Gelöste Aufgaben/JUMP/Driver Controls - Versionsgeschichte

Mechaniker: /* Parameter */

2021-03-22T15:46:32Z

Parameter

← Nächstältere Version		Version vom 22. März 2021, 15:46 Uhr
Zeile 103:		Zeile 103:
	\|coefficient of proportional contribution		\|coefficient of proportional contribution
	\|''K<sub>p</sub>''		\|''K<sub>p</sub>''
	\|		\|1
	\|1/s		\|1/s
	\|-		\|-

Mechaniker: /* Model */

2021-03-22T15:46:19Z

Model

← Nächstältere Version		Version vom 22. März 2021, 15:46 Uhr
Zeile 52:		Zeile 52:
	Thus, we set the relevant error-value to be		Thus, we set the relevant error-value to be

	::<math>\tilde{e} := min(e_1, e_2)</math>		::<math>\tilde{e} := \min(e_1, e_2)</math>

	The controller thus adds to the state variable		The controller thus adds to the state variable

Mechaniker: /* Model */

2021-03-22T15:44:04Z

Model

← Nächstältere Version		Version vom 22. März 2021, 15:44 Uhr
Zeile 81:		Zeile 81:
	::<math>p(t) = \min(\max(p^*,0),1)</math>		::<math>p(t) = \min(\max(p^*,0),1)</math>

	This constraint in the value of ''p'' brings more headache to the problem, because in integrator-part of the controller "runs-off" if the error-value <math>\tilde{e} := min(e_1, e_2)</math> is positive for a long period of the simulation. We'll see that later.		This constraint in the value of ''p'' brings more headache to the problem, because the integrator-part ''E''of the controller "runs-off" if the error-value <math>\tilde{e} := min(e_1, e_2)</math> is positive for a long period of the simulation. We'll see that later.

	==Variables==		==Variables==

Mechaniker: /* Model */

2021-03-22T15:43:14Z

Model

← Nächstältere Version		Version vom 22. März 2021, 15:43 Uhr
Zeile 27:		Zeile 27:

	==Model==		==Model==
	The most common controller in technical applications is a [[wikipedia:PID_controller\|PID-controller]]. Our target value to control is both		The most common controller in technical applications is a [[wikipedia:PID_controller\|PID-controller]] which are based on the proportional, integral, and derivative terms of the error-value. Our target value to control is both
	<ul>		<ul>
	<li>the slip-velocity ''v<sub>rel</sub>'' with set-point <math>r := v_\epsilon</math> and</li>		<li>the slip-velocity ''v<sub>rel</sub>'' with set-point <math>r := v_\epsilon</math> and</li>
Zeile 33:		Zeile 33:
	</ul>		</ul>

	We define the error values e for both as		We define the error values <u>e</u> for both as

	::<math>\begin{array}{ll}		::<math>\begin{array}{ll}
Zeile 49:		Zeile 49:
	The functions for ''e<sub>1</sub>'' ensures that "''p"'' increases e.g. if ''v<sub>rel</sub>'' < ''v<sub>ε</sub>'' and decreases otherwise. [[Datei:JUMP-driver-blockdiagram-controller.png\|mini\|Block-diagram controller]]With controller parameters ''K<sub>p</sub>, Ki, K<sub>d</sub>'' we get this diagram for the controlled system.		The functions for ''e<sub>1</sub>'' ensures that "''p"'' increases e.g. if ''v<sub>rel</sub>'' < ''v<sub>ε</sub>'' and decreases otherwise. [[Datei:JUMP-driver-blockdiagram-controller.png\|mini\|Block-diagram controller]]With controller parameters ''K<sub>p</sub>, Ki, K<sub>d</sub>'' we get this diagram for the controlled system.

	When ~~e_1~~ / ~~e_2~~		When increasing the speed to target-value ''V<sub>set</sub>'', the maximum force delivered at the point of contact ''C'' governs the acceleration of the car-body.
			Thus, we set the relevant error-value to be

			::<math>\tilde{e} := min(e_1, e_2)</math>

	The controller ~~adds~~ thus adds the state variable		The controller thus adds to the state variable

	::<math>E_I := \displaystyle \int_0^t e(\tau) d\tau</math>		::<math>E_I := \displaystyle \int_0^t \tilde{e}(\tau) d\tau</math>

	to the system. ~~And~~ we need to find		of the system.

			For the differentiator-part we would need to find

	::<math>\begin{array}{ll}		::<math>\begin{array}{ll}
Zeile 69:		Zeile 73:
	::<math>\underline{q}_D(t) = \left(E(t)\right)</math> .		::<math>\underline{q}_D(t) = \left(E(t)\right)</math> .

