Questions tagged [linear-control]
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13
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8
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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:
$$\begin{align}...
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6
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2
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Controllability of $x' = Ax + Bu(t)$ implies controllability of $\left \{ \begin{matrix} x' = Ax + By \\ y'=u(t) \end{matrix} \right.$
Suppose that the system
$$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{...
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5
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2
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Minimal realization of a MISO system
Given the following system:
$$\dot{x} = \begin{bmatrix}1 & 1 & 0 \\ 0 & 1 & 0 \\ 0 & 1 & 1 \end{bmatrix}x + \begin{bmatrix}0 & 1 \\ 1 & 0 \\ 0 & 1 \end{bmatrix} u$$...
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4
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1
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147
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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?
$$\...
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3
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0
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176
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PI or PID-regulator for control system with hysteresis relay in inner loop
I have such control system (sorry for rough drawing :) )
$G(s)$ - stable object with proper transfer function.
$1/s$ - integrator.
I need to clarify, how synthesized PI or PID controller for such ...
- 226
2
votes
1
answer
210
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Is nonlinear control slower than linear control?
Is there any scientific comparison between linear and nonlinear systems?
I often hear that
Nonlinear control is more sluggish than linear control.
which makes sense. But is there any research or ...
- 23
2
votes
1
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62
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How to solve for discrete state space matrices given input and output
I have a set of time-series data that consists of inputs $u_k$ where $
u \in R $ and $k = 1 ... T$, and outputs $ y_k $ where $ y \in R^2 $ and also $k = 1 ... T$, from a given system. I believe this ...
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2
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0
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142
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LQR control effort / control bandwidth relationship
I'm working with a linear system, having given matrices A and B
$$A = \left[\begin{array}{cc} 0 & 1 \\ -0.9 & 0 \end{array}\right]$$
$$B = \left[\begin{array}{c} 0 \\ 2 \end{array}\right]$$
...
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1
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1
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how are larger leadscrews (14mm diameter and up) fixed in place?
So looking at 12mm lead screws and below, it seems like a common method for fixing them in place is to use pillow blocks. The pillow block has set screws which clamp onto the lead screw, and you're ...
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0
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Quality of the transient response for an arbitrary transfer function
The question is simple and I rather need a reference point.
How the parameters of transients are estimated (as in the picture) from an arbitrary linear transfer function (formula is given).
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0
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1
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Feedback Control Question: Finding compensator numerator (B(s)) and denominator (A(s)) polynomials to satisfy a specific requirement
I wish to find the polynomials B(s) and A(s) in the following compensator equation:
A(s)D(s) + B(s)N(s) = F(s)
Given,
$$N(s) = s - 2$$
$$D(s) = s^2 - 1$$
$$F(s) = s^2 + 3*s + 4$$
Condition
The degree ...
0
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1
answer
81
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Intuition for blocks and Laplace form for cascading transfert function
I'm failing to understand Blocks in block diagram in control theory. Indeed, the link between transfer function of time and function of Laplace is fuzzy to me. I'm looking for a way to ground my ...
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-1
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1
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150
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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 ...
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