Questions tagged [state-space]
The state-space tag has no usage guidance.
80
questions
1
vote
0answers
28 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,...
0
votes
1answer
19 views
Offline State Estimation
Imagine I have a nonlinear system:
$$
\frac{\text{d} x}{\text{d} t} = f(x,t)\\
y = g(x).
$$
I can design a nonlinear observer to estimate the state $x$ based on the measurements $y$. However, this ...
1
vote
0answers
34 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
$$ \...
0
votes
1answer
22 views
Simulate butterworth filter with initial condition of state vector in R
I'm working in R with the packages signal and control (don't know wether these are even the best for my use case).
I have a high ...
3
votes
2answers
447 views
State space physical meaning
Let $T(s)$ be a transfer function that describes a mechanical system, where the input is force and the output is position.
And let $[A,B,C,D]$ be the equivalent state-space representation of $T(s)$, ...
2
votes
1answer
45 views
Why can't this system be adequately represented using a z-domain transfer function?
According to this question and answer the following system cannot be adequately captured by a z-transform transfer function.
$$y[n] = y[n-1] + F_{\psi}(y[n-1)) + F_{\phi}(x[n-1])$$
where $F_{\alpha}(z)...
2
votes
1answer
64 views
State-space filters in fixed-point?
I am having difficulties implementing state-space filters in (32-bit) fixed-point. This is because the coefficients have a huge dynamic range, for example (MATLAB code):
...
1
vote
0answers
27 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# ?...
0
votes
0answers
27 views
Kalman Filter - combining data from sensors with different measurement rates, does one have a good source where i can get more information about it?
someone already wrote a question about the topic, and thats exactly what i am looking for but i need a source to get more information and to cite from
in my work i combine 2 kalman-filter for ...
0
votes
0answers
12 views
Very stiff state space matrices after linearizing my Simscape model
I want to simulate and build a furuta pendulum from scratch as a project. Currently I´m having some difficulties with the simulation of my model in Simscape and I can´t figure out what´s wrong with it....
1
vote
1answer
35 views
Why is my MATLAB's bode plot wildly off?
I will give out all the details in case it is relevant. I have a MIMO state space system. I find its bode plot using MATLAB and separately using Mathematica. The plot from MATLAB is wildly off ...
1
vote
1answer
125 views
How does Overlap-Add work for IIR filter?
So let's say I'm trying to implement something like an LPC vocoder. I analyse a speech signal by breaking it up in small chunks and determining their LPC coefficients, which are by design, the ...
2
votes
1answer
56 views
Application of UKF on quaternions
I'm trying to perform a state estimation on quaternions to predict the future orientation of a human head. The only sensor data I can obtain (from the AR headset) is the current orientation of the ...
7
votes
1answer
152 views
Fundamental questions about state-space and Kalman filters
I am a dsp guy, I only did a minimum of control theory back in university. While trying to grok state space analysis and (discrete time) regular Kalman filters, I am hitting a few questions that ...
1
vote
3answers
60 views
System classification: unit-time delay
I'm reading a book on linear systems and I can't understand why the unit-time delay is a distributed system. This is the example given in the book:
I understand that the initial state of the system ...
0
votes
0answers
34 views
Using trignonometric functions in system matrix
I am currently trying to create a kinematic model based on the single-track model for vehicles.
The following equations are given:
$$
\dot{x} = v * cos(\theta) \\
\dot{y} = v * sin(\theta) \\
\dot{\...
2
votes
1answer
55 views
Got stack in calculating state-space representation
I got stack in the process of deriving a state-space representation of the following system:
There is an electrical oven described as follows:
control of the power supply $u$,
heating efficiency ...
1
vote
1answer
73 views
Is there any difference in Implementing sigma delta modulator using filters and state space model in FPGA?
Sigma delta modulation is extensively used in quantization to reduce quantization noise.
In the literature one can see different architecture for example python-deltasigma to implement a modulator. ...
