Questions tagged [state-space]
The state-space tag has no usage guidance.
108
questions
2
votes
0
answers
45
views
Direct and numerically robust conversion from zero-pole to state-space representation
Note: this question was initially asked in a different community.
Encouraged by the comments, I decided to cross-post here too.
Given (z,p,k) my goal is to convert to a state-space representation (A, ...
- 21
2
votes
1
answer
77
views
Why do they say that complex exponentials are eigenfunctions of LTI systems, when there are still transient responses?
Let $$\dot{x} = Ax+Bu$$ $$y = Cx + Du$$ be a linear ODE with $x(0)=0$. Here, I am assume $A$ is invertible.
As you can see, the relation $$H:u(.) \mapsto y(.),$$ where $(u(.),y(.))$ is a solution to ...
- 123
2
votes
1
answer
131
views
State space transformation
I have some governing equations of the form:
$$\begin{align}
\ddot \theta(t) &= \frac{MgL + mgl}{J} \theta(t) + \frac B J \dot x(t) - \frac \alpha J V + \frac {mg}{J} d - \frac{c_1}{J} \dot \theta(...
- 23
1
vote
1
answer
68
views
Controllability matrix is full rank identity matrix
What does it mean, when my system has controllability matrix that is full rank and identity matrix? Having full rank means that the system is controllable, but does the Identity feature of my ...
- 79
1
vote
1
answer
122
views
What exactly are the assumptions behind Tustin's formula? Application on state space models
I was parsing the forum when I saw this post surging out of the depths of this forum like an old Kraken. The problem is quite simple.
You have a continuous time state space model :
$$
\begin{split}
\...
- 487
2
votes
0
answers
177
views
Initial conditions of state-space realization
In a discrete-time difference equation (ARX model), the output $y[k]$ is dependent on its past values and inputs, expressed as:
$y[k] = -a_1 y[k-1] - ... - a_N y[k-N] + b_1 u[k-1] + ... + b_M u[k-M]$, ...
- 21
2
votes
0
answers
59
views
How is the transfer function of a state space representation computed in practice?
I know that if you have a linear time invariant system defined by
$$ \dot{X} = AX+BU $$ $$Y = CX$$ by "Laplacing" the previous equations, you get the following transfer function in the ...
- 487
0
votes
1
answer
127
views
How to discretize the continuous time domain state space model?
I have a dsp algorithm which is based on the below given state space model in the continuous-time domain
$$
\begin{bmatrix}
\frac{\mathrm{d}\hat{\psi}_{r_{\alpha}}}{\mathrm{d}t} \\
\frac{\mathrm{d}\...
- 375
1
vote
1
answer
34
views
Finite Difference Estimation for error propagation
For a complex system where symbolic computation of the jacobian is challenging, is estimating the jacobian via finite difference a viable option?
To be explicit I'm mostly interested in playing around ...
- 818
2
votes
1
answer
78
views
Simulation of the discrete linear Kalman filter
I have been working on a Scilab simulation of the discrete Kalman filter which is used as a state observer of the
linear dynamic system. The Scilab script for the discrete Kalman filter is as follows
<...
- 375
1
vote
1
answer
62
views
What are the Kalman filter capabilities for the state estimation in presence of the uncertainties in the system input?
I have a question regarding the capabilities of the discrete Kalman filter for estimation of the unmeasurable state variables of a dynamic system.
In the time being I have been using a discrete ...
- 375
1
vote
2
answers
137
views
First Order State Space Question
I am trying to understand the state space equation for a simple first-order LTI system. Suppose I have a system with impulse response
$$h(t) = \frac{1}{\tau}e^{\frac{-t}{\tau}} \ \theta(t)$$
In this ...
- 13
2
votes
2
answers
216
views
Does every continuous-time filter have a state-space representation?
Given a continuous-time filter with impulse response $h(t)$, is it possible to represent any $h(t)$ in state-space form?
More precisely, given the state-space representation of a single-input single-...
- 350
2
votes
1
answer
624
views
Why does sequential update of Kalman Filter work when you have multiple sensors?
If you are using a kalman filter with multiple sensing sensors there are two ways to fuse them.
One way is doing a single observation step where you include all the sensors in a single vector and a ...
- 818
1
vote
1
answer
115
views
IMU state estimation Covariance updating
EKF filter normally has a predict + update step, I am curious - how do you evolve the covariance of the state without one of the steps?
In essence I want to evolve the state of an object using an IMU ...
- 818
1
vote
0
answers
95
views
Converting a SISO LTI System to a MIMO LTI System
I have a SIMO IIR filter represented as a state space system. I'm wondering if there is a canonical way of converting a IIR filter into a MIMO system, so I can calculate $N$ terms as input at once and ...
- 115
1
vote
1
answer
229
views
Intuition for $\mathbf{P} = \mathbf{0}$ in steady-state when $\mathbf{Q} = \mathbf{0}$ (Kalman filter)
Consider the following discrete-time system:
\begin{equation}
\mathbf{x}(k+1) =
\mathbf{A}_d
\mathbf{x}(k)
+
\mathbf{B}_d
\mathbf{u}(k)
\end{equation}
\begin{equation}
y(k) =
\mathbf{C}_d
\mathbf{x}(k)...
