I am new to designing real time plant models in simulink, and i have to include a 2 way directional valve in my model, i could take the orifice model and make the pressure differentials zero when direction is from B->A. Can i use an integrator to do the same? or is there a more appropriate block that is less complicated?I am using MATLAB 2012b
Thank you!
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I am a beginner on modelica. I wanted to transpose a model found on a paper (on internet) to a modelica model.
Here is the paper :
Insulated Cable Temperature Calculation and Numerical Simulation
I am stuck in rewritting the fomulas. Second derivative on a variable different of time --> i don't know how to do.
Another way I was thinking is to use the Thermal/HeatTransfer library. But here too, I don't know how to put the blocks togethers... I think this is due to a big lack in thermodynamic knowledge from my side.
--> I don't know what block to use to simulate the conductor and the insulation layer.
Maybe this is something too difficult ?
If someone has an idea on how to start, it will be a pleasure to read you :)
I tried to use the Thermal library :
Using heat transfert lib.
I have a current source and a resistance.
The resistance will change depending on the temperature involved by the current in the resistance.
I use 0.004 as alpha for the relationship R=R20*(1+alpha(T-Tamb)).
Let's say I have a 1 meter copper conductor with a crossSection of S=16mm² = 15.10^-6m²
then the initial resistance is R = rho.L/S ≃ 1.07mΩ at 20°C
Following this example of cable : Bayka 16mm²
To get 70°C at the surface of the conductor, then the max current for a single 16mm² wire cable is 107A in air, and 160A in earth.
I took, in my example, random value of thermal conductance and capacity to get an approximative temperature near the one given in the table (~70°C).
Is this model is the good one for an insulated cable ? (no considering values)
Or I forgot something? Maybe I am wrong in the position of the blocks ?
What do you think ?
Looks reasonable to me, might be easier to use the same component for heat conduction (heat resistor or heat conductance, not both) in order to be able to compare the two values. The mathematical formulas for radial heat conduction can be found here e.g. https://web2.clarkson.edu/projects/subramanian/ch330/notes/Conduction%20in%20the%20Cylindrical%20Geometry.pdf
I would like to make a CoSimulation of LS-Dyna and MATLAB or Simulink.
The idea: A force applied in my dyna model displaces nodes in the first iteration. For the next iteration LS-Dyna passes over the nodal displacements to matlab or simulink. An algorithm calculates the new forces to be applied on each node by using the displacement of the previous iteration and gives it back to LS-Dyna and so on. I am really new to Fem and coding. Can anyone please help me out with my problem and give me ideas or solutions how to implement that?
Do u want to update your model with matlab after every iteration?If not, u can define a force curve in dyna. Of course, if the inertia of model changes little, you can read d3plot or nodout file with matlab to update your model and force.
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.
I have been trying to implement a navigation system for a robot that uses an Inertial Measurement Unit (IMU) and camera observations of known landmarks in order to localise itself in its environment. I have chosen the indirect-feedback Kalman Filter (a.k.a. Error-State Kalman Filter, ESKF) to do this. I have also had some success with an Extended KF.
I have read many texts and the two I am using to implement the ESKF are "Quaternion kinematics for the error-state KF" and "A Kalman Filter-based Algorithm for IMU-Camera Calibration" (pay-walled paper, google-able).
I am using the first text because it better describes the structure of the ESKF, and the second because it includes details about the vision measurement model. In my question I will be using the terminology from the first text: 'nominal state', 'error state' and 'true state'; which refer to the IMU integrator, Kalman Filter, and the composition of the two (nominal minus errors).
The diagram below shows the structure of my ESKF implemented in Matlab/Simulink; in case you are not familiar with Simulink I will briefly explain the diagram. The green section is the Nominal State integrator, the blue section is the ESKF, and the red section is the sum of the nominal and error states. The 'RT' blocks are 'Rate Transitions' which can be ignored.
My first question: Is this structure correct?
My second question: How are the error-state equations for the measurement models derived?
In my case I have tried using the measurement model of the second text, but it did not work.
Kind Regards,
Your block diagram combines two indirect methods for bringing IMU data into a KF:
You have an external IMU integrator (in green, labelled "INS", sometimes called the mechanization, and described by you as the "nominal state", but I've also seen it called the "reference state"). This method freely integrates the IMU externally to the KF and is usually chosen so you can do this integration at a different (much higher) rate than the KF predict/update step (the indirect form). Historically I think this was popular because the KF is generally the computationally expensive part.
