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将系统误差e和误差变化率ec的范围定义为模糊集的域,输入变量和输出变量的模糊子集设置为7个级别{NB(negative big), NM(negative medium), NS(negative small), ZO(zero), PB(positive big), PM(positive medium), PS(positive small)}, 即{负大,负中,负小,零,正小,正中,正大}。在热电偶时间常数测试系统中,模糊控制器输入量和输出量的模糊论域的选择为:e∈[-3, 3];ec∈[-3, 3];Δkp∈[-3, 3];Δki∈[-1, 1];Δkd∈[-1, 1]。
根据系统和实际情况,设该系统的e和ec为:e, ec={NB, NM, NS, ZE, PS, PM, PB}; Δkp, Δki, Δkd={NB, NM, NS, ZE, PS, PM, PB}。
根据上面各个参量的模糊论域,设定以上参量的各个量化等级如下所示:e, ec={-3, -2, -1, 0, 1, 2, 3};Δkp={-3, -2, -1, 0, 1, 2, 3}。
根据以上模糊论域和各个参量的量化等级,可以得到系统输入量与输出量的隶属函数曲线。图 3表示e和ec的隶属函数曲线。图 4表示Δkp隶属函数曲线。图 5则表示Δki, Δkd的隶属函数曲线。
针对Δkp, Δki, Δkd 3个参量的整定原则和各自的特性,获得了如下3个参量的模糊控制规则表,模糊控制规则表如表 1、表 2和表 3所示。
Table 1. Fuzzy control rule table of Δkp
ec NB NM NS ZO PS PM PB e NB PB PB PM PM PS ZO ZO NM PB PB PM PS PS ZO NS NS PM PM PM PS ZO NS NS ZO PM PM PS ZO NS NM NM PS PS PS ZO NS NS NM NM PM PS ZO NS NM NM NM NB PB ZO ZO NM NM NM NB NB Table 2. Fuzzy control rule table of Δki
ec NB NM NS ZO PS PM PB e NB NB NB NM NM NS ZO ZO NM NB NB NM NS NS ZO ZO NS NB NM NS NS ZO PS PS ZO NM NM NS ZO PS PM PM PS NM NS ZO PS PS PM PB PM ZO ZO PS PS PM PB PB PB ZO ZO PS PM PM PB PB Table 3. Fuzzy control rule table of Δkd
ec NB NM NS ZO PS PM PB e NB PS NS NB NB NB NM PS NM PS NS NB NM NM NS ZO NS ZO NS NM NM NS NS ZO ZO ZO NS NS NS NS NS ZO PS ZO ZO ZO ZO ZO ZO ZO PM PB NS PS PS PS PS PB PB PB PM PM PM PS PS PB 模糊控制器中的参量调整后如下:
$ k_{\mathrm{p}}=k_{\mathrm{p}}^{\prime}+\Delta k_{\mathrm{p}} $
(1) $ k_{\mathrm{i}}=k_{\mathrm{i}}^{\prime}+\Delta k_{\mathrm{i}} $
(2) $ k_{\mathrm{d}}=k_{\mathrm{d}}^{\prime}+\Delta k_{\mathrm{d}} $
(3) 式中,kp为比例系数,ki为积分系数,kd为微分系数,kp′, ki′和kd′是系统的初始控制器参量的值,由经验法中的试凑法调节得到;而Δkp, Δki和Δkd是模糊控制器经过一系列推理得到的输出值,即PID参量的校正量。
把(1)式~(3)式求得的kp, ki和kd 3个参量代入数字PID控制表达式(4)式中,这就是控制器的输出量,经过反馈控制器计算后,使其输出相对应的脉冲宽度调制(pulse-width modulation, PWM)波控制热电偶时间常数测试系统的驱动电源模块,进而改变平均功率,这样就实现了系统的温度控制,使其在热电偶表面形成了阶跃的温度场。
$ \begin{array}{c} u(k) = {k_{\rm{p}}}{\rm{e}}(k) + {k_{\rm{i}}}\sum\limits_{j = 0}^k e (j) + \\ {k_{\rm{d}}}[e(k) - e(k - 1)] \end{array} $
(4) 式中,u(k)为PID控制器的输出,e(k)为数字PID控制器的输入,是第k个采样时刻的偏差值。
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在温度20℃、湿度59%、标准大气压的环境下,使用本文中设计的时间常数测试系统对KQXL-18U-6型热电偶进行测试。使用数据采集卡采集热电偶调理电路的电压输出,得到受激光阶跃激励后热电偶的响应曲线,与之前PID控制测得的时间常数曲线做对比,可得如图 6所示的实验结果, 实现了测试目标。
对图 6中两组曲线进行对比分析,在Topview2000信号采集软件中经过分析可以直接得到两种不同控制方法下上升时间和超调量以及该热电偶的时间常数;在经典PID控制和模糊PID控制作用下,该型热电偶时间常数测试结果如表 4所示。
Table 4. Test results of K-type thermocouple time constant
