利用python进行pid仿真控制

一、控制对象：二阶震荡环节

1. 控制系统框图如下

1.2 初始条件
$$y(0)=0u(0)=0e(0)=0r=1$$
1.3 测试结果

原系统阶跃响应曲线

受控系统阶跃响应曲线

二、python实现

1. 传递函数

from numpy import *
from matplotlib.pyplot import *

class Transfer: # 传递函数类
    def __init__(self,num, den): # 初始化传递函数分子和分母
        self.num = array(num, dtype=float); self.den = array(den[1:], dtype=float)
         # 初始化历史输入和历史输出
        self.x = array([0]*len(num), dtype=float); self.y = array([0]*(len(den)-1), dtype=float)
        self.overflow = False # 判断是否发散震荡
    def __call__(self, x):
        if not self.overflow:
            self.x = roll(self.x, 1); self.x[0] = x # 历史输入串入新数据
            y = self.num @ self.x - self.den @ self.y # 计算输出
            self.y = roll(self.y, 1); self.y[0] = y # 历史输出串入新数据
            if y > 1e3: self.overflow = True
            return y
        else: return nan

2.PID

class PID:
    def __init__(self,Kpid, pid_method=None): # 初始化PID类
        # 初始化PID，历史误差
        self.Kpid = array(Kpid, dtype=float); self.err = array([0]*3, dtype=float)
        self.y = 0; self.overflow = False
        self.q = array([Kpid[0]*(1 + Kpid[1] + Kpid[2]), -Kpid[0]*(1 + 2*Kpid[2]), Kpid[0]*Kpid[2]], dtype=float) # 计算误差系数q
        self.pid_method = pid_method if pid_method != None else lambda q,err: q @ err # 选择PID方法
    
    def __call__(self, err):
        if not self.overflow:
            self.err = roll(self.err, 1); self.err[0] = err # 历史误差串入新数据
            self.y += self.pid_method(self.q, self.err) # 计算输出
            if self.y > 1e3:
                self.overflow = True
            return self.y
        else: return nan

3.响应参数计算

def draw(y, save=None, titleName=None): # 绘制输出阶梯图
    step(range(len(y)), y)
    if save != None: savefig(save)
def is_stable(y): # 判断系统是否稳定
    if max(abs(y)) > 1e2: return False
    dy = diff(y)
    return sum(dy[int(len(dy)*0.8):]<1e-3) / (len(dy) - int(len(dy)*0.8)) > 0.8
def over_shoot(y): # 计算输出超调量
    return abs(max(y) -1)
def idx_adjust(y): # 计算输出调整时间
    dy = diff(y); dy_stable = (dy < 1e-3) & (dy > -1e-3)
    idx = len(dy_stable) - 1
    while dy_stable[idx]:
        idx -= 1
        if idx < 0: break
    while abs(1 - y[idx]) < 2e-2:
        idx -= 1
    return idx + 1

4.测试类

class Analysor: # 系统pid参数测试类
    def __init__(self, num, den, r, t_len): # 初始化系统的分子和分母，给定值和仿真时间
        self.num = num; self.den = den; self.r = r
        self.t_len = t_len; self.record = []; self.y = None
    
    def view(self, kpid): # 仿真给定pid时系统输出
        G = Transfer(self.num, self.den); pid = PID(kpid)
        self.kpid=kpid; self.q = [kpid[0]*(1 + kpid[1] + kpid[2]), -kpid[0]*(1 + 2*kpid[2]), kpid[0]*kpid[2]]
        y = zeros(self.t_len); u = 0; u_out = zeros(self.t_len)
        for i in range(self.t_len):
            y[i] = G(u)
            e = self.r - y[i]
            u = pid(e); u_out[i] = u
        self.y = y
        return y, u_out
    def sort(self): # 对系统的pid记录排序
        content = ''
        for each in sorted(self.record):
            content += repr(each)
        with open('sort.txt', 'w') as f: f.write(content)
    def analyse(self, kpid, auto=True): # 对给定pid值下系统响应曲线分析超调和调整时间
        y = self.view(kpid) if auto else self.y
        os,ts = (over_shoot(y), idx_adjust(y)) if is_stable(y) else (nan, nan)
        return (os, ts)
    def pid(self):
        print(f'pid:{self.kpid}, q:{self.q}')

5.主程序

num, den = [0, 1, 0.5],[1, -1.5, 0.7]; pid = [0.01825, 1.3    , 3.65   ] # 系统一分子分母系数以及测试最佳pid值
r=1; y = []; t_len = 100
A = Analysor(num,den,r,t_len) # 初始化系统
y, u=A.view(pid) # 仿真最佳pid系统输出曲线，以及控制器输出曲线
draw(y)
draw(u)
print(over_shoot(y),idx_adjust(y))

链接: https://pan.baidu.com/s/1jOcjZcjDxzN8jd1NagXFrQ 提取码: k7as