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23 views

How to find the output signal of a filter using state space matrices?

I have a filter. It has two poles and two zeros. I found the state space equations and the matrices A, B, C, and D Now. I have 9 samples that I need to process with my filter. How do I use A,B,C,D ...
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1answer
34 views

Does the system matrix being singular tell us anything about the system?

If we have a linear system, represented in State Space and the A matrix is singular (det(A) == 0), can we expect any special properties from the system?
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2answers
41 views

Why is my discretized transfer function unstable when my discretized state-space model is stable?

I am working with a 30-state, 14-input linear model that is described by a state-space model: model_state_space = ss(A, B, C, D); The model is extremely slow (it ...
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1answer
21 views

How to find derivative of 2-D elliptical Gaussian function with different standard deviations along $x$ and $y$ directions?

I am trying to find the 2-D derivative of an elongated Gaussian density. The Gaussian has standard deviations $\sigma_x$ and $\sigma_y$. How can I get the scale-normalized 2-D Gaussian derivative in ...
0
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1answer
49 views

state space formulation of a sinusoidal system

Let $f=A\sin{\omega t}=x_1$ and $\dot{f}=A\omega\cos{\omega t}=\dot{x}_1=x_2$. Let the output be $y=cA\omega$, where $c=1$ is a constant. I want to represent this in a state space formulation: ...
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0answers
6 views

State Space model of a differential eqn. for use in Least Squares

The code in this page solves the Least Squares problem for the following dynamic model: $\dot{y}=ay+bu$ where $a$ and $b$ are constants, $u$ is an input. The code is as follow: ...
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0answers
20 views

Identifiability for Time Invariant State Space Models

Kevin Murphy's Kalman Filter toolbox (for Matlab) contains an example where it's the fact that the state space system in not identifiable causes problems. I include the example in it's entirety but ...
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0answers
42 views

Simulating state space model with AR(1) dynamics

I asked a question similar to this previously: Simulating a state space model However I think I have a better handle on it now and want to re-ask it: I simply want to simulate data from a state ...
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0answers
34 views

Correct Implementation of Kalmand Filter to Gaussian state space model?

I am simulating a time series from a state space model, I then want to estimate the state space model parameters from the simulated time series using a kalman filter: I have already posted my code ...
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0answers
28 views

Simulating a state space model

I want to simulate data from the following model: $\textbf{z}_k=\textbf{H}\textbf{x}_k+\textbf{v}_k$ $\textbf{v}_k \sim N(\textbf{0},\textbf{R})$ $\textbf{H}$ does not change over time $\textbf{x}$ ...
0
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1answer
68 views

Logarithm in state space equations

I want to linearize a system to this form $$\begin{bmatrix} \Delta\dot{x}_1\\ \Delta\dot{x}_2\\ \Delta\dot{x}_3 \end{bmatrix} = A\begin{bmatrix}\Delta x_1\\ \Delta x_2\\ \Delta ...
0
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1answer
70 views

How to find transfer function by state space representation matrices

A state space representation is given by: $$\dot{x}= \begin{bmatrix}0 & 0 & 0 & 0\\ 1 & 0 & 0 & 0 \\ 0&0&-2&-4\\0&0&1&0\end{bmatrix}x+\begin{bmatrix} ...
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0answers
355 views

Difference between state space and transfer function model response (in Simulink)

Why I get a different response from the same system (e.g. three phase inverter with LC filter) in state space form and in transfer function (Laplace) form when using the same PI controller values (Kp ...
6
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1answer
66 views

Can a state space model have changing state size over time?

I have worked with state space models in relation to Kalman estimation. Here I have always seen state space models with fixed state size over time, i.e. the state transition matrix is square. Let us ...
3
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0answers
74 views

What is right and full Frobenius canonical form?

I'm having a trouble here. I'm supposed to learn Frobenius canonical representation form for finding statespace matrices, but I found many different forms. Let's suppose we have a system with this ...
3
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1answer
43 views

Linearized system and State Space

I want to ask about this scheme: $u_0$ should be something as input in specific point given by the initial conditions and $y_0$ output. Block State Spase represented linearized system by A, B, C, D ...
2
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0answers
114 views

State space representation in s-domain

I was supposed to find state space representation and its matrices of this system: and I have no idea, how to do this. We were told not to transfer the system to time domain, but I can only do ...
6
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1answer
113 views

How to combine a perfect signal with a limited dynamic range with a poor one with high dynamic range?

I have two sensors that measure speed $v(t)$ of a moving vehicle. The first sensor produces a signal $f(t)$ which is a very accurate estimation of speed. However, it only works for slow to moderate ...
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0answers
104 views

Estimating the input to a system from a system state using EKF

[ Cross-posted from: http://math.stackexchange.com/questions/164169/estimating-the-input-to-a-system-from-a-system-state ] I have a system for which I have obtained a non-linear time-varying ...
5
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1answer
133 views

State space system identification

Suppose I have a real (physical) dynamical system with some sensors and actuators, and I also have an idealized state-space model of this same system. How, in general, can I adjust the model to match ...
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2answers
3k views

Is a Kalman filter suitable to filter projected points positions, given Euler angles of the capturing device?

My system is the following. I use the camera of a mobile device to track an object. From this tracking, I get four 3D points that I project on the screen, to get four 2D points. These 8 values are ...
7
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1answer
2k views

How do I find a system's impulse response from its state-space repersentation using the state transition matrix?

Suppose we have a linear represented in the standard state space notation: $$ \dot{x}(t)=Ax(t)+Bu(t)$$ $$y(t) = Cx(t) + Du(t)$$ In order to get its impulse response, it is possible to take its ...