RLC Circuit of February 10, 2011 - Revision history

Kelvin.bidwell at 08:56, 15 March 2011

2011-03-15T08:56:42Z

← Older revision		Revision as of 01:56, 15 March 2011
Line 121:		Line 121:
	xlabel('Time (seconds)')		xlabel('Time (seconds)')

	~~There is a problem with this script, because the eigenvalues of Atot are not what we tried to set them to be. If you figure out what is wrong, fix it~~! The notes that go with this work are from February 28 through March 4.		Fixed!
			The notes that go with this work are from February 28 through March 4.

Kelvin.bidwell at 08:53, 15 March 2011

2011-03-15T08:53:02Z

← Older revision		Revision as of 01:53, 15 March 2011
Line 97:		Line 97:
	H=B2-LC1B1		H=B2-LC1B1

	G=place(~~sys1~~,[-1.5 -2.5]) %Place the poles for the controller		G=place(sysr,[-1.5 -2.5]) %Place the poles for the controller
	printf("Check to see if the place did the right thing.")		printf("Check to see if the place did the right thing.")
	printf("The poles after feedback are at: ")		printf("The poles after feedback are at: ")
	controller_poles = eig(A-B*G)		controller_poles = eig(Ar-Br*G)
	G1=-G(1:1) % The minus is because we derived it with a u=+Gx and octave		G1=-G(1:1) % The minus is because we derived it with a u=+Gx and octave
	% uses u=-Gx		% uses u=-Gx

Frohro: /* Reduced Order Observer Simulation */

2011-03-07T20:22:59Z

Reduced Order Observer Simulation

← Older revision		Revision as of 13:22, 7 March 2011
Line 121:		Line 121:
	xlabel('Time (seconds)')		xlabel('Time (seconds)')

	There is a problem with this script, because the eigenvalues of Atot are not what we tried to set them to be. If you figure out what is wrong, fix it!		There is a problem with this script, because the eigenvalues of Atot are not what we tried to set them to be. If you figure out what is wrong, fix it! The notes that go with this work are from February 28 through March 4.

Frohro: /* Reduced Order Observer Simulation */

2011-03-07T20:21:36Z

Reduced Order Observer Simulation

← Older revision		Revision as of 13:21, 7 March 2011
Line 64:		Line 64:

	% This script is to design a reduced order observer and control		% This script is to design a reduced order observer and control
	% system for our RLC Circuit.		% system for our RLC Circuit.

	clear		clear

			delta_t=.0001;
			t_end=2;
			x0=[5 5 0]'

	c=2 %Capacitance		c=2 %Capacitance
	R=3 %Resistance		R=3 %Resistance
Line 80:		Line 85:
	Cr=C*T^(-1)		Cr=C*T^(-1)
	sysr=ss(Ar,Br,Cr,0);		sysr=ss(Ar,Br,Cr,0);
	C1=Cr(1)		C1=Cr(1:1)
	A11=Ar(1,1)		A11=Ar(1:1,1:1)
	A12=Ar(1,2)		A12=Ar(1:1,2:2)
	A21=Ar(2,1)		A21=Ar(2:2,1:1)
	A22=Ar(2,2)		A22=Ar(2:2,2:2)
	B1=Br(1)		B1=Br(1:1)
	B2=Br(2)		B2=Br(2:2)
	poles=[-20]		poles=[-20]
	L=place(A22',A12'*C1',poles)		L=(place(A22',A12'*C1',poles))'
	M=A21C1^(-1)-LC1A11C1^(-1)		M=A21C1^(-1)-LC1A11C1^(-1)
	H=B2-LC1B1		H=B2-LC1B1

	g=place(sys1,[-1.5 -2.5]); %Place the poles for the controller		G=place(sys1,[-1.5 -2.5]) %Place the poles for the controller
	printf("Check to see if the place did the right thing.")		printf("Check to see if the place did the right thing.")
	printf("The poles after feedback are at: ")		printf("The poles after feedback are at: ")
	controller_poles = eig(A-B*g)		controller_poles = eig(A-B*G)
			G1=-G(1:1) % The minus is because we derived it with a u=+Gx and octave
	~~More~~ to ~~come...~~.		% uses u=-Gx
			G2=-G(2:2) % The minus is because we derived it with a u=+Gx and octave
			% uses u=-Gx
			F22=A22-LC1A12

			Atot=[[A11+B1G1,A12,B1G2];[A21+B2G1, A22, B2G2];
			[LC1(A11+B1G1)+HG1+MC1,LC1A12,LC1B1G2+F22+H*G2]];
			Btot=[0 0 0]'

			systot=ss(Atot,Btot);
			polestot=pole(systot)
			t=0:delta_t:t_end;
			[X,Y]=lsim(systot, zeros(size(t))', t', x0);

			plot(t,X)
			legend('xm','xum','xhatum')
			title('Reduced Order Observer Simulation')
			xlabel('Time (seconds)')

			There is a problem with this script, because the eigenvalues of Atot are not what we tried to set them to be. If you figure out what is wrong, fix it!

