CN102621882A - 基于前馈-模糊pid控制的切纸机控制方法 - Google Patents
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Abstract
本发明涉及一种基于前馈-模糊PID控制的切纸机控制方法,系统初始化后,设定切纸长度和切刀频率,在单闭环控制加比值控制系统控制下,进行切纸,在切至完成后,停机;在原有单闭环控制加比值控制切刀速度的基础上,采用模糊PID控制来对送纸辊速度V进行控制,以提高系统的动态响应和稳态特性;即应用模糊控制方式,在PID调节器上加入模糊控制器,该模糊控制器的输入语言变量是误差值E、误差变化率ΔE,输出语言变量是PID控制器的比例增益系数KP、积分增益系数KI和微分增益系数KD,从而对PID调节器进行控制;同时在执行机构后方设置前馈控制器,解决因负载扰动所引起的送纸辊速度V的波动,同时也减小了切刀转速n的波动。
Description
技术领域
本发明涉及一种基于前馈-模糊PID控制的切纸机控制方法。
背景技术
现场圆筒切刀式切纸机的主要结构如图1所示,由退纸辊1、纵向切刀2、第一送纸辊3、第一横向切刀4、第二送纸辊5、第二横向切刀6、导纸辊7、张力传感器8等组成。工作时首先原纸从退纸辊1上的纸卷出来后,经过纵向切刀2将宽幅纸裁切成满足要求的2条或者几条窄幅纸,然后通过第一送纸辊3向前传送,其中1条纸带直接送到第一横向切刀4,另1条纸带继续向前通过第二送纸辊5送到第二横向切刀6,然后将纸横切成合乎要求的纸张,最后通过传送带送到接纸台打包。纵向切刀的位置可以改变以调整纸带的宽度,它不需要进行速度控制。两送纸辊的速度根据设计的要求进行调节,两横向切刀的速度由切纸长度和送纸速度决定。两横向切刀旋转1周切纸1次,当改变切纸长度或送纸速度,或者两者同时改变时,切刀的速度必须同时做出相应的改变。因此,对切刀速度的同步控制决定了切纸精度。
原切纸机控制系统采用的控制方式为:单闭环控制加比值控制,如图2所示,原系统缺点如下:
1.采用传统的PID调节器,送纸辊线速度V抗扰能力较差,参数修改不方便,不能进行自整定等缺点。
2.切刀控制以送纸辊实际速度V作为设定值,采用比值控制。由于外界扰动存在,送纸辊线速度V容易变化,因此切刀控制属于随动控制系统,并且切刀转速n具有一定的滞后性,所以很难保证切长L的精度。
发明内容
本发明的目的就是为解决上述问题,提供一种基于前馈-模糊PID控制的切纸机控制方法,它通过前馈控制能够大大抵消外界扰动,获得良好的控制效果。
为实现上述目的,本发明采用如下技术方案:
一种基于前馈-模糊PID控制的切纸机控制方法,系统初始化后,设定切纸长度和切刀频率,在单闭环控制加比值控制系统控制下,进行切纸,在切纸完成后,停机;
1.在原有单闭环控制加比值控制切刀速度的基础上,采用模糊PID控制来对送纸辊速度V进行控制,提高系统的动态响应和稳态特性,即应用模糊控制规则,在PID调节器上加入模糊控制器,该模糊控制器的输入语言变量是误差值E、误差变化率ΔE,输出语言变量是PID控制器的比例增益系数KP、积分增益系数KI和微分增益系数KD,从而对PID调节器进行控制;
2.模糊控制具体计算:前面所述误差E、误差变化率ΔE、比例增益系数KP、积分增益系数KI和微分增益系数KD的模糊集为:{NB,NM,NS,ZR,PS,PM,PB},NB表示负大,NM表示负中,NS表示负小,ZR表示零,PS表示正小,PM表示正中,PB表示正大,它们的论域为:{-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6},输入输出语言变量的隶属函数赋值表为:
a)E、ΔE、KP、KI、KD隶属度赋值表
b)KP控制规则为:
c)KI控制规则为:
d)KD控制规则为:
将上述三个控制规则表进行合并,得到如下49条模糊控制规则语句:
1)If(E is NB)and(ΔE is NB)then(Kp is PB)(Ki is NB)(Kd is PS)
2)If(E is NB)and(ΔE is NM)then(Kp is PB)(Ki is NB)(Kd is NS)
3)If(E is NB)and(ΔE is NS)then(Kp is PM)(Ki is NM)(Kd is NB)
4)If(E is NB)and(ΔE is ZO)then(Kp is PM)(Ki is NM)(Kd is NB)
5)If(E is NB)and(ΔE is PS)then(Kp is PS)(Ki is NS)(Kd is NB)
6)If(E is NB)and(ΔE is PM)then(Kp is ZO)(Ki is ZO)(Kd is NM)
7)If(E is NB)and(ΔE is PB)then(Kp is ZO)(Ki is ZO)(Kd is PS)
8)If(E is NM)and(ΔE is NB)then(Kp is PB)(Ki is NB)(Kd is PS)
9)If(E is NM)and(ΔE is NM)then(Kp is PB)(Ki is NB)(Kd is NS)
