Questions tagged [state-space]

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Converting an FIR Filter Model to a State Space Model for Kalman Filtering

I want to try and determine the true value of a quantity $\alpha[k]$ from observations of a related quantity $\vartheta[k]$ using a Kalman filter. The observations are of the following FIR filter form:...
3
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0answers
3k 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 ($...
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0answers
146 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 ...
2
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0answers
39 views

Mismatch between the frequency response of a transfer function and bode plot

I generate a state space model as follows (The details are not important. This part is used to get matrix A_xi and B_xi and the state space model is xi(k+1) = A_xi*xi(k)+B1_xi*u0(k); y(k) = x(k)): <...
2
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0answers
37 views

State space representation using a given nilppotent matrix

I want to build a question on state space using a given, nilpotent matrix, $A$. $$q[n+1]=Aq[n]+Bx[n]$$ $$y[n]=Cq[n]+Dx[n]$$ Usually, I am using the canonical form so there is no problem extracting $A,...
2
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0answers
585 views

Derivation of ZOH Discretization

I'm trying to understand the derivation of the zero order hold discretization method, and I have a couple of questions about some of the steps. I think I understand the first part, this is just the ...
2
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0answers
65 views

Calculating pre-history of recursive filter from state space representation when optimising for initial z

For a recursive filter, suppose a set of $b$ and $a$ coefficients have been calculated. Assume a state-space representation for which an initial set of $z$-values have also been calculated as in ...
2
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0answers
227 views

Identifiability of a state space model (Dynamic Linear Model)

Take a general linear Gaussian state space model (SSM)(aka Dynamic Linear Model DLM): \begin{align} X_{t+1}&=FX_t + V_t\\ Y&=HX_t+W_t\\ V_t &\sim \mathcal N(0,Q)\\ W_t &\sim \...
1
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0answers
168 views

Recursive Least Square For Filtering

I just started doing research on Recursive Least Square for filtering noises such as sensors and dc motors noises. The only thing I've seen on the internet was Theoretical information about RLS but ...
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0answers
43 views

Augment State Space Model with Derivative of State

Problem How do you augment a state space model with the derivative of a state? I know how to augment a state space model with the integral of a state by doing the following. Given a linear system $$ \...
1
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0answers
51 views

Are there any State Space Control C libraries?

I'm searching for a C library which implements methods needed for state space control (e.g. state feedback controller and state observer equations). Googling various terms only brought up a non-C (C# ?...
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0answers
69 views

identifying overshoots in given state space system with step inputs

Suppose I have the following state space system: $$ \dot{x}(t) = Ax(t) + Bu, \quad y(t) = Lx(t), \quad x(0) = x_0 $$ where $A$, $B$ and $L$ are real matrices, $u$ is a constant real vector (so that ...
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0answers
31 views

Kalman Filtering and space parametrization

I am familiar with Kalman filtering given a linear (time-invariant) state space model. However, the state space parametrization is not unique. Given a controllable and observable state space model (A,...
1
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0answers
8 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: ...
1
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0answers
70 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 ...
1
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0answers
82 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
98 views

Simulate butterworth filter with initial condition of state vector in R

I'm working in R with the packages signal and control (don't know wether these are even the best for my use case). I have a high ...
0
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1answer
126 views

Continuous time double exponential filtering in state space form?

I'm trying to determine the continuous time formulation of the double exponential filter so that I can adapt it more flexibly for my particular problem. Typically, this model is expressed as a pair ...
0
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0answers
45 views

How do I derive complicated robotic motion models easily?

I have a filter that tracks a robot. I want it to use a 2D coordinated turn polar velocity motion model (from page 15 here): But I want to expand on this motion model: I want an additional velocity ...
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0answers
280 views

State Space conversion of Sinusoidal model

i would like to learn how to convert sinusoidal model into state space form which has following equation our model consist of sum of periodic components with additive of white noise, given by ...
-1
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2answers
225 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 ...