分数阶pid代码怎么写

分数阶PID（Proportional-Integral-Derivative）控制是一种常用于系统控制的方法，与传统的整数阶PID控制相比，分数阶PID具有更好的性能和适应性。以下是一个简单的分数阶PID控制的代码示例：

import numpy as np

def fractional_pid_control(input_signal, Kp, Ki, Kd, Ts, alpha, beta, gamma):
    N = len(input_signal)
    output_signal = np.zeros(N)
    error_integral = np.zeros(N)
    error_derivative = np.zeros(N)
    error_previous = 0
    for k in range(N):
        error = input_signal[k] - output_signal[k]
        error_integral[k] = Ts**alpha * ((1-alpha) * error_integral[k-1] + Ts**-alpha * error)
        if k >= 2:
            error_derivative[k] = Ts**beta * ((1-beta) * error_derivative[k-1] + Ts**-beta * (error - error_previous))
        else:
            error_derivative[k] = 0  # at the beginning, no derivative
        output_signal[k] = Kp * error + Ki * error_integral[k] + Kd * error_derivative[k] + gamma * input_signal[k]
        error_previous = error
    return output_signal

# Example usage
input_signal = np.random.rand(100)  # example input signal
Kp = 1  # proportional gain
Ki = 1  # integral gain
Kd = 1  # derivative gain
Ts = 0.01  # sampling time
alpha = 0.5  # fractional order for integral
beta = 0.7  # fractional order for derivative
gamma = 0.5  # feedforward term

output_signal = fractional_pid_control(input_signal, Kp, Ki, Kd, Ts, alpha, beta, gamma)  # obtain output signal

这个代码示例实现了一个基本的分数阶PID控制器。其中，`input_signal`是输入信号，`Kp`、`Ki`和`Kd`分别是比例增益、积分增益和微分增益，`Ts`是采样时间，`alpha`和`beta`是分数阶，`gamma`是前馈项。函数`fractional_pid_control`返回一个数组`output_signal`，为输出信号。可以根据需要修改参数和输入信号进行实际应用。