10)If(E is NM)and(ΔE is NS)then(Kp is PM)(Ki is NM)(Kd is NB)
11)If(E is NM)and(ΔE is ZO)then(Kp is PS)(Ki is NS)(Kd is NM)
12)If(E is NM)and(ΔE is PS)then(Kp is PS)(Ki is NS)(Kd is NM)
13)If(E is NM)and(ΔE is PM)then(Kp is ZO)(Ki is ZO)(Kd is NS)
14)If(E is NM)and(ΔE is PB)then(Kp is NS)(Ki is ZO)(Kd is ZO)
15)If(E is NS)and(ΔE is NB)then(Kp is PM)(Ki is NB)(Kd is ZO)
16)If(E is NS)and(ΔE is NM)then(Kp is PM)(Ki is NM)(Kd is NS)
17)If(E is NS)and(ΔE is NS)then(Kp is PM)(Ki is NS)(Kd is NM)
18)If(E is NS)and(ΔE is ZO)then(Kp is PS)(Ki is NS)(Kd is NM)
19)If(E is NS)and(ΔE is PS)then(Kp is ZO)(Ki is ZO)(Kd is NS)
20)If(E is NS)and(ΔE is PM)then(Kp is NS)(Ki is PS)(Kd is NS)
21)If(E is NS)and(ΔE is PB)then(Kp is NS)(Ki is PS)(Kd is ZO)
22)If(E is ZO)and(ΔE is NB)then(Kp is PM)(Ki is NM)(Kd is ZO)
23)If(E is ZO)and(ΔE is NM)then(Kp is PM)(Ki is NM)(Kd is NS)
24)If(E is ZO)and(ΔE is NS)then(Kp is PS)(Ki is NS)(Kd is NS)
25)If(E is ZO)and(ΔE is ZO)then(Kp is ZO)(Ki is ZO)(Kd is NS)
26)If(E is ZO)and(ΔE is PS)then(Kp is NS)(Ki is PS)(Kd is NS)
27)If(E is ZO)and(ΔE is PM)then(Kp is NM)(Ki is PM)(Kd is NS)
28)If(E is ZO)and(ΔE is PB)then(Kp is NM)(Ki is PM)(Kd is ZO)
29)If(E is PS)and(ΔE is NB)then(Kp is PS)(Ki is NM)(Kd is ZO)
30)If(E is PS)and(ΔE is NM)then(Kp is PS)(Ki is NS)(Kd is ZO)
31)If(E is PS)and(ΔE is NS)then(Kp is ZO)(Ki is ZO)(Kd is ZO)
32)If(E is PS)and(ΔE is ZO)then(Kp is NS)(Ki is PS)(Kd is ZO)
33)If(E is PS)and(ΔE is PS)then(Kp is NS)(Ki is PS)(Kd is ZO
34)If(E is PS)and(ΔE is PM)then(Kp is NM)(Ki is PM)(Kd is ZO)
35)If(E is PS)and(ΔE is PB)then(Kp is NM)(Ki is PB)(Kd is ZO)
36)If(E is PM)and(ΔE is NB)then(Kp is PS)(Ki is ZO)(Kd is PB)
37)If(E is PM)and(ΔE is NM)then(Kp is ZO)(Ki is ZO)(Kd is PS)
38)If(E is PM)and(ΔE is NS)then(Kp is NS)(Ki is PS)(Kd is PS)
39)If(E is PM)and(ΔE is ZO)then(Kp is NM)(Ki is PS)(Kd is PS)
40)If(E is PM)and(ΔE is PS)then(Kp is NM)(Ki is PM)(Kd is PS)
41)If(E is PM)and(ΔE is PM)then(Kp is NM)(Ki is PB)(Kd is PS)
42)If(E is PM)and(ΔE is PB)then(Kp is NB)(Ki is PB)(Kd is PB)
43)If(E is PB)and(ΔE is NB)then(Kp is ZO)(Ki is ZO)(Kd is PB)
44)If(E is PB)and(ΔE is NM)then(Kp is ZO)(Ki is ZO)(Kd is PM)
