Solve state space equation by ODE45

In order to solve an ODE using ode45, you need to first define the function to describe the complete dynamics. In the linear state space system you provided, the definition of u is missing. In general, u can be designed as a linear feedback control law, such as u = Kx, where K is a 50-by-50 matrix. Let me give you a simpler example here. Suppose we have A = [0 1; -2 3]; B = [0;1]; K = [-1 -1]; Then, the system function can be constructed as

function  dx = sys(t, x)
   A = [0 1; -2 3]; B = [0;1]; K = [-1 -1]; 
   u = K*x
   dx = A*x + B*u;
end

Please save the above function in an MATLAB file and name is as sys.m

Then, in a separate MATLAB script file or in the command window, you can simulate the system by executing the following

>> tspan = [0 10];
>> iniCon = [1;-1]
>> [t, y] = ode45(@sys, tspan, iniCon);

If you would like to show the simulation result in a figure, try executing >> plot(t,y)

For more details regarding ode45, see here .

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savvas 2015-10-5

How is the sys.m file altered for a two input system?

Sunil Ojwani 2018-12-28

how i plot control input u with tspan

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Answer 2

Babak 2014-8-9

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/146782-solve-state-space-equation-by-ode45#answer_148008

Thank you Yu Jiang. After your explanation I could get answer from the solver but still I have a problem for updating. Please have a look on attached picture.

I must update X and U in next step. as you said I must update U inside the function but it didn't work.

function xdot=sys(t,X,A,B,Lsr,Tm)

p=4;Tl=0;Tm=0; J=0.03832; Vab=208;Vbc=208;

U=[Vab,Vbc,zeros(1,46),((Tm-Tl)/J),0]';

xdot=A*X+B*U;

Is=[xdot(1,1),xdot(2,1),-(xdot(1,1)-xdot(2,1))];% 1st calculation

Tm=(p/2)*Is*(Lsr)*xdot(3:48,1); % 2nd calculation

U=[Vab,Vbc,zeros(1,46),((Tm-Tl)/J),0]'; %use 1st and 2nd to update U

end

[t,y]=ode45(@(t,X) sys(t,X,A,B,Lsr,Tm),tspan,X);

X=y; % Update X

Two problems:

1- how can I update the U inside (or outside) the function? (I need xdot to update U)

2- When I solved the equation the dimension of y is not [50,1], then I can not use it as a input again.(X=y ?)

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Yu Jiang 2014-8-9

编辑：Yu Jiang 2014-8-11

From what I understand, this is not an issue with MATLAB, but an issue with control theory.

In standard state-space-based control design, the control signal u is usually a function of x, not a function of xdot. If it is the later case, I think you may need to do some math to rearrange the terms with dot operation to the left-hand side of the equation.

Again, bear in mind that ode45 is used for autonomous systems in the form of dx = f(t,x). No derivative terms of x should appear on the right hand side. If you define Tm using xdot and use it as part of the input u, you are actually introducing xdot to the right hand side of the equation.

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Answer 3

Delcio Macaia 2016-10-19

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/146782-solve-state-space-equation-by-ode45#answer_239762

在 MATLAB Online 中打开

Heloo, i have some questions to ask i have a state space, dx/dt = Ax(t) + Bu(t) , y = C x(t) + D u(t) i know all the values and the size of the matrix's

A is a (6*6)matrix B is a (6*1)matrix C is a (6*6) matrix D is a (6*1) mtrix

 i need to input a signal in my state space system, the signal is a vector (6000*2),
 in the first column i have the time and the second column i have the acelerations

Ts is my simple time Ts = 0.02 the interval of the integration is 0 to 120 [0 120]

 so if i put in matlab --> sys = ss(A,B,C,D,Ts ) 
 how can i input my signal and how can a solve it whit the ODE45 ?

THANKS

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Answer 4

Yasir Ghazi 2017-11-15

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链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/146782-solve-state-space-equation-by-ode45#answer_291346

在 MATLAB Online 中打开

I have Linearized model state-space show below [I need to plot output (P&Q) in matlab ]

 where
a=[-100 -628.32 -1000 0 0 0 0 0 0 0 0;226.19 -100 0 -1000 0 0 0 0 0 0 0;100000 0 0 -628.32 -104790 0 102500 0 0 0 0;0 1e6 226.19 0 0 -37726 0 36902 0 0 0;0 0 325.55 0 -45.54 -376.99 44.375 50.528 212.38 0 0;0 0 0 325.55 376.99 -45.54 -50.528 44.375 -14.612 0 0;0 0 0 0 28.905 0 -29.551 1.5489 1591.1 0 0;0 0 0 0 0 28.905 -1.5489 -29.551 -109.47 0 0;0 0 0 0 0.87472 -0.060182 -0.89748 0.014545 -1.0531 16849 42.123;0 0 0 0 0 0 0 0 -0.025 0 1;0 0 0 0 0 0 0 0 1.25 -20000 -55.302];
b=[4331.6 5243.1 0 0 0;0 -6371.2 -97980 0 0;22411 -4527.5 -7979600 0 0;-7619.9 -17920000 3041500 0 0;-222.94 0 0 0 0;24.59 0 0 0 0;-1591.1 0 0 0 0;109.47 0 0 0 0;0.39844 0 0 0 0;0 0 0 0 0;0 0 0 22.848 -5.3188];
c=[9798 0 0 0 0 0 0 0 0 0 0;0 -16330 0 0 0 0 0 0 0 0 0];
d=[219.62 0 -24528 0 0;108.44 136279 137990 0 0];
and  Input, state and output variables at the operating point for linearization

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ANIL KUMAR BALLA 2019-3-30

i need to give speed bump and steering as inputs to my state space block, but my inputs are in graphical form how to give these two inputs to the same state space block.

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