Frohro: /* Reduced Order Observer Simulation */

2011-03-03T21:04:49Z

Reduced Order Observer Simulation

← Older revision		Revision as of 14:04, 3 March 2011
Line 65:		Line 65:
	% This script is to design a reduced order observer and control		% This script is to design a reduced order observer and control
	% system for our RLC Circuit.		% system for our RLC Circuit.

	clear		clear
	c=2 %Capacitance		c=2 %Capacitance

Frohro at 21:04, 3 March 2011

2011-03-03T21:04:20Z

← Older revision		Revision as of 14:04, 3 March 2011
Line 58:		Line 58:

	[[File:RLC_control_delay.png\|600px]]		[[File:RLC_control_delay.png\|600px]]

			===Reduced Order Observer Simulation===

			Here is the code for simulating the reduced order observer:

			% This script is to design a reduced order observer and control
			% system for our RLC Circuit.

			clear
			c=2 %Capacitance
			R=3 %Resistance
			L=4 %Inductance
			A=[[0 -1/L];[1/c -1/(R*c)]]
			B=[1/L; 0]
			C=[0 1]
			D=0
			sys1=ss(A,B,C,D);
			T=fliplr(eye(2)) %Transformation Matrix for swapping states
			Ar=TAT^(-1) %Transformed system
			Br=T*B
			Cr=C*T^(-1)
			sysr=ss(Ar,Br,Cr,0);
			C1=Cr(1)
			A11=Ar(1,1)
			A12=Ar(1,2)
			A21=Ar(2,1)
			A22=Ar(2,2)
			B1=Br(1)
			B2=Br(2)
			poles=[-20]
			L=place(A22',A12'*C1',poles)
			M=A21C1^(-1)-LC1A11C1^(-1)
			H=B2-LC1B1

			g=place(sys1,[-1.5 -2.5]); %Place the poles for the controller
			printf("Check to see if the place did the right thing.")
			printf("The poles after feedback are at: ")
			controller_poles = eig(A-B*g)

			More to come....

Frohro at 18:52, 23 February 2011

2011-02-23T18:52:05Z

← Older revision		Revision as of 11:52, 23 February 2011
Line 56:		Line 56:

	The controller exacerbates the overshoot because the observer has significant error on one state variable until about .2 seconds. In order to help the situation, we can just not drive the circuit until the observer has caught up. This cuts the overshoot roughly in half.		The controller exacerbates the overshoot because the observer has significant error on one state variable until about .2 seconds. In order to help the situation, we can just not drive the circuit until the observer has caught up. This cuts the overshoot roughly in half.

			[[File:RLC_control_delay.png\|600px]]

Frohro at 18:48, 23 February 2011

2011-02-23T18:48:18Z

← Older revision		Revision as of 11:48, 23 February 2011
Line 53:		Line 53:
	polestot_transformed=eig(TAtotTI);		polestot_transformed=eig(TAtotTI);

	[[File:RLC_control.png]]		[[File:RLC_control.png\|600px]]

	The controller exacerbates the overshoot because the observer has significant error on one state variable until about .2 seconds. In order to help the situation, we can just not drive the circuit until the observer has caught up. This cuts the overshoot roughly in half.		The controller exacerbates the overshoot because the observer has significant error on one state variable until about .2 seconds. In order to help the situation, we can just not drive the circuit until the observer has caught up. This cuts the overshoot roughly in half.

Frohro at 18:46, 23 February 2011

2011-02-23T18:46:02Z

← Older revision		Revision as of 11:46, 23 February 2011
Line 52:		Line 52:
	TAtotTI=TAtotT^(-1);		TAtotTI=TAtotT^(-1);
	polestot_transformed=eig(TAtotTI);		polestot_transformed=eig(TAtotTI);

			[[File:RLC_control.png]]

	The controller exacerbates the overshoot because the observer has significant error on one state variable until about .2 seconds. In order to help the situation, we can just not drive the circuit until the observer has caught up. This cuts the overshoot roughly in half.		The controller exacerbates the overshoot because the observer has significant error on one state variable until about .2 seconds. In order to help the situation, we can just not drive the circuit until the observer has caught up. This cuts the overshoot roughly in half.

Frohro at 18:43, 23 February 2011

2011-02-23T18:43:41Z

← Older revision		Revision as of 11:43, 23 February 2011
Line 52:		Line 52:
	TAtotTI=TAtotT^(-1);		TAtotTI=TAtotT^(-1);
	polestot_transformed=eig(TAtotTI);		polestot_transformed=eig(TAtotTI);

			The controller exacerbates the overshoot because the observer has significant error on one state variable until about .2 seconds. In order to help the situation, we can just not drive the circuit until the observer has caught up. This cuts the overshoot roughly in half.