45)If(E is PB)and(ΔE is NS)then(Kp is NM)(Ki is PS)(Kd is PM)
46)If(E is PB)and(ΔE is ZO)then(Kp is NM)(Ki is PM)(Kd is PM)
47)If(E is PB)and(ΔE is PS)then(Kp is NM)(Ki is PM)(Kd is PS)
48)If(E is PB)and(ΔE is PM)then(Kp is NB)(Ki is PB)(Kd is PS)
49)If(E is PB)and(ΔE is PB)then(Kp is NB)(Ki is PB)(Kd is PB)
3.负载干扰具有不确定性和非线性,但负载扰动能够通过张力传感器检测其大小,并通过变送器转换成与张力大小成正比的电压信号UF,并以前馈补偿形式引入系统中,消除扰动对系统的影响,减小负载干扰引起的速度波动和切纸误差,提高切纸机对负载的抗干扰能力。
4.直流电机为例,给出前馈控制系统框图,并进行前馈传递函数求解。
根据直流电机电枢回路电压方程和电机动力学方程可得直流电机数学模型。
对上式进行拉普拉斯变换并简化整理得到直流电机系统框图如图4所示。
设前馈传递函数为g(s),引入前馈补偿后直流电机系统框图如图5所示。
本发明在传统PID调节器上增加了模糊控制器,并按照相应模块控制规则控制送纸辊的线速度V,同时增加了前馈控制器,前馈控制能够很好解决因负载扰动所引起的送纸辊速度V的波动,同时也减小了切刀转速n的波动,因此切纸长度精确度大大提高。根据上述两种方法,得到基于前馈-模糊PID控制的切纸机控制系统,系统框图如图6所示。
本发明的有益效果是:能够改进造纸厂切纸机升速、降速时间长、精度低等问题能够改善系统动态性能;同时能够提高切纸机在稳速运行中系统抗干扰能力。
附图说明
图1为切纸机结构示意图;
图2为现有切纸机控制方式图;
图3为本发明中模糊控制的隶属度函数图;
图4为直流电机系统框图;
图5为引入前馈补偿后直流电机系统框图;
图6为本发明改进后的控制系统图;
图7为本发明控制程序流程图。
其中,1退纸辊、2纵向切刀、3第一送纸辊、4第一横向切刀、5第二送纸辊、6第二横向切刀、7导纸辊、8张力传感器。
具体实施方式
下面结合附图与实施例对本发明做进一步说明。
图3-图7中,基于前馈-模糊PID控制的切纸机控制方法,系统初始化后,设定切纸长度和切刀频率,在单闭环控制加比值控制系统控制下,进行切纸,在切至完成后,停机;
1.在原有单闭环控制加比值控制切刀速度的基础上,采用模糊PID控制来对送纸辊速度V进行控制,提高系统的动态响应和稳态特性,即应用模糊控制规则,在PID调节器上加入模糊控制器,该模糊控制器的输入语言变量是误差值E、误差变化率ΔE,输出语言变量是PID控制器的比例增益系数KP、积分增益系数KI和微分增益系数KD,从而对PID调节器进行控制;
2.模糊控制具体计算:前面所述误差E、误差变化率ΔE、比例增益系数KP、积分增益系数KI和微分增益系数KD的模糊集为:{NB,NM,NS,ZR,PS,PM,PB},NB表示负大,NM表示负中,NS表示负小,ZR表示零,PS表示正小,PM表示正中,PB表示正大,它们的论域为:{-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6},输入输出语言变量的隶属函数赋值表为:
a)E、ΔE、KP、KI、KD隶属度赋值表
b)KP控制规则为:
c)KI控制规则为:
d)KD控制规则为:
将上述三个控制规则表进行合并,得到如下49条模糊控制规则语句:
1)If(E is NB)and(ΔE is NB)then(Kp is PB)(Ki is NB)(Kd is PS)
2)If(E is NB)and(ΔE is NM)then(Kp is PB)(Ki is NB)(Kd is NS)
3)If(E is NB)and(ΔE is NS)then(Kp is PM)(Ki is NM)(Kd is NB)
4)If(E is NB)and(ΔE is ZO)then(Kp is PM)(Ki is NM)(Kd is NB)
5)If(E is NB)and(ΔE is PS)then(Kp is PS)(Ki is NS)(Kd is NB)
6)If(E is NB)and(ΔE is PM)then(Kp is ZO)(Ki is ZO)(Kd is NM)
7)If(E is NB)and(ΔE is PB)then(Kp is ZO)(Ki is ZO)(Kd is PS)
8)If(E is NM)and(ΔE is NB)then(Kp is PB)(Ki is NB)(Kd is PS)
9)If(E is NM)and(ΔE is NM)then(Kp is PB)(Ki is NB)(Kd is NS)
10)If(E is NM)and(ΔE is NS)then(Kp is PM)(Ki is NM)(Kd is NB)
