I am trying to write a non-linear optimization program using fmincon. I want MATLAB to read through a data set and compare those values to the constraints. (It is the size of an electrical generator based on electric and heat demand over a one month period).
How do I start this off?
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I'm running a simulink model from simulink using matlab. My system is mainly in matlab, but I run the slx file and export the outputs to be used in matlab. The simulation is run for 48 seconds (1 second representing an hour). When I get the outputs, I'm expecting it to be the same quality as when I view it in simulink, but it's not. Here is an example of what my data looks like in simulink:
Here is how it looks like when I plot it in matlab (the number of samples becomes 307 when exported)
I tried to change the step size in simulink or change the solver, but this distorted my simulink output as the following.
My solver is ode45, how do I control the sampling frequency of my data so that I don't get different resolution after exporting it to matlab.
P.S Once I export it, I will interpolate the data so that I get samples in between the hours (a sample every minute instead of every hours). If I can do it at once by changing the step size then that will be perfect.
following your advice, I got this plot when I plot it vs time instead of samples
Thank you
You are using a variable-step solver (ODE45) and thus there is a very high chance you won't get a consistent sampling frequency.
The only way to ensure/control the sampling frequency is to use a fixed-step solver (ode4 for instance).
However, as to why the data looks different between the Simulink scope and the plotted data, for variable timestep solvers there is refine factor (configuration parameters -> Data Import/Export -> Additional Parameters). This is by default set to 1. Set this to 100 and you should get a more consistent-looking sample density.
What should be known about the refine factor?
To get smoother output and have a better time resolution, it is much faster to change the refine factor instead of reducing the step size.
When the refine factor is changed, the solvers generate additional points by evaluating a continuous extension formula at those points.
The refine factor applies to variable-step solvers and is most useful when you are using ode45.
Usually a value of 4 produces much smoother results.
https://blogs.mathworks.com/simulink/2009/07/14/refining-the-output-of-a-simulation/
https://uk.mathworks.com/help/simulink/gui/refine-factor.html
There is a nonlinear system which name is 'lect7'(lect7).
I Use Matlab commands trim and linmod to find the operating point (OP) and linearize the system model at that OP (My sys)
I'm interested to know is there any way to get system matrix (A,B,C,D) online and at any cycle in matlab simulink?(I mean in my nonlinear system the Gain (0.707) can changes with time so matrix (A,B,C,D) which obtain using this way doesn't have accuracy when times goes.Is there any way to get these matrix at any time and get the accuracy error between nonlinear model and approximated linear system in simulink online and at every cycle?)
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'm using the genetic algorithm from the MATLAB Global Optimization Toolbox with SimEvents, in order to implement a mixed integer optimization making use of simulation outputs to evaluate the fitness function. My model is pretty similar to the one described in this video from MathWorks website:
http://www.mathworks.it/videos/optimizing-manufacturing-production-processes-68961.html
Reading the documentation, I found that ga can solve constrained problems only if such constraints are linear inequalities. The constraints are supposed to be written as functions of the problem's variables, that in this case are the number of resources used during the simulation.
I would like, instead, to set a constraint that takes into account another simulation output (e.g. the drain utilization), i.e. minimize
objfun = backlog*10000 + cost
where backlog is a simulation output (obtained using simOut.get), considering the following constraint:
drain_utilization > 0.7
where drain_ utilization is another simulation output (again, obtained using simOut.get).
Is it possible or this feature is not supported by the Global Optimization Toolbox?
Thank you in advance and forgive me for any improper term, but I'm new to the Global Optimization Toolbox.