control algorithm rise rime/ms overshoot/% time constant/ms classic PID 907.8 0 446.9 fuzzy PID 570.4 1.7 421.1 通过实验结果对比,容易发现:经典PID控制下K型热电偶时间常数测试结果为446.9ms,模糊PID控制下K型热电偶时间常数测试结果为421.1ms; 实际控制中,模糊PID控制器进入稳态的时间相对经典PID控制,缩短了许多,其阶跃温度源的上升时间更短,所以使得测试结果中热电偶对于准阶跃激励的响应时间更短;可见模糊PID控制器在控制稳定性上比传统PID控制效果要好,同样是控制目标,采用模糊PID控制器来实现,不仅能够减少调节时间、提高控制稳定性,还能够减少能量损耗,相比于传统PID控制器各项其它性能也较优。使用经典PID控制器测试K型热电偶时间常数测试系统超调量为0,使用模糊控制器测试K型热电偶时间常数的超调量为1.7%;由实验结果发现,经典PID控制由于参量选择相对合理,使得其超调量近乎为0,模糊PID控制器由于其Δkp, Δkp较大,使得上升时间变得更快,但是也同时使得其产生了一定的超调量,超调量在合理范围内,可忽略不计。
模糊PID控制器因为不依赖于被控对象的精确数学模型以及不断在线对参量进行整定,使得其抗干扰性方面要优于经典PID控制器。由分析可知,模糊控制器较经典PID控制器在控制激光器出光和对热电偶加热过程中有着更为精准的控制,模糊控制器控制效果更佳,更适宜于复杂系统的控制。
基于快速激光恒温区的热电偶时间常数的测量
Measurement method of thermocouple time constant based on fast laser constant temperature zone
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摘要: 为了解决热电偶时间常数测试中阶跃温度问题, 采用模糊控制算法反馈控制激光器的输出功率, 设计了一种新的参量自适应模糊比例-积分-微分控制算法的闭环控制系统, 并进行了理论分析和实验验证, 测得某K型热电偶的时间常数为421.1ms。结果表明, 该算法能有效缩短平衡时间和增强控温系统的抗干扰能力。该结果对热电偶的校准研究是有帮助的, 具有一定的工程参考及应用价值。Abstract: In order to solve the step temperature problem during test of thermocouple time constant, fuzzy control algorithm was used to feedback control the laser output power, a new parameter adaptive fuzzy proportion-integration-differentiation control algorithm was implemented and the hardware of closed-loop control system was analyzed. The experimental results show that, the time constant data of K-type thermocouple is 421.1ms. The algorithm can effectively shorten the balance time and enhance the anti-interference ability of the temperature control system. This research is helpful for the calibration research of thermocouples, and has certain engineering reference and application value.
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Table 1. Fuzzy control rule table of Δkp
ec NB NM NS ZO PS PM PB e NB PB PB PM PM PS ZO ZO NM PB PB PM PS PS ZO NS NS PM PM PM PS ZO NS NS ZO PM PM PS ZO NS NM NM PS PS PS ZO NS NS NM NM PM PS ZO NS NM NM NM NB PB ZO ZO NM NM NM NB NB Table 2. Fuzzy control rule table of Δki
ec NB NM NS ZO PS PM PB e NB NB NB NM NM NS ZO ZO NM NB NB NM NS NS ZO ZO NS NB NM NS NS ZO PS PS ZO NM NM NS ZO PS PM PM PS NM NS ZO PS PS PM PB PM ZO ZO PS PS PM PB PB PB ZO ZO PS PM PM PB PB Table 3. Fuzzy control rule table of Δkd
ec NB NM NS ZO PS PM PB e NB PS NS NB NB NB NM PS NM PS NS NB NM NM NS ZO NS ZO NS NM NM NS NS ZO ZO ZO NS NS NS NS NS ZO PS ZO ZO ZO ZO ZO ZO ZO PM PB NS PS PS PS PS PB PB PB PM PM PM PS PS PB Table 4. Test results of K-type thermocouple time constant
control algorithm rise rime/ms overshoot/% time constant/ms classic PID 907.8 0 446.9 fuzzy PID 570.4 1.7 421.1 -
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