Cruise control - Revision history

Murray at 16:39, 24 November 2024

2024-11-24T16:39:50Z

Murray at 16:39, 24 November 2024

2024-11-24T16:39:36Z

Murray: /* Python code */

2023-05-28T15:51:53Z

Python code

Murray: /* Python code */

2023-05-28T15:49:32Z

Python code

Murray at 15:47, 28 May 2023

2023-05-28T15:47:20Z

Murray at 04:24, 26 June 2021

2021-06-26T04:24:41Z

Murray at 04:22, 26 June 2021

2021-06-26T04:22:52Z

Murray at 04:22, 26 June 2021

2021-06-26T04:22:24Z

Murray: /* Anti-windup compensation */

2020-12-30T07:07:51Z

Anti-windup compensation

Murray: /* Anti-windup compensation */

2020-12-30T07:06:52Z

Anti-windup compensation

@@ Line 16: / Line 16: @@
 Figures making use of this model:
 {{#ask: [[Category:Figures]] [[Requires::cruise.py]] | format=ul | sort=Sort key}}
 == Introduction ==

← Older revision		Revision as of 16:39, 24 November 2024
Line 13:		Line 13:

	Note: the Python code on this page makes use of the [https://python-control.org Python Control Systems Library], an open source software toolbox for control systems analysis.		Note: the Python code on this page makes use of the [https://python-control.org Python Control Systems Library], an open source software toolbox for control systems analysis.
		+
		+	Figures making use of this model:
		+	{{#ask: [[Category:Figures]] [[Requires::cruise.py]] \| format=ul \| sort=Sort key}}
		+

	== Introduction ==		== Introduction ==

@@ Line 62: / Line 62: @@
 === Python code ===
-The model for the system above can be built using the [[https:python-control.org|Python Control Toolbox]].  The code blocks in this section can be used to generate the plots above.
+The model for the system above can be built using the [[https:python-control.org|Python Control Toolbox]].  The code blocks in this section can be used to generate the plots above.  The vehicle dynamics and PI controller are defined in [[https:github.com/murrayrm/fbs2e-python/blob/main/cruise.py|cruise.py]] (via GitHub).
-{{Code block|Package initialization (from [[https:github.com/murrayrm/fbs2e-python/blob/main/cruise.py|cruise.py]])}}
+{{Code block|Package initialization}}
 {{Code start}}
 import numpy as np

@@ Line 64: / Line 64: @@
 The model for the system above can be built using the [[https:python-control.org|Python Control Toolbox]].  The code blocks in this section can be used to generate the plots above.
-{{Code block|Package initialization (from [[http:github.com/murrayrm/fbs2e-python/blob/main/cruise.py|cruise.py]]}}
+{{Code block|Package initialization (from [[https:github.com/murrayrm/fbs2e-python/blob/main/cruise.py|cruise.py]])}}
 {{Code start}}
 import numpy as np

@@ Line 64: / Line 64: @@
 The model for the system above can be built using the [[https:python-control.org|Python Control Toolbox]].  The code blocks in this section can be used to generate the plots above.
-{{Code block|Package initialization}}
+{{Code block|Package initialization (from [[http:github.com/murrayrm/fbs2e-python/blob/main/cruise.py|cruise.py]]}}
 {{Code start}}
 import numpy as np

@@ Line 5: / Line 5: @@
 ! GitHub URL
 | https://github.com/murrayrm/fbs2e-python/blob/main/cruise.py
 |}

← Older revision		Revision as of 04:22, 26 June 2021
Line 1:		Line 1:
		+	{{righttoc}}
		+
	{\| class="wikitable"		{\| class="wikitable"
	\|-		\|-

@@ Line 703: / Line 703: @@
 The right figure below shows what happens when a controller with anti-windup is applied to the system. Because of the feedback from the actuator model, the output of the integrator is quickly reset to a value such that the controller output is at the saturation limit.  The behavior is drastically different from that on the left and the large overshoot is avoided. The tracking gain used in the simulation is <math>k_\text{aw} = 2</math> which is an order of magnitude larger than the integral gain <math>k_\text{i} = 0.2</math>.
-{|
+{| align=center
 |-
 | width=45% |

@@ Line 699: / Line 699: @@
 === Anti-windup compensation ===
-The windup effect is illustrated in the left figure below, which shows what happens when a car encounters a hill that is so steep (6 degrees) that the throttle saturates when the cruise controller attempts to maintain speed. When encountering the slope at time <math>t=5/math>, the velocity decreases and the throttle increases to generate more torque. However, the torque required is so large that the throttle saturates. The error decreases slowly because the torque generated by the engine is just a little larger than the torque required to compensate for gravity. The error is large and the integral continues to build up until the error reaches zero at time 25, but the controller output is still  larger than the saturation limit and the actuator remains saturated. The integral term starts to decrease and the velocity settles to the desired value at time <math>t = 40</math>. Also notice the large overshoot.
+The windup effect is illustrated in the left figure below, which shows what happens when a car encounters a hill that is so steep (6 degrees) that the throttle saturates when the cruise controller attempts to maintain speed. When encountering the slope at time <math>t=5</math>, the velocity decreases and the throttle increases to generate more torque. However, the torque required is so large that the throttle saturates. The error decreases slowly because the torque generated by the engine is just a little larger than the torque required to compensate for gravity. The error is large and the integral continues to build up until the error reaches zero at time 25, but the controller output is still  larger than the saturation limit and the actuator remains saturated. The integral term starts to decrease and the velocity settles to the desired value at time <math>t = 40</math>. Also notice the large overshoot.
 The right figure below shows what happens when a controller with anti-windup is applied to the system. Because of the feedback from the actuator model, the output of the integrator is quickly reset to a value such that the controller output is at the saturation limit.  The behavior is drastically different from that on the left and the large overshoot is avoided. The tracking gain used in the simulation is <math>k_\text{aw} = 2</math> which is an order of magnitude larger than the integral gain <math>k_\text{i} = 0.2</math>.
@@ Line 706: / Line 706: @@
 |-
 | width=45% |
-[[Image:cruise-windup.png|border|300px|Simulation of PI cruise control with windup. The figure shows the speed v and the throttle u for a car that encounters a slope that is so steep that the throttle saturates. The controller output is a dashed line. The controller parameters are kp = 0.5 and ki = 0.1.]]
+[[Image:cruise-windup.png|border|400px|Simulation of PI cruise control with windup. The figure shows the speed v and the throttle u for a car that encounters a slope that is so steep that the throttle saturates. The controller output is a dashed line. The controller parameters are kp = 0.5 and ki = 0.1.]]
 | width=10% |
 | width=45% |
-[[Image:cruise-antiwindup.png|border|300px|Simulation of PI cruise control with anti-windup. The figure shows the speed v and the throttle u for a car that encounters a slope that is so steep that the throttle saturates. The controller output is a dashed line. The controller parameters are kp = 0.5, ki = 0.1. and kaw =2. The anti-windup compensator eliminates the overshoot by preventing the error from building up in the integral term of the controller.]]
+[[Image:cruise-antiwindup.png|border|400px|Simulation of PI cruise control with anti-windup. The figure shows the speed v and the throttle u for a car that encounters a slope that is so steep that the throttle saturates. The controller output is a dashed line. The controller parameters are kp = 0.5, ki = 0.1. and kaw =2. The anti-windup compensator eliminates the overshoot by preventing the error from building up in the integral term of the controller.]]
 |}