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Questions tagged [linear-systems]

27 questions
8
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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
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6
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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
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5
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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
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2
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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
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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
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1
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Control method for system with high disturbance

I have a system that is basically an open plastic bag floating at sea, with one pump inlet (analog control) and one control valve outlet. I have pressure sensors inside and outside the «plastic bag». I want to control two states, flow rate through…
pjoltergeist
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1 answer

Distillation column linear algebra example

Some books and learning resources use steady-state distillation columns as an example problem to introduce linear systems of equations in linear algebra and numerical computing; for…
Federico Poloni
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1
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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
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1
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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
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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
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1
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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
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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
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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
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Deriving a linear state space representation for a cart with 2 weights

I am trying to derive a (linears) state space representation for a system of a cart with 2 weights and a Force applied. I have derived the following equation for the different Forces in the system: $$ F+(M+m)q''+ml[-\theta_1''…
Homer Sanchez
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LQR control guarantee for a controllable subspace

Suppose I have a discrete-time linear dynamical system with no assumptions made about its properties e.g. stability, controllability, reachability. I have an arbitrary target $x^*$ chosen from its controllable subspace. Is it guaranteed that I can…
dkv
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