184 lines
6.5 KiB
Python
184 lines
6.5 KiB
Python
import numpy as np
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#based on https://en.wikipedia.org/wiki/PID_controller#Discrete_implementation
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# performance parameters for controllers
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def trap_int(vec,timestep):
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# numerical integration via the trapeziod rule to calculate the performance parameters
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l = np.size(vec)
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int = 0
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for i in range(l-1):
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int = int + (vec[i]+vec[i+1])/2*timestep
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return int
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def ISE_fun(error_history,timestep):
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# calcuate the integral of square error
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e = np.array(error_history)
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dt = timestep
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ise = trap_int(e**2,dt)
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return ise
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def IAE_fun(error_history,timestep):
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# calcuate the integral of absolute error
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e = np.array(error_history)
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dt = timestep
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iae = trap_int(np.abs(e),dt)
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return iae
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def ITSE_fun(error_history,timestep):
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# calcuate the integral of time multiply square error
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e = np.array(error_history)
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dt = timestep
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n = np.size(e)
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t = np.arange(0,n)*dt
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itse = trap_int(t*e**2,dt)
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return itse
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def ITAE_fun(error_history,timestep):
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# calcuate the integral of time multiply absolute error
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e = np.array(error_history)
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dt = timestep
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n = np.size(e)
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t = np.arange(0,n)*dt
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itae = trap_int(np.abs(e),dt)
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return itae
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# P controller
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class P_controller_class:
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# def __init__(self,setpoint,proportionality_constant):
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# self.SP = setpoint
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# self.Kp = proportionality_constant
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# self.error_history = []
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# self.control_variable = 0.1
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# self.lower_limit = -0.1 # default
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# self.upper_limit = +0.1 # default
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# def set_control_variable_limits(self,lower_limit,upper_limit):
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# self.lower_limit = lower_limit
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# self.upper_limit = upper_limit
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# def calculate_error(self,process_variable):
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# self.error = self.SP-process_variable
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# self.error_history.append(self.error)
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# def get_control_variable(self):
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# new_control = self.control_variable+self.Kp*(self.error_history[-1]-self.error_history[-2])
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# if new_control < self.lower_limit:
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# new_control = self.lower_limit
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# if new_control > self.upper_limit:
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# new_control = self.upper_limit
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# self.control_variable = new_control
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# # print(new_control)
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# return new_control
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def __init__(self):
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pass
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# PI controller
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class PI_controller_class:
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# init
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def __init__(self,setpoint,deadband,proportionality_constant,Ti,timestep,lower_limit=0.,upper_limit=1.):
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self.SP = setpoint
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self.db = deadband
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self.Kp = proportionality_constant
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self.Ti = Ti # ~integration time
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self.dt = timestep
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# use a list to be able to append more easily - will get converted to np.array when needed
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self.error_history = [0]
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self.cv_lower_limit = lower_limit # limits for the controll variable
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self.cv_upper_limit = upper_limit # limits for the controll variable
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# setter
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def set_setpoint(self,setpoint):
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self.SP = setpoint
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def set_control_variable(self,control_variable, display_warning=True):
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if display_warning == True:
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print('WARNING! You are setting the control variable of the PI controller manually! \
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Consider using the .update_controll_variable() method instead.')
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self.control_variable = control_variable
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# getter
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def get_current_control_variable(self):
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return self.control_variable
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def get_error_history(self):
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return self.error_history[1:]
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def get_performance_indicators(self,ISE=True,IAE=True,ITSE=True,ITAE=True):
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# calculate and return the performance indicators of the error history
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ise = np.nan
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iae = np.nan
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itse = np.nan
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itae = np.nan
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# self.error_history[1:] because the first value of the error history is set to [0]
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# to avoid special case handling in the calculation of the control variable
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if ISE == True:
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ise = ISE_fun(self.error_history[1:],self.dt)
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if IAE == True:
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iae = IAE_fun(self.error_history[1:],self.dt)
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if ITSE == True:
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itse = ITSE_fun(self.error_history[1:],self.dt)
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if ITAE == True:
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itae = ITAE_fun(self.error_history[1:],self.dt)
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return ise,iae,itse,itae
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def get_info(self):
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new_line = '\n'
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# :<10 pads the self.value to be 10 characters wide
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print_str = (f"Controller has the following attributes: {new_line}"
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f"----------------------------- {new_line}"
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f"Type = PI Controller {new_line}"
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f"Setpoint = {self.SP:<10} {new_line}"
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f"Deadband = {self.db:<10} {new_line}"
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f"Proportionality constant = {self.Kp:<10} {new_line}"
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f"Integration time = {self.Ti:<10} [s] {new_line}"
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f"Current control variable = {round(self.control_variable,3):<10} {new_line}"
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f"Lower limit CV = {self.cv_lower_limit:<10} {new_line}"
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f"Upper limit CV = {self.cv_upper_limit:<10} {new_line}"
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f"Simulation timestep = {self.dt:<10} [s] {new_line}"
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f"----------------------------- {new_line}")
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print(print_str)
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# methods
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def calculate_error(self,process_variable):
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# calculate the error and expand the err history
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self.error = process_variable-self.SP
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self.error_history.append(self.error)
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def update_control_variable(self,process_variable):
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# calculate the current control variable and make sure it does not exceed the limits
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self.calculate_error(process_variable)
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# initialize some variables
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cv = self.control_variable
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Kp = self.Kp
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Ti = self.Ti
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dt = self.dt
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e0 = self.error_history[-1]
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e1 = self.error_history[-2]
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# test if the error exceeds the deadband range
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# only if that is the case, change control variable
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if abs(self.error) > self.db:
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new_control = cv+Kp*(e0-e1)+dt/Ti*e0
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# ensure that the controll variable stays within the predefined limits
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if new_control < self.cv_lower_limit:
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new_control = self.cv_lower_limit
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if new_control > self.cv_upper_limit:
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new_control = self.cv_upper_limit
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else:
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new_control = cv
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# set the control variable attribute
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self.set_control_variable(new_control,display_warning=False)
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