You have also fed your IMU into the KF block as u, which I am assuming is the "command" input to the KF. This is an alternative to the external integrator. In a direct KF you would treat your IMU data as measurements. In order to do that, the IMU would have to model (position, velocity, and) acceleration and (orientation and) angular velocity: Otherwise there is no possible H such that Hx can produce estimated IMU output terms). If you instead feed your IMU measurements in as a command, your predict step can simply act as an integrator, so you only have to model as far as velocity and orientation.
You should pick only one of those options. I think the second one is easier to understand, but it is closer to a direct Kalman filter, and requires you to predict/update for every IMU sample, rather than at the (I assume) slower camera framerate.
Regarding measurement equations for version (1), in any KF you can only predict things you can know from your state. The KF state in this case is a vector of error terms, and thus you can only predict things like "position error". As a result you need to pre-condition your measurements in z to be position errors. So make your measurement the difference between your "estimated true state" and your position from "noisy camera observations". This exact idea may be represented by the xHat input to the indirect KF. I don't know anything about the MATLAB/Simulink stuff going on there.
Regarding real-world considerations for the summing block (in red) I refer you to another answer about indirect Kalman filters.
Q1) Your SIMULINK model looks to be appropriate. Let me shed some light on quaternion mechanization based KF's which I've worked on for navigation applications.
Since Kalman Filter is an elegant mathematical technique which borrows from the science of stochastics and measurement, it can help you reduce the noise from the system without the need for elaborately modeling the noise.
All KF systems start with some preliminary understanding of the model that you want to make free of noise. The measurements are fed back to evolve the states better (the measurement equation Y = CX). In your case, the states that you are talking about are errors in quartenions which would be the 4 values, dq1, dq2, dq3, dq4.
KF working well in your application would accurately determine the attitude/orientation of the device by controlling the error around the quaternion. The quaternions are spatial orientation of any body, understood using a scalar and a vector, more specifically an angle and an axis.
The error equations that you are talking about are covariances which contribute to Kalman Gain. The covariances denote spread around the mean and they are useful in understanding how the central/ average behavior of the system is changing with time. Low covariances denote less deviation from the mean behavior for any system. As KF cycles run the covariances keep getting smaller.
The Kalman Gain is finally used to compensate for the error between the estimates of the measurements and the actual measurements that are coming in from the camera.
Again, this elegant technique first ensures that the error in the quaternion values converge around zero.
Q2) EKF is a great technique to use as long as you have a non-linear measurement construction technique. Be very careful in using EKF if their are too many transformations in your system, i.e don't try to reconstruct measurements using transformation on your states, this seriously affects the model sanctity and since noise covariances would not undergo similar transformations, there would be a chance of hitting singularity as soon as matrices are non-invertible.
You could look at constant gain KF schemes, which would save you from covariance propagation and save substantial computation effort and time. These techniques are quite new and look very promising. They actively absorb P(error covariance), Q(model noise covariance) and R(measurement noise covariance) and work well with EKF schemes.
I'm simulating a shaft system in Simulink, where I have to find the displacement of a mass. I'm not sure how to model this in Simulink because of the shaft and pulley. I'm looking through the documentation and the closest thing I see to a shaft is the wheel and axle block. But the shafts are connected by a flexible shaft, which is similar to a spring. Any ideas?
This is a fairly trivial task when using SimScape, which is especially made to simulate physical systems. You'll find most of the blocks you need ready from the library.
I've used SimScape to create a model of a complete hybrid truck... In Simulink it can be done, but you'll need to build your own differential equations for the task. In your case, the flexible axle could be translated to another block with a spring/damper system inside.
If you haven't got access to SimScape, you may also consider to use .m (matlab) files to write your differential equations. This can then be used as a block in Simulink, varying (only) a few parameters over time.
Take this step by step:
1. Draw a free body diagram, write out equations for all the forces as a function of displacement, velocity and acceleration of every element (including rotation obviously). For instance, you know that force on the box m will be *c*dy/dt* plus whatever the pulley experiences.
2. Sort out the rotation of the rod first. You know that *T=I*d(omega)/dt* if you get rid of the rest of the system. So, do something analogous to the car engine example of MatLab: Divide the input T by I to get the acceleration, integrate it to get velocity and one more time to get rotational displacement.
3. Keep adding bits one by one. First, you know that there will be a moment proportional to k*(theta_1-theta_2) acting. This will oppose the motion of rod 1 and act to create motion of rod 2. Add a new "branch" to your model to get theta_2 same way you got theta_1.
4. Go on including further elements...