2
votes
1answer
250 views
Kalman Filter EM Estimation of Covariances
The question might be very simple, but I get a strange result from Kalman Filter. Let us consider the simplest state-space model, the random walk plus noise:
$$
y_{t} = x_{t} + \varepsilon_{t}\\
x_{t} ...
3
votes
0answers
207 views
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:...
1
vote
2answers
54 views
Equations for particle filter
The particle filter is based on the state and observation model equations
$x_{t+1}=f_t(x_t, v_t)$
$y_t=h_t(x_t, u_t)$
The idea is to randomly generate some particles then propagate them through the ...
2
votes
0answers
553 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 ...
0
votes
1answer
86 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
votes
0answers
40 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 ...
2
votes
0answers
58 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 ...
0
votes
1answer
1k views
How to model state space for complex valued system correctly in SIMULINK (MATLAB)?
When trying to use the default state-space model block, if there is a complex number valued in the matrices, there will be an error
To resolve that, firstly I need to look at pseudo reference model ...
3
votes
1answer
236 views
What is wrong with my residue partial expansion method? (Transfer Function into State-Space Modal/Diagonal Form)
I'm using reference from here and here.
This is Laplace transfer function of DC Control Speed System:
$$\frac{\omega(s)}{V(s)}=\frac{K}{(Js+b)(Ls+R)+K^2}$$
Where,
$\omega$ is the motor angular ...
3
votes
1answer
916 views
Python toolboxes for state-space estimation via subspace estimation
Is there (open-source) toolboxes for state-space estimation via subspace estimation in Python?
I know this is used in Matlab's n4sid function, but I didn't found any Python's implementation (even in ...
3
votes
3answers
201 views
Discrete State Space Model - Why Are We Calculating $ x \left[ k + 1 \right] $ Instead of $ \dot{\boldsymbol{x}} \left( t \right) $?
A continuous state space model is defined as follows.
$$
\dot{\boldsymbol{x}}(t) = A \boldsymbol{x}(t)+ B \boldsymbol{u}(t) \\
\boldsymbol{y}(t)= C \boldsymbol{x}(t)+ D \boldsymbol{u}(t)
$$
If we ...
0
votes
0answers
195 views
State Space conversion of Sinusoidal model
i would like to learn how to convert sinusoidal model into state space form which has following equation
our model consist of sum of periodic components with additive of white noise, given by ...
0
votes
1answer
297 views
A State space model for discrete Sine wave Using kalma filter
I'm looking to apply an optimal LQR filter to a discrete signal of the form
$$
x[n]=A\sin(\omega_0n+\phi)+v[n]
$$
The amplitude $A$ and the phase $\phi$ are unknown variables I want to estimate using ...
3
votes
1answer
331 views
State-Space Representation of Forward and Backward Filters
In [1], the author shows an efficient way of implementing the forward and backward filter using matrices. One can also implement this using filtfilt command in ...
9
votes
2answers
3k views
Initial conditions for systems described in state space - LTI or not?
Suppose we have some system given by
$$\begin{aligned}
\dot{x}(t) &= Ax(t) +Bu(t) \\
y(t) &= Cx(t)+Du(t)
\end{aligned}$$
where $x(t)$ are the state variables, $y(t)$ is the output and $u(t)$ ...
5
votes
1answer
1k views
Bilinear transformation of continuous time state space system
I'm trying to understand the derivation of the bilinear transform for a set of continuous time state-space matrices. I've found plenty of websites which list steps to perform the conversion (here 1 or ...
1
vote
1answer
92 views
Learner level information on Kalman filtering for different input kinds
I am learning Kalman filters and have seen example on data as state varaibles that have real values / numeric. However, in digital communication the information is in digital - bits. So, can Kalman ...
1
vote
2answers
174 views
MATLAB: Implementing Least Squares Estimator for a Given Model
The formula to estimate $\mathbf{h}$ is then
$$\hat{\mathbf{h}} = (X^T X)^{-1} X^T \vec{y}\tag{2}$$
I think this can be implemented in Matlab using ...
