Questions tagged [linear-control]
16 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:
$$\begin{align}
A &= \begin{bmatrix} 0 & 1 & 0 \\
…
FirefoxMetzger
- 203
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6
votes
2 answers
Controllability of $x' = Ax + Bu(t)$ implies controllability of $\left \{ \begin{matrix} x' = Ax + By \\ y'=u(t) \end{matrix} \right.$
Suppose that the system
$$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
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- 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
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4
votes
1 answer
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?
$$\begin{aligned} \dot{x} &= A x + B u \\ y &= C x + D…
Alessandro
- 41
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3
votes
0 answers
PI or PID-regulator for control system with hysteresis relay in inner loop
I have such control system (sorry for rough drawing :) )
$G(s)$ - stable object with proper transfer function.
$1/s$ - integrator.
I need to clarify, how synthesized PI or PID controller for such object, that include inner-loop with…
ayr
- 232
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- 9
2
votes
1 answer
How to solve for discrete state space matrices given input and output
I have a set of time-series data that consists of inputs $u_k$ where $
u \in R $ and $k = 1 ... T$, and outputs $ y_k $ where $ y \in R^2 $ and also $k = 1 ... T$, from a given system. I believe this system can be modeled in discrete canonical…
ian.cooke
- 31
- 3
2
votes
0 answers
LQR control effort / control bandwidth relationship
I'm working with a linear system, having given matrices A and B
$$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
2
votes
1 answer
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 any claim based on practical experience which…
user15940
- 23
- 2
1
vote
1 answer
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 all set. However, the common size pillow blocks are…
gerrgheiser
- 191
- 8
0
votes
0 answers
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
- 101
0
votes
1 answer
What is the relationship between classical control: transfer functions/frequency domain and the swing-up problem of an inverted pendulum
I am still pretty new to control theory, but I have been studying both classical and modern state space/optimal control ideas. I am having trouble understanding what the frequency domain/transfer function view is on some of the challenges of optimal…
krishnab
- 105
- 4
0
votes
1 answer
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 understanding of transfer functions in both domain in…
NRagot
- 101
- 1
0
votes
1 answer
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).
ayr
- 232
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0
votes
1 answer
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 of B(s) should be less than the degree of A(s)
-1
votes
1 answer
Why the control input for in the operating point is not considered in the control?
One method of controlling a nonlinear system is linearizing the model in an operating point and gain scheduling the controller. The operating point includes a state and an input (the trim input) so when you design a controller for the linear system,…