	The output "p" of the submodel is not a state variable, but		The output "p" of the submodel is not directly a state variable, but

			::<math>p^*(t) = K_p\cdot e(t) + K_i\cdot E(t) + K_d\cdot \dot{e}(t) </math>

			But since the DC/DC-converter can only take values between 0 ... 1 we define

			::<math>p(t) = \min(\max(p^*,0),1)</math>

	::<math>~~p(t) = K_p~~\~~cdot e(t) + K_i\cdot E(t) + K_d\cdot \dot~~{e}(t) </math>		This constraint in the value of ''p'' brings more headache to the problem, because in integrator-part of the controller "runs-off" if the error-value <math>\tilde{e} := min(e_1, e_2)</math> is positive for a long period of the simulation. We'll see that later.

	==Variables==		==Variables==

Mechaniker: /* Model */

2021-03-22T15:29:30Z

Model

← Nächstältere Version		Version vom 22. März 2021, 15:29 Uhr
Zeile 36:		Zeile 36:

	::<math>\begin{array}{ll}		::<math>\begin{array}{ll}
	e_1 &= f(\tilde{v}) \text{ with } \tilde{v} = \frac{\displaystyle v_{rel}}{\displaystyle v_{\varepsilon}}; \text{ here we choose }\\		e_1 &= f_1(\tilde{v}) \text{ with } \tilde{v} = \frac{\displaystyle v_{rel}}{\displaystyle v_{\varepsilon}}; \text{ here we choose }\\
	&= 1-\tilde{v}		&= 1+\tilde{v}
	\end{array}</math>		\end{array}</math>

Zeile 43:		Zeile 43:

	::<math>\begin{array}{ll}		::<math>\begin{array}{ll}
	e_2 &= f(\tilde{v}) \text{ with } \tilde{v} = \frac{\displaystyle v_{~~rel~~}}{\displaystyle v_{~~\varepsilon~~}}; \text{ here we choose }\\		e_2 &= f_2(\tilde{v}) \text{ with } \tilde{v} = \frac{\displaystyle v_{c}}{\displaystyle V_{set}}; \text{ here we choose }\\
	&= 1-\tilde{v}		&= 1-\tilde{v}
	\end{array}</math>.		\end{array}</math>.

	The ~~function~~ for ''e'' ensures that "''p"'' increases if ''v<sub>rel</sub>'' < ''v<sub>ε</sub>'' and decreases otherwise. [[Datei:JUMP-driver-blockdiagram-controller.png\|mini\|Block-diagram controller]]With controller parameters ''K<sub>p</sub>, Ki, K<sub>d</sub>'' we get this diagram for the controlled system.		The functions for ''e<sub>1</sub>'' ensures that "''p"'' increases e.g. if ''v<sub>rel</sub>'' < ''v<sub>ε</sub>'' and decreases otherwise. [[Datei:JUMP-driver-blockdiagram-controller.png\|mini\|Block-diagram controller]]With controller parameters ''K<sub>p</sub>, Ki, K<sub>d</sub>'' we get this diagram for the controlled system.

			When e_1 / e_2


	The controller adds thus adds the state variable		The controller adds thus adds the state variable

Mechaniker: /* Model */

2021-03-22T15:26:03Z

Model

← Nächstältere Version		Version vom 22. März 2021, 15:26 Uhr
Zeile 27:		Zeile 27:

	==Model==		==Model==
	The most common controller in technical applications is a [[wikipedia:PID_controller\|PID-controller]]. Our target value to control is ''v<sub>rel</sub>''~~, our~~ set-point is		The most common controller in technical applications is a [[wikipedia:PID_controller\|PID-controller]]. Our target value to control is both
			<ul>
			<li>the slip-velocity ''v<sub>rel</sub>'' with set-point <math>r := v_\epsilon</math> and</li>
			<li>the cruising-velocoty ''v<sub>c</sub>'' with set-point <math>r := V_{set}</math>.</li>
			</ul>

	~~::<math>r := v_\epsilon</math> .~~		We define the error values e for both as

	and ~~we define the error value e as~~		::<math>\begin{array}{ll}
			e_1 &= f(\tilde{v}) \text{ with } \tilde{v} = \frac{\displaystyle v_{rel}}{\displaystyle v_{\varepsilon}}; \text{ here we choose }\\
			&= 1-\tilde{v}
			\end{array}</math>

			and

	::<math>\begin{array}{ll}		::<math>\begin{array}{ll}
	e &= f(\tilde{v}) \text{ with } \tilde{v} = \frac{\displaystyle v_{rel}}{\displaystyle v_{\varepsilon}}; \text{ here we choose }\\		e_2 &= f(\tilde{v}) \text{ with } \tilde{v} = \frac{\displaystyle v_{rel}}{\displaystyle v_{\varepsilon}}; \text{ here we choose }\\
	&= 1-\tilde{v}		&= 1-\tilde{v}
	\end{array}</math> .		\end{array}</math>.

	The function for ''e'' ensures that "''p"'' increases if ''v<sub>rel</sub>'' < ''v<sub>ε</sub>'' and decreases otherwise. [[Datei:JUMP-driver-blockdiagram-controller.png\|mini\|Block-diagram controller]]With controller parameters ''K<sub>p</sub>, Ki, K<sub>d</sub>'' we get this diagram for the controlled system.		The function for ''e'' ensures that "''p"'' increases if ''v<sub>rel</sub>'' < ''v<sub>ε</sub>'' and decreases otherwise. [[Datei:JUMP-driver-blockdiagram-controller.png\|mini\|Block-diagram controller]]With controller parameters ''K<sub>p</sub>, Ki, K<sub>d</sub>'' we get this diagram for the controlled system.

