I am trying to run my simulink file which have pid controller connected to s-function block.
When i set three values parameters of pid which are proportional, integral and derivatives it takes too long to run the whole process. Why this is happened?
In the dialog box of my pid diagram, for porportional value, its equal to the value which correspond to the constant amplitude oscillation.
Then for integral, its equal to Kcu/Ti. Ti is the ultimate period(Pu)/2 and
lastly for derivatives, its equal tu Kcu*Td and Td is Pu /8. This is refer to ziegler nichols method. and again my question is why it takes too long to running this file?
MATLAB S-functions are slow because they run in the MATLAB interpreter. Consider implementing it using Simulink blocks or using a "Embedded MATLAB Function" (pre-R2011a) or "MATLAB Function" (R2011a+) block.
Read Guy and Seth's thoughts on Simulation performance.
#Nzbuu is right about the Matlab S-functions.
But I think the problem here could be somewhere else: #Syarina are you saying that the Simulink simulation gets slower after you set the proportional coefficient for the controller? If you simulate the plant alone, in this case the S-function, do you notice a significant difference in the execution speed? If it is really so, I suppose the PID controller makes the ODE system stiff. This means that the different states of the ODE system have really different dynamics - some are very fast, some are very slow. Using an ode-solver that is not suited for stiff equations you will find the simulation much slower (actually you would have luck if it converges at all).
My suggestion is try to change the solver - for example ode15s.
Related
Hopefully, I will be able to explain my question well.
I am working on Nonlinear model predictive control implementation.
I have got 3 files:
1). a simulink slx file which is basically a nonlinear pendulum model.
2). A function file, to get the cost function from the simulink model.
3). MPC code.
code snippet of cost function
**simOut=sim('NonlinearPendulum','StopTime', num2str(Np*Ts));**
%Linearly interpolates X to obtain sampled output states at time instants.
T=simOut.get('Tsim');
X=simOut.get('xsim');
xt=interp1(T,X,linspace(0,Np*Ts,Np+1))';
U=U(1:Nu);
%Quadratic cost function
R=0.01;
J=sum(sum((xt-repmat(r,[1 Np+1])).*(xt-repmat(r,[1 Np+1]))))+R*(U-ur)*...
(U-ur)';
Now I take this cost function and optimize it using fmincon to generate a sequence of inputs to be applied to the model, using my MPC code.
A code snippet of my MPC code.
%Constraints -1<=u(t)<=1;
Acons=[eye(Nu,Nu);-eye(Nu,Nu)];
Bcons=[ones(Nu,1);ones(Nu,1)];
options = optimoptions(#fmincon,'Algorithm','active-set','MaxIter',100);
warning off
for a1=1:nf
X=[]; %Prediction output
T=[]; %Prediction time
Xsam=[];
Tsam=[];
%Nonlinear MPC controller
Ubreak=linspace(0,(Np-1)*Ts,Np); %Break points for 1D lookup, used to avoid
% several calls/compilations of simulink model in fmincon.
**J=#(v) pendulumCostFunction(v,x0,ur,r(:,a1),Np,Nu,Ts);**
U=fmincon(J,U0,Acons,Bcons,[],[],[],[],[],options);
%U=fmincon(J,U0,Acons,Bcons);
U0=U;
UUsam=[UUsam;U(1)];%Apply only the first selected input
%Apply the selected input to plant.
Ubreak=[0 Ts]; %Break points for 1D lookup
U=[UUsam(end) UUsam(end)];
**simOut=sim('NonlinearPendulum','StopTime', num2str(Ts));**
In both the codes, I have marked the times we call our simulink model. Now, issue is that to run this whole simulation for just 5 seconds it takes around 7-8 minutes on my windows machine, MATLAB R2014B.
Is there a way to optimize this? As, I am planning to extend this algorithm to 9th order system unlike 2nd order pendulum model.
If, anyone has suggestion on using simulink coder to generate C code:
I have tried that, and the problem I face is that I don't know what to do with the several files generated. Please be as detailed as possible.
From the code snippets, it appears that you are solving a linear time invariant model with a quadratic objective. Here is some MATLAB (and Python) code for an overhead crane pendulum and inverted pendulum, both with state space linear models and quadratic objectives.
One of the ways to make it run faster is to avoid a Simulink interface and a shooting method for solving the MPC. A simultaneous method with orthogonal collocation on finite elements is faster and also enables higher index DAE model forms if you'd like to use a nonlinear model.
Recently I have been performing simulations on some dynamical system, where all the dynamical quantities are interdependent. To therefore simulate the dynamics I performed loops over small time steps dt<<1 and changed the quantities within each iteration. The simulations were done in respectively Mathematica and Matlab.
I got nice results but simulations could take quite long due to the slow iteration process. Generally I hear that one should avoid for loops like I have used, because they slow down the simulation greatly. On the other hand however I am clueless on how to do the simulations without iterations in small time steps. Therefore I ask you: For a dynamical system, where every quantity must be changed in ultra small time steps, what are then the possible methods for for simulating the dynamics.
