Figure 1.18: Air–fuel controller based on selectors - Revision history

Murray at 18:51, 16 November 2024

2024-11-16T18:51:15Z

Murray at 16:29, 28 May 2023

2023-05-28T16:29:57Z

Murray at 16:22, 28 May 2023

2023-05-28T16:22:15Z

Murray at 05:56, 29 August 2021

2021-08-29T05:56:56Z

Murray at 05:46, 24 June 2021

2021-06-24T05:46:29Z

Murray at 05:45, 24 June 2021

2021-06-24T05:45:05Z

Murray at 05:43, 24 June 2021

2021-06-24T05:43:46Z

Murray: Created page with "{{Figure |Chapter=Introduction |Figure number=1.18 |Figure title=Air–fuel controller based on selectors |GitHub URL=https://github.com/murrayrm/fbs2e-python/blob/main/figure..."

2021-06-24T05:40:11Z

Created page with "{{Figure |Chapter=Introduction |Figure number=1.18 |Figure title=Air–fuel controller based on selectors |GitHub URL=https://github.com/murrayrm/fbs2e-python/blob/main/figure..."

New page

{{Figure
|Chapter=Introduction
|Figure number=1.18
|Figure title=Air–fuel controller based on selectors
|GitHub URL=https://github.com/murrayrm/fbs2e-python/blob/main/figure-1.18-airfuel_selectors.py
}}
[[Image:figure-1.18-airfuel_selectors.png]]

'''Figure 1.18:''' Air–fuel controller based on selectors. The left figure shows the system architecture. The letters R and Y in the PI controller denote the input ports for reference and measured signal respectively. The right figure shows a simulation where the power reference r is changed stepwise at t = 1 and t = 15. Notice that the normalized air flow is larger than the normalized fuel flow both for increasing and decreasing reference steps.

<nowiki>
# figure-1.18-airfuel_selectors.py - Air-fuel control example
# RMM, 20 Jun 2021
#
# Air–fuel controller based on selectors. The right figure shows a
# simulation where the power reference r is changed stepwise at t = 1 and t
# = 15. Notice that the normalized air flow is larger than the normalized
# fuel flow both for increasing and decreasing reference steps.

# Package import
import numpy as np
import matplotlib.pyplot as plt
import control as ct
import cruise

#
# Air and fuel (oil) dynamics and controllers
#
# These dynamics come from Karl Astrom and are embedded in a SIMULINK
# diagram used for the initial part of the book. The basic structure for
# both the air and fuel controllers is a PI controller with output feedback
# for the proportional term and integral feedback on the error. This cuts
# the feedthrough term for the proportional feedback and gives a smoother
# step response (see Figure 11.1b for the basic structure).
#

# Min selector for oil PI controller input
min_block = ct.NonlinearIOSystem(
updfcn=None, outfcn=lambda t, x, u, params: min(u),
name='min', inputs=['u1', 'u2'], outputs='y')

# Max selector for air PI controller input
max_block = ct.NonlinearIOSystem(
updfcn=None, outfcn=lambda t, x, u, params: max(u),
name='max', inputs=['u1', 'u2'], outputs='y')

# Oil and air flow dynamics (from KJA SIMULINK diagram)
Po = ct.tf([1], [1, 1])
Pa = ct.tf([4], [1, 4])

# PI controller for oil flow
kpo = 2; kio = 4
Cio = ct.tf([kio], [1, 0])
Cpo = kpo
oil_block = ct.LinearIOSystem(
ct.tf2ss(Po * Cio / (1 + Po * (Cio + Cpo))),
name="oil", inputs='r', outputs='y')

# PI controller for air flow
kpa = 1; kia = 1
Cia = ct.tf([kia], [1, 0])
Cpa = kpa
air_block = ct.LinearIOSystem(
ct.tf2ss(Pa * Cia / (1 + Pa * (Cia + Cpa))),
name="air", inputs='r', outputs='y')

