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.
Related
I am learning to build neural networks for regression problems. It works well approximating linear functions. Setup with 1-5–1 units with linear activation functions in hidden and output layers does the trick and results are fast and reliable. However, when I try to feed it simple quadratic data (f(x) = x*x) here is what happens:
With linear activation function, it tries to fit a linear function through dataset
And with TANH function it tries to fit a a TANH curve through the dataset.
This makes me believe that the current setup is inherently unable to learn anything but a linear relation, since it's repeating the shape of activation function on the chart. But this may not be true because I've seen other implementations learn curves just perfectly. So I may be doing something wrong. Please provide your guidance.
About my code
My weights are randomized (-1, 1) inputs are not normalized. Dataset is fed in random order. Changing learning rate or adding layers, does not change the picture much.
I've created a jsfiddle,
the place to play with is this function:
function trainingSample(n) {
return [[n], [n]];
}
It produces a single training sample: an array of an input vector array and a target vector array.
In this example it produces an f(x)=x function. Modify it to be [[n], [n*n]] and you've got a quadratic function.
The play button is at the upper right, and there also are two input boxes to manually input these values. If target (right) box is left empty, you can test the output of the network by feedforward only.
There is also a configuration file for the network in the code, where you can set learning rate and other things. (Search for var Config)
It's occurred to me that in the setup I am describing, it is impossible to learn non–linear functions, because of the choice of features. Nowhere in forward pass we have input dependency of power higher than 1, that's why I am seeing a snapshot of my activation function in the output. Duh.
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).
How do I generate following signal in simulink:
t=(0:1000)/1000*10*pi;
I want to build the model of the following matlab code:
t=(0:1000)/1000*10*pi;
x = (t).*sin(t);
y = (t).*cos(t);
z = t;
This is fairly basic stuff. Have you gone through any Simulink tutorial, introduction videos/webinars or even the getting started guide of the documentation?
Here are a few suggestions to help you answer your question:
Set the stop time of your model to 1000s and use a fixed-step solver with a step time of 1s.
Use a Clock block with a decimation of 1. That's your 0:1000 vector.
Feed the output of your Clock block to a Gain block, with the gain set to 1/(10000*pi). That's your t vector.
Feed your t signal to two Trigonometric Function blocks, one set to sin and one set to cos. That will generate two signals, sin(t) and cos(t).
Now multiply your t signal with your sin(t) signal using a Product block, to generate your x signal (t*sin(t)).
Do the same thing with t and cos(t) to generate your y signal. z is already done since it's equal to t.
EDIT following comments
The answer to your comment is really basic Simulink stuff. You should learn how to use Simulink before trying to do advance stuff like VR in Simulink. It's a bit like trying to run before you can walk.
Here are a few resources that may be useful:
Simulink Videos and Examples
Simulink Webinars
Simulink tutorial
Getting Started with Simulink in the Simulink Documentation
I don't know much about VRML, but be aware that the coordinate system in VRML is different from that in MATLAB/Simulink (see http://www.mathworks.co.uk/help/sl3d/vrml.html). You should also have a look at Virtual World Connection to a Model in the Simulink 3D Animation documentation.
I have a system with a Model Predictive Controller and PID Controller.
Assuming I have models for each controller and can express them in discrete time, please how do I integrate them together to simulate properties of the system in matlab?
Thanks
... continuing from the comments.
This is what Simulink is made for. Of course there are ways to do it without Simulink, but often you still use Simulink tools and functions just without the graphical Interface.
I assume you have your transfer functions "on paper". So you need the tf function to define your system model.
G = tf(num,den)
num and den are the coefficient vectors of your transfer function of numerator and denumerator. In Simulink you use the Transfer Fcn block and you define it with
G.num{1} %Numerator coefficients
G.den{1} %Denumerator coefficients
Your PID-controller cannot be defined using this block, as Simulink requires a higher or equal order for the denumerator. Instead use the PID controller Block. You need to calculate the Proportional, Integral and Differential gain before.
Then read the documentation about the MPC toolbox - I'm not familiar with it and can't help you on that - it is explained how you can create an mpc object regarding all your constraints (see your other question).
Then you have various options to transform your mpc object into something Simulink can deal with. I'd recommend the ss - the state space model - which can be implemented using the state space block. There is also a MPC Controller block, I don't have the toolbox - but you'll be able to find out how it can be used.
Finally you find source blocks, like a step to generate a test signal. And there are Sinks, in the easiest case scope to display your results. You can also save them to workspace or whatever...
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.