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Notes_1_flight - S/Mpc 5‘ FFEE 34 at”[ox/CE?” 3455...

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Vé’flé’éfl/V 5, A/WMMX @4er 24,94, 7/15/09 4:54 PM P:\ae36l\AE36l O6 MATLAB\Space Capsulel del O9.m l of 1 __—____________—_~___——_———_—_—————_—- ___._._____———_————~—-_——-———_——-— %space capsule with feedback dynamics %differential equation 9 0 function dedemo %ode45 demo 0, a clear all clc 0, o Ml=lOOO K=8000 xf=l tspan=O:0.0l:lO; XO=[O 0]; [t,x]=ode45(@derhs,tspan,x0,,M1,K,Xf); figure(l) plot(t,x(:,l)) title('displacement time history') xlabel('time') ylabel('displacement') function dxdt=derhs(t,X,Ml,K,xf) %right hand side for ode45 demo dxdt=[x(2) —(K/Ml)*x(l)+K/Ml*xf]; 7/15/09 4:55 PM P:\ae36l\AE36l 06 MATLAB\Space Capsulel de2 09.m l of 1 W %space capsule with proportional plus derivative control differential equation 0\° 0\° 0\° 0\° function dedemo i %ode45 demo clear all clc Ml=lOOO ‘ K=8000 E alpha=l beta=l xf=l tspan=O:0.0l:5; x0=[0 -(K/Ml)*beta*xf]; I [t,x]=ode45(@derhs,tspan,x0,,M1,K,alpha,beta,xf); figure(l) plot(t,x(:,l)) title('displacement time history') x1abel('time') ylabel('displacement') function dxdt=derhs(t,x,Ml,K,alpha,beta,xf) %right hand side for ode45 demo dxdt=[—(K/Ml)*beta*x(l)+x(2)+(K/Ml)*beta*xf -(K/Ml)*alpha*x(l)+K/M1*alpha*xf]; 7/15/09 4:47 PM P:\ae36l\AE361 O6 MATLAB\Space Capsulel de2 lti O9.m l of l %space capsule with proportional plus derivative control differential equation o\° o\° o\° o\° function dedemo %ode45 demo 0 6 _: clear all -§ clc °/ 0 Ml=1000 K=8000 alpha=l beta=1 xf=l a=[—(K/Ml)*beta l;—(K/M1)*alpha O]; b=[(K/Ml)*beta;K/Ml*alpha]; c=[l 01; d=[O] SYS=ss(a,b,c,d); tspan=O:0.01:3; %for this initial condition the force xf=l at t=0 %corresponds to a constant input % x0=[0 —(K/Ml) *beta*xf]} %for this initial condition the force xf=0 at t=0 and then %jumps to xf=l. Or responds to a unit step function XO=[O O] [t,x]=ode45(@derhs,tspan,x0,,a,b,c,d,xf); figure(l) plot(t,x(:,l)) title('displacement time history') xlabel('time') ylabel('displacement') figure(2) step(SYS) title('displacement time history') xlabel('time') .ylabel('displacement') function dxdt=derhs(t,X,a,b,c,d,xf) %right hand side for ode45 demo dxdt=a*x+b*xf; 7/15/09 4:48 PM P:\ae36l\AE36l 06 MATLAB\Space Capsulel de3 09.m l of l ========================================================================================== %space capsule with proportional plus %derivative control and feedback dynamics j %differential equation function dedemo %ode45 demo clear all clc Ml=lOOO K=8000 alpha=l l beta=1 i Xf=l tau=lO tspan=O:0.01:5; XO=[O -(K/Ml)*beta*xf 0]; [t,x]=ode45(@derhs,tspan,x0,,Ml,K,alpha,beta,tau,xf) figure(l) plot(t,x(:,l)) I title('displacement time history') xlabel('time') ylabel('displacement') function dxdt=derhs(t,x,Ml,K,alpha,beta,tau,xf) x %right hand side for ode45 demo dxdt=[x(2)~K*(beta/Ml)*x(3)+K*(beta/Ml)*xf l —K*(alpha/Ml)*X(l)+K*(alpha/M1)*xf —tau*x(3)+tau*x(l)]; 7/15/09 4:48 PM P:\ae36l\AE361 06 MATLAB\Space Capsulel de4 O9.m l of l %space capsule with proportional plus %derivative control,feedback dynamics %and actuator dynamics%space capsule with feedback dynamics lg %differential equation function dedemo %ode45 demo 0 5 , clear all 3 clc °/ 0 Ml=1000 K=332 alpha=l beta=4 xf=l tau1=7 tau2=10 tspan=0:0.0l:20; x0=[0 O —K*taul*beta*xf 0]; [t,x]=ode45(@derhs,tspan,xo,,Ml,K,alpha,beta,taul,tau2,xf); figure(l) é plot(t,x(:,l)) title('displacement time history') xlabel('time') ylabel('displacement') function dxdt=derhs(t,x,Ml,K,alpha,beta,taul,tau2,xf) %right hand side for ode45 demo dxdt=[x(2) (l/M1)*x(3)—K*(taul/Ml)*beta*x(4)+K*(taul/Ml)*beta*xf —taul*x (3) '-K* (taul*alpha—taul"2*beta) *x (4) +K* (taul*alpha—taul"2*beta) *Xf i i g i —tau2*x(4)+tau2*x(l)]; i ¥ 7/15/09 4:49 PM P:\ae36l\AE361 O6 MATLAB\Space Capsulel de4 lti O9.m l of 1 ====================================================================================== %space capsule with proportional plus %derivative control,feedback dynamics °and actuator dynamics in LTI form differential equation 0\° 0\° 0\° 0\ function dedemo %ode45 demo a 6 “s‘ "f clear all clc °/ 0 E Ml=lOOO K=332 alpha=l beta=4 Xf=l taul=7 tau2=10 a=[0 1 O O;O 0 1/Ml —K*(taul/Ml)*beta ;O 0 ~taul —K*(taul*alpha—taul‘2*beta);tau2 O 0 —K tau2]; b=[O;taul/Ml*beta;taul*alpha—taul*2*beta;O]; C=[O O O l]; d=[0]; x tspan=O:0.0l:20; XO=[0 0 —K*taul*beta*xf O]; [t,x]=ode45(@derhs,tspan,x0,,a,b,c,d,K,xf); figure(l) plot(t,x(:,l)) i title('displacement time history') xlabel('time') ylabel('displacement') ‘ function dxdt=derhs(t,x,a,b,c,d,K,xf) %right hand side for ode45 demo dxdt=a*X+K*b*Xf; éwmg 77M? //\//42?mM/f* JyvvrfiMiw/ATI) x ; Mix «ya [52% V : [CJX =+ [fijfi Aflmww 512:9) Kw» W m» w W MM away MK! ng KKK {'ng fix AK fag“; K/XM [-3.7/ '[b]/ [C 7/ [4/] //V&F-/>E/\/&FW7’ or 77/442: 4%?“ Viagra D S /5’ 5w , X 3 WquM I WJ‘QZXwé/W’gégé’ -/~ G $2M AVE @fiM U (2”4’47 )‘L" Mf/v 73%? 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