#
# Air-fuel selector dynamics
#
# The selector dynamics are based on the diagram Figure 1.18a, where we have
# already pre-computing the transfer function around the process/controller
# pairs (so the air and oil blocks have input 'R' and output 'Y' from the
# diagram). We use the interconnect function along with named signals to
# set everything up.
#

airfuel = ct.interconnect(
[min_block, max_block, oil_block, air_block],
connections = (
['oil.r', 'min.y'],
['air.r', 'max.y'],
['min.u2', 'air.y'],
['max.u1', 'oil.y']),
inplist = [['min.u1', 'max.u2']], inputs='ref',
outlist = ['air.y', 'oil.y'], outputs=['air', 'oil'])

#
# Input/output response
#
# Finally, we simulate the dynamics with an input singla as showin in Figure
# 1.18b, consisting of a step increase from 0 to 1 at time t = 1 sec and
# then a decrease from 1 to 0.5 at time t = 15 sec.
#

T = np.linspace(0, 30, 101)
ref = np.array([
0 if t <= 1 else
1 if t <= 15 else
0.5 for t in T])
t, y = ct.input_output_response(airfuel, T, ref)

# Plot the results
plt.subplot(2, 2, 1)
plt.plot(t, ref, t, y[0], t, y[1])

plt.legend(['ref', 'air', 'fuel'])
plt.xlabel('Time $t$ [sec]')
plt.ylabel('Normalized signals')
</nowiki>

@@ Line 5: / Line 5: @@
 |GitHub URL=https://github.com/murrayrm/fbs2e-python/blob/main/figure-1.18-airfuel_selectors.py
 }}
-[[Image:figure-1.18-airfuel-blk.png|height=300px]] &nbsp;
+[[Image:figure-1.18-airfuel-blk.png|300px]] &nbsp;
 [[Image:figure-1.18-airfuel_selectors.png]]

@@ Line 5: / Line 5: @@
 |GitHub URL=https://github.com/murrayrm/fbs2e-python/blob/main/figure-1.18-airfuel_selectors.py
 }}
-[[Image:figure-1.18-airfuel-blk.png]] &nbsp;
+[[Image:figure-1.18-airfuel-blk.png|height=300px]] &nbsp;
 [[Image:figure-1.18-airfuel_selectors.png]]

@@ Line 38: / Line 38: @@
 # Min selector for oil PI controller input
-min_block = ct.NonlinearIOSystem(
+min_block = ct.nlsys(
      updfcn=None, outfcn=lambda t, x, u, params: min(u),
      name='min', inputs=['u1', 'u2'], outputs='y')
 # Max selector for air PI controller input
-max_block = ct.NonlinearIOSystem(
+max_block = ct.nlsys(
      updfcn=None, outfcn=lambda t, x, u, params: max(u),
      name='max', inputs=['u1', 'u2'], outputs='y')
@@ Line 55: / Line 55: @@
 Cio = ct.tf([kio], [1, 0])
 Cpo = kpo
-oil_block = ct.LinearIOSystem(
+oil_block = ct.tf(
-     ct.tf2ss(Po * Cio / (1 + Po * (Cio + Cpo))),
+     Po * Cio / (1 + Po * (Cio + Cpo)),
      name="oil", inputs='r', outputs='y')
@@ Line 63: / Line 63: @@
 Cia = ct.tf([kia], [1, 0])
 Cpa = kpa
-air_block = ct.LinearIOSystem(
+air_block = ct.tf(
-     ct.tf2ss(Pa * Cia / (1 + Pa * (Cia + Cpa))),
+     Pa * Cia / (1 + Pa * (Cia + Cpa)),
      name="air", inputs='r', outputs='y')

@@ Line 2: / Line 2: @@
 |Chapter=Introduction
 |Figure number=1.18
 |Figure title=Air–fuel controller based on selectors
 |GitHub URL=https://github.com/murrayrm/fbs2e-python/blob/main/figure-1.18-airfuel_selectors.py