Mechaniker: /* Parameter */

2021-03-22T15:07:44Z

Parameter

← Nächstältere Version		Version vom 22. März 2021, 15:07 Uhr
Zeile 104:		Zeile 104:
	\|m/s		\|m/s
	\|}		\|}
	~~<hr/>~~
	[[Gelöste Aufgaben/JUMP/E-Motor and Drive-Train\|next workpackage: e-motor and drive-train →]]		[[Gelöste Aufgaben/JUMP/E-Motor and Drive-Train\|next workpackage: e-motor and drive-train →]]

			<hr/>
	'''References'''		'''References'''

	# Yuan, Lei; Chen, Hong; Ren, Bingtao; Zhao, Haiyan: Model predictive slip control for electric vehicle with four in-wheel motors, Proceedings of the 34th Chinese Control Conference July 28-30, 2015, Hangzhou, China, p 7895-7900		# Yuan, Lei; Chen, Hong; Ren, Bingtao; Zhao, Haiyan: Model predictive slip control for electric vehicle with four in-wheel motors, Proceedings of the 34th Chinese Control Conference July 28-30, 2015, Hangzhou, China, p 7895-7900
	# ...		# ...

Mechaniker: /* Parameter */

2021-03-22T15:07:12Z

Parameter

← Nächstältere Version		Version vom 22. März 2021, 15:07 Uhr
Zeile 107:		Zeile 107:
	[[Gelöste Aufgaben/JUMP/E-Motor and Drive-Train\|next workpackage: e-motor and drive-train →]]		[[Gelöste Aufgaben/JUMP/E-Motor and Drive-Train\|next workpackage: e-motor and drive-train →]]

	~~<hr/>~~
	'''References'''		'''References'''

	# Yuan, Lei; Chen, Hong; Ren, Bingtao; Zhao, Haiyan: Model predictive slip control for electric vehicle with four in-wheel motors, Proceedings of the 34th Chinese Control Conference July 28-30, 2015, Hangzhou, China, p 7895-7900		# Yuan, Lei; Chen, Hong; Ren, Bingtao; Zhao, Haiyan: Model predictive slip control for electric vehicle with four in-wheel motors, Proceedings of the 34th Chinese Control Conference July 28-30, 2015, Hangzhou, China, p 7895-7900
	# ...		# ...

Mechaniker: /* Parameter */

2021-03-22T15:07:00Z

Parameter

← Nächstältere Version		Version vom 22. März 2021, 15:07 Uhr
Zeile 76:		Zeile 76:
	!name		!name
	!symbol		!symbol
			!value
	!unit		!unit
	\|-		\|-
	\|coefficient of proportional contribution		\|coefficient of proportional contribution
	\|''K<sub>p</sub>''		\|''K<sub>p</sub>''
			\|
	\|1/s		\|1/s
	\|-		\|-
	\|coefficient of integrator contribution		\|coefficient of integrator contribution
	\|''K<sub>i</sub>''		\|''K<sub>i</sub>''
			\|100
	\|1/s^2		\|1/s^2
	\|-		\|-
	\|coefficient of differential contribution		\|coefficient of differential contribution - not employed
	\|''K<sub>d</sub>''		\|''K<sub>d</sub>''
			\|
	\|1		\|1
			\|-
			\|max. tolerated battery temperature
			\|''T<sub>B,max</sub>''
			\|60
			\|°C
			\|-
			\|target-speed (choose very high when you want "pedal to the metal")
			\|''V<sub>set</sub>''
			\|10
			\|m/s
	\|}		\|}
			<hr/>
	[[Gelöste Aufgaben/JUMP/E-Motor and Drive-Train\|next workpackage: e-motor and drive-train →]]		[[Gelöste Aufgaben/JUMP/E-Motor and Drive-Train\|next workpackage: e-motor and drive-train →]]

Mechaniker: /* Model */

2021-03-16T12:45:04Z

Model

← Nächstältere Version		Version vom 16. März 2021, 12:45 Uhr
Zeile 47:		Zeile 47:

	::<math>\begin{array}{ll}		::<math>\begin{array}{ll}
	\dot{e} &= \frac{\displaystyle \d e(t)}{\displaystyle d t}\\		\dot{e} &= \frac{\displaystyle d\, e(t)}{\displaystyle d\, t}\\
	&=\frac{\displaystyle 1}{\displaystyle v_{red}} \cdot \frac{\displaystyle d v_{rel}(t)}{\displaystyle d t}\\		&=\frac{\displaystyle 1}{\displaystyle v_{red}} \cdot \frac{\displaystyle d v_{rel}(t)}{\displaystyle d t}\\
	\end{array}</math>		\end{array}</math>