Questions tagged [linear-systems]
22 questions
8
votes
1 answer
Why is it impossible to create an observer for this not fully observable system?
Consider a 1D point-mass moving along an axis. A force $u$ is applied as control. There is no gravity or other forces involved. The system can be described in state space equations as:
$$\begin{align}
A &= \begin{bmatrix} 0 & 1 & 0 \\
…
FirefoxMetzger
- 203
- 1
- 5
6
votes
2 answers
Controllability of $x' = Ax + Bu(t)$ implies controllability of $\left \{ \begin{matrix} x' = Ax + By \\ y'=u(t) \end{matrix} \right.$
Suppose that the system
$$x'(t)=Ax(t)+Bu(t)$$
is controllable in $\mathbb{R}^n$, where $A$ is $n \times n$, $B$ is $ n \times m$ and $u(t)$ is $m \times 1$
Show that the system
$$\left \{ \begin{array}{rclccc} x'(t) &=& Ax(t) &+& By(t)& \\…
Giiovanna
- 201
- 1
- 2
5
votes
2 answers
Minimal realization of a MISO system
Given the following system:
$$\dot{x} = \begin{bmatrix}1 & 1 & 0 \\ 0 & 1 & 0 \\ 0 & 1 & 1 \end{bmatrix}x + \begin{bmatrix}0 & 1 \\ 1 & 0 \\ 0 & 1 \end{bmatrix} u$$
$$y = \begin{bmatrix}1 & 1 & 1 \end{bmatrix} x$$
I need to find the minimal…
Unnamed
- 229
- 2
- 5
2
votes
1 answer
How to solve for discrete state space matrices given input and output
I have a set of time-series data that consists of inputs $u_k$ where $
u \in R $ and $k = 1 ... T$, and outputs $ y_k $ where $ y \in R^2 $ and also $k = 1 ... T$, from a given system. I believe this system can be modeled in discrete canonical…
ian.cooke
- 31
- 3
2
votes
0 answers
LQR control effort / control bandwidth relationship
I'm working with a linear system, having given matrices A and B
$$A = \left[\begin{array}{cc} 0 & 1 \\ -0.9 & 0 \end{array}\right]$$
$$B = \left[\begin{array}{c} 0 \\ 2 \end{array}\right]$$
assume we have full state and no feedtrough matrix $D$…
venom
- 183
- 4
1
vote
1 answer
why Type III systems has at least two gain margins?
I heard the following statement https://engineering.stackexchange.com/a/54322/40848
if we have a type III system, or one that has three or more low-frequency poles that we're closing around, then we have at least two gain margins: a low-frequency…
zymaster
- 15
- 4
1
vote
1 answer
Finding a signal output $y(n)$ with input signal $x(n)$ and impulse response $h(n)$ with a DTFT
I am studying for my Digital Signal Processing course and I am stucking on the following exercise:
Given an $\text{LTI}$-system with input signal $$x(n)=\frac{1}{4^n}u(n)$$
and impulse response $$h(n)=\frac{1}{2^n}u(n),$$
calculate the output…
NoHomotopy
- 11
- 2
1
vote
2 answers
System identification of a simple motor with only position measurements
(Cross-posting from statistics stackexchange)
Say we have a permanent-magnet DC motor that roughly obeys the system equation
$$\ddot{x}(t) = \alpha \dot{x}(t) + \beta u(t) + \gamma $$
where $x(t)$ is the displacement of the rotor and $u(t)$ the…
user3716267
- 113
- 4
1
vote
1 answer
Linear Nastran model not converging
I am running a SOL 101 linear statics FEA. If I fix down the whole geometry it converges. But anything less than around 90% fix down and it will sit there crunching away at the numbers forever. This is with no other boundary conditions, forces, etc.…
user1402154
- 151
- 6
1
vote
0 answers
Lyaponuv stability condition of linear systems for homogenous P in V(x) = x^T P x
I am currently learning about using Lyaponuv functions to find Linear Matrix Inequalities (LMIs) as conditions for stability of a linear time invariant system.
i.e.
$$
\dot{x}(t) = Ax(t)
$$
is stable if there exists a function $V(x)$ such that…
Chryron
- 141
- 2
1
vote
0 answers
how do i formulate a kalman filter for an upwash coefficient?
I want to make a kalman filter that will estimate the upwash coefficient $C_{\alpha_{up}}$
my state vector: $ X_k=[u \ v \ w \ C_{\alpha_{up}} ]^T $
My measurement vector: $ Z_k =[\alpha_m \ \beta_m \ V_m]^T $
My control input vector: $ U_k =[\dot…
aadil095
- 111
- 1
0
votes
2 answers
Why are the phase indicators different between the open loop bode plot and the closed loop bode plot?
I have an open-loop transfer function G
num=105*conv([1 1],[1 2 43.25]);
den=conv([2 0 0],conv([1 2 82],[1 2 101]));
G=tf(num,den);
and a closed-loop function of G/(1+G). Here are the open-loop bode diagram and closed-loop bode diagram for that…
zymaster
- 15
- 4
0
votes
1 answer
What is the effect of the resonant frequency of the system function Porter diagram on the stability of the system and how to analyze it?
I am a novice in automatic control, the theoretical basis is not very good. We have a large electric clamping jaw, single degree of freedom, the motor is controlled by the torque output, the motor has a maximum stable clamping stiffness (This…
zymaster
- 15
- 4
0
votes
0 answers
Estimating the effective area and temperature coeffecient of a solar panel
I have a bunch of solar panels, each one is connected to an inverter.
For each solar panel I have two sensors, a wind and a west sensor.
From every inverter, I collect the power output.
The readings are collected for every 5 minutes, and I have a…
rish
- 1
0
votes
1 answer
Looking for a linear actuator that can carry a transverse load? Does such a product exist?
I am looking for a product that works like a linear actuator where you can control how far it extends but it can also hold a transverse load at the furthest point of extension.
What I am looking for would be similar to common consumer models such as…
belza00
- 1