11)If(E is NM)and(ΔE is ZO)then(Kp is PS)(Ki is NS)(Kd is NM)
12)If(E is NM)and(ΔE is PS)then(Kp is PS)(Ki is NS)(Kd is NM)
13)If(E is NM)and(ΔE is PM)then(Kp is ZO)(Ki is ZO)(Kd is NS)
14)If(E is NM)and(ΔE is PB)then(Kp is NS)(Ki is ZO)(Kd is ZO)
15)If(E is NS)and(ΔE is NB)then(Kp is PM)(Ki is NB)(Kd is ZO)
16)If(E is NS)and(ΔE is NM)then(Kp is PM)(Ki is NM)(Kd is NS)
17)If(E is NS)and(ΔE is NS)then(Kp is PM)(Ki is NS)(Kd is NM)
18)If(E is NS)and(ΔE is ZO)then(Kp is PS)(Ki is NS)(Kd is NM)
19)If(E is NS)and(ΔE is PS)then(Kp is ZO)(Ki is ZO)(Kd is NS)
20)If(E is NS)and(ΔE is PM)then(Kp is NS)(Ki is PS)(Kd is NS)
21)If(E is NS)and(ΔE is PB)then(Kp is NS)(Ki is PS)(Kd is ZO)
22)If(E is ZO)and(ΔE is NB)then(Kp is PM)(Ki is NM)(Kd is ZO)
23)If(E is ZO)and(ΔE is NM)then(Kp is PM)(Ki is NM)(Kd is NS)
24)If(E is ZO)and(ΔE is NS)then(Kp is PS)(Ki is NS)(Kd is NS)
25)If(E is ZO)and(ΔE is ZO)then(Kp is ZO)(Ki is ZO)(Kd is NS)
26)If(E is ZO)and(ΔE is PS)then(Kp is NS)(Ki is PS)(Kd is NS)
27)If(E is ZO)and(ΔE is PM)then(Kp is NM)(Ki is PM)(Kd is NS)
28)If(E is ZO)and(ΔE is PB)then(Kp is NM)(Ki is PM)(Kd is ZO)
29)If(E is PS)and(ΔE is NB)then(Kp is PS)(Ki is NM)(Kd is ZO)
30)If(E is PS)and(ΔE is NM)then(Kp is PS)(Ki is NS)(Kd is ZO)
31)If(E is PS)and(ΔE is NS)then(Kp is ZO)(Ki is ZO)(Kd is ZO)
32)If(E is PS)and(ΔE is ZO)then(Kp is NS)(Ki is PS)(Kd is ZO)
33)If(E is PS)and(ΔE is PS)then(Kp is NS)(Ki is PS)(Kd is ZO
34)If(E is PS)and(ΔE is PM)then(Kp is NM)(Ki is PM)(Kd is ZO)
35)If(E is PS)and(ΔE is PB)then(Kp is NM)(Ki is PB)(Kd is ZO)
36)If(E is PM)and(ΔE is NB)then(Kp is PS)(Ki is ZO)(Kd is PB)
37)If(E is PM)and(ΔE is NM)then(Kp is ZO)(Ki is ZO)(Kd is PS)
38)If(E is PM)and(ΔE is NS)then(Kp is NS)(Ki is PS)(Kd is PS)
39)If(E is PM)and(ΔE is ZO)then(Kp is NM)(Ki is PS)(Kd is PS)
40)If(E is PM)and(ΔE is PS)then(Kp is NM)(Ki is PM)(Kd is PS)
41)If(E is PM)and(ΔE is PM)then(Kp is NM)(Ki is PB)(Kd is PS)
42)If(E is PM)and(ΔE is PB)then(Kp is NB)(Ki is PB)(Kd is PB)
43)If(E is PB)and(ΔE is NB)then(Kp is ZO)(Ki is ZO)(Kd is PB)
44)If(E is PB)and(ΔE is NM)then(Kp is ZO)(Ki is ZO)(Kd is PM)
45)If(E is PB)and(ΔE is NS)then(Kp is NM)(Ki is PS)(Kd is PM)
