Dynamic Simulation Tutorial with DWSIM and Python, Part 3: Adding a PID Controller

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Dialog-warning.png This tutorial requires advanced or above average Python programming skills.
Dialog-information.png You'll need at least DWSIM v5.1 on Windows, Linux or macOS to follow/reproduce the tasks within this tutorial.

Introduction

We will add a PID Controller to control the outlet hot water temperature (PV) at 50 C (SP) by changing the cooling water flow using the valve opening as the manipulated variable (MV).

The PID class

Our PID code uses a modified version of the Python PID Class which can be found here: https://github.com/ivmech/ivPID

Create a new script and name it 'PID'. Add the following content to it:

#!/usr/bin/python
#
# This file is part of IvPID.
# Copyright (C) 2015 Ivmech Mechatronics Ltd. <bilgi@ivmech.com>
#
# IvPID is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# IvPID is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program.  If not, see <http://www.gnu.org/licenses/>.

# title           :PID.py
# description     :python pid controller
# author          :Caner Durmusoglu
# date            :20151218
# version         :0.1
# notes           :
# python_version  :2.7
# ==============================================================================

import clr
from System import DateTime

"""Ivmech PID Controller is simple implementation of a Proportional-Integral-Derivative (PID) Controller in the Python Programming Language.
More information about PID Controller: http://en.wikipedia.org/wiki/PID_controller
"""


class PID:
    """PID Controller
    """

    def __init__(self, P=0.2, I=0.0, D=0.0):

        self.Kp = P
        self.Ki = I
        self.Kd = D

        self.sample_time = 0.00
        self.current_time = 0.00
        self.last_time = self.current_time

        self.clear()

    def clear(self):
        """Clears PID computations and coefficients"""
        self.SetPoint = 0.0

        self.PTerm = 0.0
        self.ITerm = 0.0
        self.DTerm = 0.0
        self.last_error = 0.0

        # Windup Guard
        self.int_error = 0.0
        self.windup_guard = 20.0

        self.output = 0.0

    def update(self, feedback_value, currentime):
        """Calculates PID value for given reference feedback

        .. math::
            u(t) = K_p e(t) + K_i \int_{0}^{t} e(t)dt + K_d {de}/{dt}

        .. figure:: images/pid_1.png
           :align:   center

           Test PID with Kp=1.2, Ki=1, Kd=0.001 (test_pid.py)

        """
        error = self.SetPoint - feedback_value

        self.current_time = currentime
        delta_time = self.current_time - self.last_time
        delta_error = error - self.last_error

        if (delta_time >= self.sample_time):
            self.PTerm = self.Kp * error
            self.ITerm += error * delta_time

            if (self.ITerm < -self.windup_guard):
                self.ITerm = -self.windup_guard
            elif (self.ITerm > self.windup_guard):
                self.ITerm = self.windup_guard

            self.DTerm = 0.0
            if delta_time > 0:
                self.DTerm = delta_error / delta_time

            # Remember last time and last error for next calculation
            self.last_time = self.current_time
            self.last_error = error

            self.output = self.PTerm + (self.Ki * self.ITerm) + (self.Kd * self.DTerm)

    def setKp(self, proportional_gain):
        """Determines how aggressively the PID reacts to the current error with setting Proportional Gain"""
        self.Kp = proportional_gain

    def setKi(self, integral_gain):
        """Determines how aggressively the PID reacts to the current error with setting Integral Gain"""
        self.Ki = integral_gain

    def setKd(self, derivative_gain):
        """Determines how aggressively the PID reacts to the current error with setting Derivative Gain"""
        self.Kd = derivative_gain

    def setWindup(self, windup):
        """Integral windup, also known as integrator windup or reset windup,
        refers to the situation in a PID feedback controller where
        a large change in setpoint occurs (say a positive change)
        and the integral terms accumulates a significant error
        during the rise (windup), thus overshooting and continuing
        to increase as this accumulated error is unwound
        (offset by errors in the other direction).
        The specific problem is the excess overshooting.
        """
        self.windup_guard = windup

    def setSampleTime(self, sample_time):
        """PID that should be updated at a regular interval.
        Based on a pre-determined sampe time, the PID decides if it should compute or return immediately.
        """
        self.sample_time = sample_time

Adding a PID

For illustration purposes, add a new Adjust object to the flowsheet and set its manipulated object to 'FV-01' and controlled object to 'cooled_water'. The actual controlling won't be done by this object calculation routine, but rather by our PID script.

