热器具有双路输出的特点, 提出了一种双路动态输出法, 通过理论分析了该方法可以消除环境对黑体温度的影响.对于环境温度变化较大的, 采用继电器法PID参数自整定的方式来消除; 对于黑体运行过程中环境温度变化较小的, 采用双路动态输出法来减少影响.最后, 结合实验数据, 引入性能指标, 验证了本文所述方法对黑体的温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整定法则
Table 1 Ziegler-Nichols setting rule
控制器类型 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 比例积分微分模糊规则
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 阶跃响应(抗干扰)性能指标
Table 3 Step response (anti-interference) performance index
条件 IAE ITAE PV TV 综合1 (综合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 稳定精度测试(55 ℃)
Table 4 Stability accuracy testing (55 ℃)
条件 绝对误差 (℃) 绝对精度 均方差 TV 综合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 性能指标
Table 5 Performance index
条件 综合1 综合2 综合3 性能指标 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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