Questions tagged [linear-control]

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1answer
69 views

designing compensator with certain specification

Ηere is an open-loop transfer function and specifications for compensator design. I defined the required poles and defined the angles according to the normal procedure of the root locus method and ...
1
vote
1answer
109 views

Is nonlinear control slower than linear control?

Is there any scientific comparison between linear and nonlinear systems? I often hear that Nonlinear control is more sluggish than linear control. which makes sense. But is there any research or ...
4
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1answer
109 views

How to design the right input to obtain a desired output for a linear system?

If I have a state-space model, so that matrices $A$, $B$, $C$ and $D$ are known, how can I design the right input $u$, so that $y$ is a desired signal, say, a sine wave with constant amplitude? $$\...
5
votes
2answers
284 views

Minimal realization of a MISO system

Given the following system: $$\dot{x} = \begin{bmatrix}1 & 1 & 0 \\ 0 & 1 & 0 \\ 0 & 1 & 1 \end{bmatrix}x + \begin{bmatrix}0 & 1 \\ 1 & 0 \\ 0 & 1 \end{bmatrix} u$$...
8
votes
1answer
271 views

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}...
6
votes
2answers
224 views

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{...