Dynamic pid.jpg

Running the Closed-Loop Dynamic Model

Create a new script and name it 'RunDynamicProcess_ClosedLoop', with the following content:

import clr
import System
from System import *
from System.Threading import *

clr.AddReference('System.Core')
clr.AddReference('DWSIM.GlobalSettings')
clr.ImportExtensions(System.Linq)

from DWSIM.GlobalSettings import *

source = Flowsheet.Scripts.Values.Where(lambda x: x.Title == 'Functions').FirstOrDefault().ScriptText.replace('\r', '')
exec(source)

initvars = Flowsheet.Scripts.Values.Where(lambda x: x.Title == 'InitVars').FirstOrDefault().ScriptText.replace('\r', '')
exec(initvars)

pidclass = Flowsheet.Scripts.Values.Where(lambda x: x.Title == 'PID').FirstOrDefault().ScriptText.replace('\r', '')
exec(pidclass)

maxtime = Flowsheet.ExtraProperties.MaxTime
length = maxtime / Flowsheet.ExtraProperties.TimeStep

time = [0.0 + x*(maxtime - 0.0)/length for x in range(int(length))]

source_level = {}
sink_level = {}
hot_water_flow = {}
hot_water_temp = {}
cooling_water_flow = {}
cooling_water_temp = {}
valve_opening = {}

pid_sp = {}
pid_pv = {}
pid_mv = {}

perturbed_hotwater = False

controller = Flowsheet.GetFlowsheetSimulationObject("PID Controller")

P = 0.5
I = 0.01
D = 0.1

pid = PID(P, I, D)

pid.SetPoint = 1.0
pid.sample_time = 0.01

controller.ExtraProperties.TotalError = 0.0

for t in time:
	Flowsheet.SupressMessages = False
	Flowsheet.WriteMessage("Time Step: " + str(int(t+1)) + "/" + str(int(maxtime)))
	Flowsheet.SupressMessages = True
	Flowsheet.ExtraProperties.CurrentTime = t
	if (t >= Flowsheet.ExtraProperties.HotWaterPerturbationTime and not perturbed_hotwater): 
		StorePrePerturbationVariables()
		SetHotWaterMassFlow(Flowsheet.ExtraProperties.PerturbationValue)
		Flowsheet.ExtraProperties.LastPerturbationTime = t
		perturbed_hotwater = True
	Flowsheet.SolveFlowsheet2()
	CalcSourceTankLevel()
	CalcSinkTankLevel()
	source_level[t] = GetSourceTankLevel()
	sink_level[t] = GetSinkTankLevel()
	hot_water_flow[t] = GetHotWaterMassFlow()
	hot_water_temp[t] = GetHotWaterOutletTemperature()
	cooling_water_flow[t] = GetCoolingWaterMassFlow() 
	cooling_water_temp[t] = GetCoolingWaterOutletTemperature()
	valve_opening[t] = GetValveOpening()
	pid_sp[t] = 1.0
	pid_pv[t] = GetHotWaterOutletTemperature()/(50.0 + 273.15)
	pid.update(GetHotWaterOutletTemperature()/(50.0 + 273.15), t)
	pid_mv[t] = (pid.SetPoint - pid.output) * GetValveOpening()/50.0
	SetValveOpening((pid.SetPoint - pid.output) * GetValveOpening())
	controller.ExtraProperties.TotalError += ((pid_sp[t] - pid_pv[t]) * Flowsheet.ExtraProperties.TimeStep) ** 2

Flowsheet.SupressMessages = False

outputresults = Flowsheet.Scripts.Values.Where(lambda x: x.Title == 'GenerateCharts').FirstOrDefault().ScriptText.replace('\r', '')
exec(outputresults)

Notice that our PID variables (SP, PV and MV) are normalized (SP = 1.0).

We will run our PID controller initially with Kp = 0.5, Ki = 0.01 and Kd = 0.1.

Modify the 'GenerateCharts' script to include the following commands before the last one:

	if (controller != None):
	
		chart3 = Plot()
		chart3.Model = Common.CreatePlotModel(Array[float](time), Array[float](pid_sp.values()), "PID Output", "P = " + str(P) + ", I = " + str(I) + ", D = " + str(D), "time (s)", "SP") 
		chart3.Model.AddYAxis("PV", "pv", OxyPlot.Axes.AxisPosition.Right, 1) 
		chart3.Model.AddLineSeries(Array[float](time), Array[float](pid_mv.values()), "MV")
		chart3.Model.AddLineSeriesWithKeys(Array[float](time), Array[float](pid_pv.values()), "PV", "pv", "x")
		chart3.Model.InvalidatePlot(True)
		
		form3 = Common.GetDefaultEditorForm("PID Output", 600, 600, chart3, False)
		form3.Show()

Run the closed loop model. You should get the following after a successfull run:

Dynamic pidresults.jpg

Download File

Download the simulation file with what has been done so far: dynamic_part3.dwxmz

Return to Part 2: Building the Dynamic Model

Proceeed to Part 4: Tuning the PID Controller through Non-Linear Optimization