9
votes
Accepted
Is nonlinear control slower than linear control?
"Linear" imposes a set of restrictions. "Non-linear" simply means there are no restrictions.
Many non-linear control schemes can be faster than linear ones. Linear control schemes are restricted to ...
- 11.4k
5
votes
Accepted
Which course to take? Optimal control? Nonlinear control?
In nonlinear control theory, you will recognize most concepts such as controllability and observability where the linear case is often a special case of the nonlinear case. I would highly recommend ...
- 98
3
votes
Accepted
A clarifying question on Lasalle invariance principle
A set is invariant with respect to its dynamics if $x(t_0)\in M \implies x(t)\in M$, this is not the case for the set $E$.
The set $E = \left\lbrace x\in \Omega \mid \dot{V}(x) = 0 \right\rbrace$ does ...
- 884
3
votes
Accepted
High pass filter and differential equation relationship
It can be noted that the high-pass filter can also be written as
$$
\frac{s}{s + \omega} = 1 - \frac{\omega}{s + \omega},
$$
such that
$$
\frac{s}{s + \omega} Y(s) = Y(s) - \underbrace{\frac{\omega}{s ...
- 1,653
2
votes
High pass filter and differential equation relationship
You can show it with Laplace transform. Let's say Y = ℒ[y], H = ℒ[η], and ω_p is the filter pole. (Let's not simply call it ω -- when omega is used as a parameter rather than a variable, a subscript ...
- 1,387
2
votes
Accepted
How do I study the frequency response of a physical system with Arduino?
The arduino does impose some limits. But a classical frequency identification is build from a few steps:
As the other comments already suggest, the design of a suitable input. As mentioned, a ...
- 1,069
2
votes
Accepted
Input signal rescaling block
Input signal: ±U V.
Scaled output signal: ±1 V.
Required gain: $ \frac 1 U $.
Figure 1. Possible solutions.
If U > 1 then a simple potential divider may suffice. $ V_{OUT} = \frac {R_2}{R_1+R_2} $...
- 10.3k
2
votes
A clarifying question on Lasalle invariance principle
The sets $M$ and $E$ can be different. The set $E$ only considers $\dot{V}=0$ while $M$ also considers $f(x)$. Namely, invariant set means that for all $x(0) \in M$ the solution $x(t)\in M$ for all $t&...
- 1,653
2
votes
Non-Linear Analysis Convergence Problem in Ansys
Your model contains a lot of nonlinearities, therefore achieving convergence is not easy. I would try gradually adding each nonlinearity to narrow down where the solver is struggling:
turn off large ...
- 75
1
vote
Real examples of complex PID regulators
There are lots of "tricky" control situations which require completely different modifications to the PID algorithm. Here are a few:
Systems where the outputs go dead intermittently ...
- 1,901
1
vote
Non-Linear Analysis Convergence Problem in Ansys
You should be able to see Newton-Rapson residuals and element violations. Just turn them on in the 'solution information' field:
Choose a value bigger than zero, like 4.
You should also be able to ...
- 156
1
vote
Non-Linear Analysis Convergence Problem in Ansys
First of all, you didn't even mention distinctly that what does the first image that you have inserted here illustrate and represent. What is X axis and what is Y axis. There are numerous graphs ...
- 1,337
1
vote
How could I verify the stability of a real system with non-linearities?
Simple answer: tune the controller such that it avoids saturation / rate limits at all cost, then use standard stability analysis techniques.
Complex answer: Stability techniques like bode and nyquist ...
- 1,069
1
vote
Zero overshoot criterion from the initial point $x_0$ to the final $x_*$, $x_*$ unknown in advance
Im going to step out of the comment section as it is fairly limited. The quickest answer to the question:
Is it possible to somehow form a transient process (with given properties) if the steady ...
- 1,069
1
vote
Accepted
Which way of solving from nonlinear control to choose?
Taking the time derivative of $y$ yields:
$$
\dot{y}=\frac{\partial f}{\partial x}(f(x)+u)
$$
We need $y(t)=y(0) e^{-\beta t}$ but this is possible if and only if $\dot{y}=-\beta y $ , if the hessian ...
- 126
1
vote
Changing the quality of the transient process in a nonlinear system (Part II)
The problem is complicated by the fact that the function f(t) and the point at which its minimum/maximum x∗ is located, generally speaking, are not known to us.
So if I understand it correctly: $f(t)$...
- 1,069
1
vote
Accepted
Numeric quadrature vs summation of running costs in model predictive control
MPC finds the optimal input $u^*$ which is the input that minimizes the cost function $J$ or $c$. This means that regardless of what this actual value is, its proven to be its minimum. As such, ...
- 1,069
1
vote
Accepted
Fixed end points optimal control problem
I think I have found an answer and please correct me if there are any other reasons apart from the following justification.
Since $x^{*}(t)=\{x(t)\in\Omega|J(x)<\min J(y), \forall { y \in \Omega}\}$...
- 215
1
vote
Adding phase error to a system based on phase margin
Being able to check the response of a system, particularly of a MIMO system, to a bunch of unknown external disturbances is very crucial when designing a controller. These external unknown ...
- 1,019
1
vote
Control of a nonlinear static MIMO System
Based on your comment, it seems like you are trying to control a dynamical system to track some reference trajectory subject to Gaussian disturbances. Suppose you have some kind of model for the ...
- 461
1
vote
Accepted
Bounds to prove exponential stablity for given Lyapunov function
You don't necessarily have to find exact constants $k_1,k_2,k_3$, only need to show that there exists some positive constants. In your example above, I can say that
$$
\dot{V} \leq -\bigg(\frac{x_1 +...
- 461
1
vote
Which course to take? Optimal control? Nonlinear control?
In control systems, the main focus is the design of a controller for machines or robots, here we mainly deal with linear systems application of linear control theory.
While non-linear systems is an ...
- 84
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