Questions tagged [state-space]

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50 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 ...
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1answer
59 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. ...
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1answer
63 views

KalmanFilter 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} ...
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0answers
123 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:...
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1answer
41 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 ...
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0answers
74 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 ...
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1answer
30 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 ...
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0answers
38 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
41 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 ...
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1answer
534 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 ...
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1answer
144 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 ...
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1answer
531 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 ...
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3answers
123 views

Discrete State Space Model: Why Are We Calculating $ x \left[ k + 1 \right] $ Instead of $ \dot{\textbf{x}}(t) $?

A continuous state space model is defined as follows. $$ \dot{\textbf{x}}(t)=\textbf{A}\textbf{x}(t)+\textbf{B}\textbf{u}(t) \\ \textbf{y}(t)=\textbf{C}\textbf{x}(t)+\textbf{D}\textbf{u}(t) $$ If we ...
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0answers
122 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 ...
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1answer
214 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 ...
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1answer
234 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 ...
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2answers
2k 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 $u(t)$ ...
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1answer
748 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 ...
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1answer
81 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 ...
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2answers
121 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 ...
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2answers
134 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....
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2answers
604 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., ...
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0answers
66 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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1answer
252 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 ...
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1answer
222 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 ...
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1answer
311 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 ...
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0answers
241 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 ...
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1answer
366 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{...
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0answers
29 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,...
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1answer
87 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:...
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2answers
341 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 ...
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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
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1answer
134 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, $$...
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0answers
218 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 \...
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1answer
186 views

Expectation maximization of moving average with binary source input

I am trying to do blind system identification of a univariate linear FIR model: I am unsure if the approach is correct or not and any help to further proceed with the maximization will be great. ...
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1answer
6k views

Why eigen values and poles of a system are equivalent?

In control systems engineering, the stability of a system (modeled in the form of Transfer Function) is determined by the poles of the system in the right or left hand sides. When the model is ...
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1answer
238 views

Is this model nonlinear?

I have this state-space model: Is this state space model nonlinear? If it is, why is that?
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2answers
276 views

How to form Kalman filtering matrices for a problem with variable acceleration?

Assuming we have time vector $T$ with constant time step $dt$ position vector $X$ velocity vector $V$ acceleration vector $A$ All vectors $X, V, A$ have noise on their measurement ( $n_x$ , $n_v$ , ...
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1answer
75 views

State Space representation

I'm trying to change this filter transfer function to state space representation $ y_t=\frac{1+b_1 z^{-1}}{1+a_1 z^{-1} +a_2 z^{-2}}u_t $ I tried writing it as time series $ y_t+a_1 y_{t-1}+...
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1answer
729 views

The two types of stability and “Why exponential”

When I was learning about LTI systems, I noticed that LTI system is said to be BIBO stable if and only if its square sum of impulse response is finite. This expression is found on many textbook of ...
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1answer
154 views

Doubt in state space representation

$y$ is scalar observations and so C will be a 1x2 matrix. I want to represent the following model as a state space representation so as to estimate the hidden states from the noisy observations $y$ ...
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3answers
7k views

When Is a Kalman Filter Different from a Moving Average?

this thread asks when a discrete time Kalman filter is better/different from a simple moving average of the observations: Why use a Kalman filter instead of keeping a running average? there's no ...
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1answer
1k views

kalman filter with time-varying noise?

in regular discrete-time (1 dimensional) kalman filter, it is assumed that we have white gaussian noise affecting the transitions and the observations: $x(t+1) = Ax + w$ $y(t) = Cx(t) + v$ ...
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2answers
597 views

How to intuitively understand the state space formulation of discrete time system?

The SS formulation of DT system is given by $$x[(k+1)T] = Ax(kT) + Bu(kT)$$ $$y(kT) = Cx(kT) + Du(kT)$$ Note: T is the sampling period and often omited Can someone explain to me why the state ...
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2answers
100 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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2answers
660 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
2k 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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2answers
157 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 ...
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1answer
1k 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: $\dot{...
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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: ...