46)If(E is PB)and(ΔE is ZO)then(Kp is NM)(Ki is PM)(Kd is PM)
47)If(E is PB)and(ΔE is PS)then(Kp is NM)(Ki is PM)(Kd is PS)
48)If(E is PB)and(ΔE is PM)then(Kp is NB)(Ki is PB)(Kd is PS)
49)If(E is PB)and(ΔE is PB)then(Kp is NB)(Ki is PB)(Kd is PB)
3.负载干扰具有不确定性和非线性,但负载扰动能够通过张力传感器检测其大小,并通过变送器转换成与张力大小成正比的电压信号UF,并以前馈补偿形式引入系统中,消除扰动对系统的影响,减小负载干扰引起的速度波动和切纸误差,提高切纸机对负载的抗干扰能力。
4.以直流电机为例,给出前馈控制系统框图,并进行前馈传递函数求解。
根据直流电机电枢回路电压方程和电机动力学方程可得直流电机数学模型。
式中:Ud为电枢电压;id为电枢回路电流;R,La分别为电枢电阻和电感;E为电机反电动势;Ce,Cm分别为电动势常数及转矩常数;Tm为电机电磁转矩;TL为负载转矩;为转动惯量;n为电机转速。
对上式进行拉普拉斯变换并简化整理得到直流电机系统框图如图4所示。
设前馈传递函数为g(s),引入前馈补偿后直流电机系统框图如图5所示。
Claims (3)
1.一种基于前馈-模糊PID控制的切纸机控制方法,系统初始化后,设定切纸长度和切刀频率,在单闭环控制加比值控制系统控制下,进行切纸,在切至完成后,停机;其特征是:
在原有单闭环控制加比值控制切刀速度的基础上,采用模糊PID控制来对送纸辊速度V进行控制,以提高系统的动态响应和稳态特性;即应用模糊控制方式,在PID调节器上加入模糊控制器,该模糊控制器的输入语言变量是误差值E、误差变化率ΔE,输出语言变量是PID控制器的比例增益系数KP、积分增益系数KI和微分增益系数KD,从而对PID调节器进行控制;
同时在执行机构后方设置前馈控制器,对张力传感变送器发出的电压信号UF进行处理,并与执行机构输出信号一并控制送纸辊电机,解决因负载扰动所引起的送纸辊电机速度V的波动,同时也减小了切刀转速n的波动。
2.如权利要求1所述的基于前馈-模糊PID控制的切纸机控制方法,其特征是,所述模糊控制具体计算过程为:所述误差E、误差变化率ΔE、比例增益系数KP、积分增益系数KI和微分增益系数KD的模糊集为:{NB,NM,NS,ZR,PS,PM,PB},NB表示负大,NM表示负中,NS表示负小,ZR表示零,PS表示正小,PM表示正中,PB表示正大,它们的论域为:{-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6},输入输出语言变量的隶属函数赋值表为:
a)E、ΔE、KP、KI、KD隶属度赋值表
b)KP控制规则为:
c)KI控制规则为:
d)KD控制规则为:
将上述三个控制规则表进行合并,得到如下49条模糊控制规则语句:
1)If(E is NB)and(ΔE is NB)then(Kp is PB)(Ki is NB)(Kd is PS)
2)If(E is NB)and(ΔE is NM)then(Kp is PB)(Ki is NB)(Kd is NS)
3)If(E is NB)and(ΔE is NS)then(Kp is PM)(Ki is NM)(Kd is NB)
4)If(E is NB)and(ΔE is ZO)then(Kp is PM)(Ki is NM)(Kd is NB)
5)If(E is NB)and(ΔE is PS)then(Kp is PS)(Ki is NS)(Kd is NB)
6)If(E is NB)and(ΔE is PM)then(Kp is ZO)(Ki is ZO)(Kd is NM)
7)If(E is NB)and(ΔE is PB)then(Kp is ZO)(Ki is ZO)(Kd is PS)
8)If(E is NM)and(ΔE is NB)then(Kp is PB)(Ki is NB)(Kd is PS)
9)If(E is NM)and(ΔE is NM)then(Kp is PB)(Ki is NB)(Kd is NS)
10)If(E is NM)and(ΔE is NS)then(Kp is PM)(Ki is NM)(Kd is NB)
11)If(E is NM)and(ΔE is ZO)then(Kp is PS)(Ki is NS)(Kd is NM)
12)If(E is NM)and(ΔE is PS)then(Kp is PS)(Ki is NS)(Kd is NM)
13)If(E is NM)and(ΔE is PM)then(Kp is ZO)(Ki is ZO)(Kd is NS)
14)If(E is NM)and(ΔE is PB)then(Kp is NS)(Ki is ZO)(Kd is ZO)
15)If(E is NS)and(ΔE is NB)then(Kp is PM)(Ki is NB)(Kd is ZO)