- 75
1
vote
0
answers
27
views
Stability analysis of hybrid discrete-continuous systems
I'm trying to derive the overall state-space system model for a hybrid system, in order to plot its eigenvalues.
The system is shown as follows:
Which is originally from this paper: Modeling and ...
2
votes
2
answers
108
views
For continuous systems that in Quasi-static / Static Equilibrium are Memoryless?
A. BACKGROUND:
Apparently this question’s answer says this some static systems have memory especially those that hysteresis: Confusion about 'memoryless' meaning
So the word static to me ...
- 21
8
votes
2
answers
954
views
What sensors can be fused using the Kalman Filter framework
I was recently introduced to the concept of Kalman filtering in the context of projectile tracking. A classmate recommended this to me, and what intrigued me most was its ability to fuse different ...
- 213
3
votes
1
answer
72
views
Linear Time-Invariant system without State-space form
I would like to know whether there is any LTI system that does not have state-space representation, but do have a convolution representation. and vice-versa. Can you name some examples for me to ...
- 79
1
vote
1
answer
82
views
How does sampling jitter affect state estimation?
Suppose I have some process which is governed by:
$$ \vec{x_{k+1}} = A\vec{x_k} + B\vec{u_k} + w_k$$
where $u_k$ is the input, and $w_k$ is process disturbance.
This process is continuous time in ...
- 115
0
votes
1
answer
41
views
How to check that the state observer works appropriately?
I have implemented a discrete state observer for a given dynamic system in continuous time domain in following form
$$\bar{\mathbf{x}}(k) = \mathbf{A}_d\cdot\hat{\mathbf{x}}(k-1) + \mathbf{B}_d\cdot \...
- 375
2
votes
0
answers
72
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)):
<...
- 53
4
votes
1
answer
625
views
How to linearize this state space model and write it in discrete form?
This might not be trivial nor short so in advance thank you all who read this in attempt to help.
I'm building a Kalman filter in matlab and I'm fairly certain the software itself is working correctly ...
- 73
0
votes
1
answer
62
views
State-space model and/or TF for a $K$-th order linear system given the signal sequence
The discrete-time signal $x_n$ is a sum of $K$ discrete-time complex damped exponential:
\begin{equation}
x_n = \sum_{k=1}^{K} \underbrace{(a_k e^{j\phi_k})}_{c_k}
{\underbrace{e^{\{(- \...
- 79
1
vote
2
answers
2k
views
How to get state-space equations form from a block diagram?
This is the block diagram that I'd like to transform into a state-space representation, where $u_{1}$ and $u_{2}$ are inputs and $y_{1}$ and $y_{2}$ are the outputs of the system
I tried to place ...
- 73
2
votes
2
answers
66
views
Methods for time series estimation in time domain
I am trying to estimate the clean form of a time series, $u(t)$ that is corrupted by additive White Gaussian noise $w(t)$ at a particular SNR. The received signal is:
$$y(t) = u(t) + w(t)$$
My first ...
- 291
1
vote
1
answer
231
views
States transformation of the bilinear transform
I have used the bilinear (or tustin) transform for a while, have been though the derivation of it and also through the concept of frequency warping.
Something that I still not understand that is ...
- 13
0
votes
1
answer
25
views
What does it mean for a transfer function to have multiple sets of zeros in the numerator?
I was looking at the source code for Matlab's tf2ss function and I noticed that it parses the numerator assuming that it is a matrix, not a vector. So I looked at ...
- 163
1
vote
0
answers
603
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 ...
- 11
2
votes
0
answers
48
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,...
- 672
0
votes
1
answer
130
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
0
answers
160
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
$$ \...
- 11
0
votes
1
answer
342
views
Simulate butterworth filter with initial condition of state vector in R
I'm working in R with the packages signal and control (don't know wether these are even the best for my use case).
I have a high ...
- 109
4
votes
2
answers
740
views
State space physical meaning
Let $T(s)$ be a transfer function that describes a mechanical system, where the input is force and the output is position.
And let $[A,B,C,D]$ be the equivalent state-space representation of $T(s)$, ...
- 154
2
votes
1
answer
86
views
Why can't this system be adequately represented using a z-domain transfer function?
According to this question and answer the following system cannot be adequately captured by a z-transform transfer function.
$$y[n] = y[n-1] + F_{\psi}(y[n-1)) + F_{\phi}(x[n-1])$$
where $F_{\alpha}(z)...
- 123
2
votes
1
answer
121
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):
...
- 492
1
vote
0
answers
157
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# ?...
- 11
0
votes
1
answer
50
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 ...
- 103
1
vote
1
answer
396
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 ...
- 129
4
votes
1
answer
248
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 ...
- 429
7
votes
1
answer
706
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 ...
- 3,310
1
vote
4
answers
271
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 ...
- 121
1
vote
1
answer
87
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 ...
- 25
2
votes
1
answer
131
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. ...
- 131
4
votes
2
answers
1k
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} ...
- 171
3
votes
0
answers
493
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:...
- 29
1
vote
2
answers
91
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 ...
- 3,012
2
votes
0
answers
772
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 ...
- 191