I have managed to estimate an 'idpoly' m for my time series Z(1,:) using the 'arx' command in Matlab. Unfortunately I do not know how to use this model m for anything else.
How do I know input a second series Z(2,:) into the model to see how well it predicts on the validation data?
Thanks
Use lsim to simulate your idpoly with an arbitrary time input.
Arnaud
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In using neural networks for solving differential equations, using MATLAB, I could find derivative of the model using the command 'dlgradient'. i.e.
gradientsU = dlgradient(sum(U,'all'),{dlX},'EnableHigherDerivatives',true)
where U is the model found using fullyconnect and dlX is the input.
Now, how we can calculate derivative at a particular point of the model U.
To be specific I wanted to add derivative of the model at a particular point, say U_0=U'(5) to the loss function. So, how can I compute that?
I have followed the documentation given in MATLAB, given by,
"To evaluate Rosenbrock's function and its gradient at the point [–1,2], create a dlarray of the point and then call dlfeval on the function handle #rosenbrock.
x0 = dlarray([-1,2]);
[fval,gradval] = dlfeval(#rosenbrock,x0);
But I have already called using dlfeval to evaluate the model, so, not able to call dlfeval again. And when I'm trying to directly compute using the command dlfeval(#U,U_0), the output is always zero.
It will be really helpful if some insight could be provided. Thanks in advance.
Documentation and examples on the dsp.KalmanFilter is really scarce. I want to run the Kalman filter in prediction-only mode, where I pass just the control vector as input and no corrections. Can't seem to find a way to do that since the step function takes 2 parameters.
Prediction step is just multiplying the current state by the model matrix.
Why no do it yourself?
I would like to make a discrete filter, where the sampling rate can be controlled by an input. I am trying to understand how the discrete filter block looks, "under its own mask." Is there anyway to retrieve the code behind this block so it can be modified for my use?
You can use an user-defined function as a filter, pick the filter transfer function, translate it into a difference equation (the discrete-time equivalant to the diferrential equation), implement that difference equation in a function and feed the sampling rate as an input (the sampling rate will appear as a constant in your difference equation).
The block is too complex and has too many options to simply be able to look under the mask. Your best option is to have a look at the documentation, which does show some detailed implementation of the block in some articular cases to get an idea and then try to recreate the discrete filter you want from basic building blocks, using a constant sample time at first, until you can validate your own implementation against the Simulink library block. Only then, start considering how you will change the sample time. Your main problem though is that the filter coefficients will change with the sample time, so you need to be able to re-calculate them on the fly. It's not an easy problem, I don't even know if it's possible.
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 have set up a model using SimMechanics. It outputs data at the times where the solver steps to. Is there any possibility to have some kind of dense output such that it is possible to interpolate these data to get the solution at arbitrary points without losing the high order of the integrator?
In Matlab this is easily possible using the function deval after the integration of one of the built-in ODE integrators.
In SimMechanics I can select these integrators, too. Is there some kind of analouge way to deval?
Yes, it's possible, although it's a Simulink functionality, not specific to SimMechanics. In the Configuration Parameters of the model, you can set the model to Produce Specified Output Only (see http://www.mathworks.co.uk/help/simulink/gui/data-import-export-pane.html#bq9_fhw-1), under Data Import/Export. This way, only the outputs you specify will be produced regardless of the time steps taken by the solver.