16)If(E is NS)and(ΔE is NM)then(Kp is PM)(Ki is NM)(Kd is NS)
17)If(E is NS)and(ΔE is NS)then(Kp is PM)(Ki is NS)(Kd is NM)
18)If(E is NS)and(ΔE is ZO)then(Kp is PS)(Ki is NS)(Kd is NM)
19)If(E is NS)and(ΔE is PS)then(Kp is ZO)(Ki is ZO)(Kd is NS)
20)If(E is NS)and(ΔE is PM)then(Kp is NS)(Ki is PS)(Kd is NS)
21)If(E is NS)and(ΔE is PB)then(Kp is NS)(Ki is PS)(Kd is ZO)
22)If(E is ZO)and(ΔE is NB)then(Kp is PM)(Ki is NM)(Kd is ZO)
23)If(E is ZO)and(ΔE is NM)then(Kp is PM)(Ki is NM)(Kd is NS)
24)If(E is ZO)and(ΔE is NS)then(Kp is PS)(Ki is NS)(Kd is NS)
25)If(E is ZO)and(ΔE is ZO)then(Kp is ZO)(Ki is ZO)(Kd is NS)
26)If(E is ZO)and(ΔE is PS)then(Kp is NS)(Ki is PS)(Kd is NS)
27)If(E is ZO)and(ΔE is PM)then(Kp is NM)(Ki is PM)(Kd is NS)
28)If(E is ZO)and(ΔE is PB)then(Kp is NM)(Ki is PM)(Kd is ZO)
29)If(E is PS)and(ΔE is NB)then(Kp is PS)(Ki is NM)(Kd is ZO)
30)If(E is PS)and(ΔE is NM)then(Kp is PS)(Ki is NS)(Kd is ZO)
31)If(E is PS)and(ΔE is NS)then(Kp is ZO)(Ki is ZO)(Kd is ZO)
32)If(E is PS)and(ΔE is ZO)then(Kp is NS)(Ki is PS)(Kd is ZO)
33)If(E is PS)and(ΔE is PS)then(Kp is NS)(Ki is PS)(Kd is ZO
34)If(E is PS)and(ΔE is PM)then(Kp is NM)(Ki is PM)(Kd is ZO)
35)If(E is PS)and(ΔE is PB)then(Kp is NM)(Ki is PB)(Kd is ZO)
36)If(E is PM)and(ΔE is NB)then(Kp is PS)(Ki is ZO)(Kd is PB)
37)If(E is PM)and(ΔE is NM)then(Kp is ZO)(Ki is ZO)(Kd is PS)
38)If(E is PM)and(ΔE is NS)then(Kp is NS)(Ki is PS)(Kd is PS)
39)If(E is PM)and(ΔE is ZO)then(Kp is NM)(Ki is PS)(Kd is PS)
40)If(E is PM)and(ΔE is PS)then(Kp is NM)(Ki is PM)(Kd is PS)
41)If(E is PM)and(ΔE is PM)then(Kp is NM)(Ki is PB)(Kd is PS)
42)If(E is PM)and(ΔE is PB)then(Kp is NB)(Ki is PB)(Kd is PB)
43)If(E is PB)and(ΔE is NB)then(Kp is ZO)(Ki is ZO)(Kd is PB)
44)If(E is PB)and(ΔE is NM)then(Kp is ZO)(Ki is ZO)(Kd is PM)
45)If(E is PB)and(ΔE is NS)then(Kp is NM)(Ki is PS)(Kd is PM)
46)If(E is PB)and(ΔE is ZO)then(Kp is NM)(Ki is PM)(Kd is PM)
47)If(E is PB)and(ΔE is PS)then(Kp is NM)(Ki is PM)(Kd is PS)
48)If(E is PB)and(ΔE is PM)then(Kp is NB)(Ki is PB)(Kd is PS)
49)If(E is PB)and(ΔE is PB)then(Kp is NB)(Ki is PB)(Kd is PB)。
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