0
votes
2answers
138 views
Effect of sampling
I have this continuos-time system
$$\dot{x}=Ax+Bu$$
where
\begin{equation}A=\begin{bmatrix}0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & \phantom{0}2.8040 & -\phantom{0}5....
3
votes
2answers
826 views
Control design: under what conditions can closed-loop poles be placed arbitrarily?
Say we have a single-input linear system $\dot{\mathbf{x}} = A\mathbf{x}+Bu$. With full-state feedback ($u=-G\mathbf{x}$), it is straightforward to arbitrarily place the $n$ closed-loop poles (i.e., ...
1
vote
0answers
68 views
identifying overshoots in given state space system with step inputs
Suppose I have the following state space system:
$$
\dot{x}(t) = Ax(t) + Bu, \quad y(t) = Lx(t), \quad x(0) = x_0
$$
where $A$, $B$ and $L$ are real matrices, $u$ is a constant real vector (so that ...
0
votes
1answer
352 views
Discrete time non-linear time invariant system dynamics descriptions (state-space or input-output relationship)
For the sake of simplicity the following notation $a_k := a[k]$ is assumed for time sequences.
A completely general discrete-time (DT) non-linear(NL) time-invariant (TI) dynamical system can be ...
0
votes
1answer
244 views
Conceptual Question on equalization technique in rayleigh fading channel based on a paper
Question Link http://www.raymaps.com/index.php/theoretical-ber-of-m-qam-in-rayleigh-fading/
gives theoretical expressions for BER in Rayleigh fading channel. Can I use the expression for 64-QAM in ...
0
votes
1answer
389 views
$N$ point moving average filters in state space
I am new to this filter, I did read about them, but could find out a state space notation of these:
$$y(n)=\frac{1}{N}\sum_{m=0}^{N-1}x(n-m)$$
Are moving average filters an LTI systems?
And how do ...
2
votes
0answers
268 views
Scipy.signal.dimpulse(system): how to translate a StateSpace to a “system”? [closed]
The command scipy.signal.dimpulse(system, x0=None, t=None, n=None) does not seem to accept a scipy StateSpace as an input to its ...
0
votes
1answer
527 views
Designing observer with non-observable system
I have this state-space system
\begin{align}
\dot{x}&=\begin{bmatrix}1 & 0\\3 & -2\end{bmatrix}x+\begin{bmatrix}10\\0 \end{bmatrix}u\\
y&=\begin{bmatrix}1 & 0\end{bmatrix}x
\end{...
1
vote
0answers
30 views
Kalman Filtering and space parametrization
I am familiar with Kalman filtering given a linear (time-invariant) state space model.
However, the state space parametrization is not unique. Given a controllable and observable state space model (A,...
2
votes
1answer
95 views
State space equation from differential equation
I have very general system. I don't know whether it is electrical or mechanical or whatever. This system can be modeled by the following differential equation
$$\dot q = \frac{Tf_1-f_2}{T+1}$$
where:...
2
votes
2answers
572 views
Why is it necessary to have two state variables
I am learning about control theory.
Let's consider this system.
$$
m a(t) + b v(t) + k x(t) = f(t)
$$
$a$ is acceleration
$v$ is velocity
$x$ is displacement
$f$ is external force
In my ...
4
votes
1answer
149 views
How can the order of a transfer function be derived from its equivalent state space representation?
Suppose I have a discrete state space model:
\begin{align}
\theta[k+1] &= A \theta[k] + B u[k]\\
y[k] &= C \theta[k]
\end{align}
I know that the equivalent transfer function can be found by ...
2
votes
1answer
139 views
How to represent the nonlinear model as a state space in Unscented Kalman Filter
There is an Autoregressive model of order 1 (AR(1)) that is excited by a non-linear signal as the input:
$$x_t = \rho x_{t-1} + u_t \tag{1}$$
The time series $u_t$ is generated from a nonlinear map,
$$...
2
votes
0answers
223 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 \...