The straightforward approach is to write the problem as a set of differential equations and use the ODE solving capabilities of either system. Both MATLAB and Mathematica have advanced (and customizable) numerical differential equation solvers, and they both support special "events" in the differential equations that can't be expressed using a simple formula (e.g. the event of a ball bouncing back from the floor).
For Mathematica, first check out NDSolve, WhenEvent then later the Advanced Numerical Differential Equation Solving tutorial.
From your description it sounds like you may be using a naive ODE solving method such as the Euler method. Using a better numerical ODE solving technique can give significant effective speedups (by not forcing you to use "ultra small time steps").
If performance is paramount, consider re-implementing the simulation in a low-level language like C or C++, and possibly making it callable from Mathematica (LibraryLink) to allow easy data analysis and visualization.
I believe I am doing something fundamentally wrong when trying to import and test a transfer function in Simulink which was created within the System Identification Toolbox (SIT).
To give a simple example of what I am doing.
I have an input which is an offset sinusoidal wave from 12 seconds to 25 seconds with an amplitude of 1 and a frequency of 1.5rad/s which gives a measured output.
I have used SIT to create a simple 2 pole 1 zero transfer function which gives the following agreement:
I have then tried to import this transfer function into Simulink for investigation in the following configuration which has a sinusoidal input of frequency 1.5rad/s and a starting t=12. The LTI system block refers to the transfer function variable within the workspace:
When I run this simulation for 13 seconds the input to the block is as expected but the post transfer function signal shows little agreement with what would be expected and is an order of magnitude out.
pre:
post:
Could someone give any insight into where I am going wrong and why the output from the tf in simulink shows little resemblance to the model output displayed in the SIT. I have a basic grasp of control theory but I am struggling to make sense of this.
This could be due to different initial conditions used in SimuLink and the SI Toolbox, the latter should estimate initial conditions with the model, while Simulink does nothing special with initial conditions unless you specify them yourself.
To me it seems that your original signals are in periodic regime, since your output looks almost like a sine wave as well. In periodic regime, initial conditions have little effect. You can verify my assumption by simulating your model for a longer amount of time: if at the end, your signal reaches the right amplitude and phase lag as in your data, you will know that the initial conditions were wrong.
In any case, you can get the estimated initial state from the toolbox, I think using the InitialState property of the resulting object.
Another thing that might go wrong, is the time discretization that you use in Simulink in case you estimated a continuous time model (one in the Laplace variable s, not in z or q).
edit: In that case I would recommend you check what Simulink uses to discretize your CT model, by using c2d in MATLAB and a setup like the one below in Simulink. In MATLAB you can also "simulate" the response to a CT model using lsim, where you have to specify a discretization method.
This set-up allows you to load in a CT model and a discretized variant (in this case a state-space representation). By comparing the signals, you can see whether the discretization method you use is the same one that SimuLink uses (this depends on the integration method you set in the settings).
I wrote a code to solve a system using ode45 and ode15s in matlab. I am wondering if I can improve the speed of the code using multiple core (or parallel code) in my script.
Anyone have tried this ??
Thanks
No, you can't.
All numerical integrators, ode45 and friends included, use some form of iterative scheme to solve the user-implemented (coupled) non-linear (partial) differential equations.
Each new step in the iterative schemes of ode45/15s/.. (to compute the new state of the system) depends on the previous step (the old state of the system), therefore, these numerical integrators cannot be parallelized effectively.
The only speedup you can do that's likely to have a big impact is to optimize your implementation of the differential equation.
From my experience, the only way to use multiple cores for ODE suite solvers in MATLAB is to use "parfor loop" to start multiple computations together at the same time, your single computation not be any faster, but you can start many with different parameters and have multiple solutions after that long wait. So if you need to start ODE many times that might speed up your work.
To speed up one ODE function it also a good idea to play with RelTol and AbsTol settings (changes time form seconds to hours), using Jpattern option can also be very helpful (my almost tridiagonal pattern made it run twice as fast). If your differential equation is simple maybe try to compile it first, or at least vectorize (I used to write some part of code in Java and then point MATLAB to use compiled .class file). Obviously the length of your solution vector plays important role, so don't make it more than a few hounded.
I have a Simulink model that includes the following subsystem.
The bm_train_adapter block will call a MATLAB function of the same name, passing all the input arguments in a single vector.
The subsystem has been given a sample time of 900 (secs), which is why all the signals are colored in red (for discrete signals).
However, in the debugger I have observed that the bm_train_adapter function gets called twice at each simulation timestep. This yields horribly wrong results since the function includes side-effects.
Why is Simulink calling my interpreted MATLAB function more than once per timestep? How can I prevent this?
I think this is because of your solver setup. In your Configuration Parameters window, check out the Solver Options pane.
I believe the discrete and ode1 solvers will call once per timestep. ode2 will call twice per timestep, ode4 will call 4 times per timestep, etc.
This behavior is very helpful for simulating continuous dynamics, but it can be confusing when interacting with discrete elements.
The reason was that my model had algebraic loops caused by unit delay blocks in subsystems. To solve these loops, the solver had no choice but to evaluate some blocks more than once.
The solution was to move out all unit delays from their subsystems.