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 ...
Olin Lathrop's user avatar
  • 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 ...
link's user avatar
  • 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 ...
useless-machine's user avatar
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 ...
fibonatic's user avatar
  • 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 ...
Pete W's user avatar
  • 1,550
2 votes
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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 ...
Petrus1904's user avatar
  • 1,069
2 votes
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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} $...
Transistor's user avatar
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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&...
fibonatic's user avatar
  • 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 ...
meshWorker's user avatar
2 votes
Accepted

What is the relationship between classical control: transfer functions/frequency domain and the swing-up problem of an inverted pendulum

how to formulate this same problems as a transfer function or in the frequency domain? I mean I could compute the transfer function for the pendulum equation. The range of motion involved in bringing ...
AJN's user avatar
  • 1,109
1 vote

Linear and nonlinear model outputs are different using the same input

Agree 100% with Tim Wescott. Here is a little more detail: Imagine an oscillator containing a nonlinear spring, that stiffens up when presented with large amplitudes. That extra stiffness tends to ...
niels nielsen's user avatar
1 vote

Linear and nonlinear model outputs are different using the same input

What are you missing? You are using two different models, and getting two different results. There should be no surprise in this. When you linearize a nonlinear* system around a point, you are ...
TimWescott's user avatar
  • 2,652
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 ...
Drew's user avatar
  • 1,931
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 ...
Orbit's user avatar
  • 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 ...
Rameez Ul Haq's user avatar
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 ...
Petrus1904's user avatar
  • 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 ...
Petrus1904's user avatar
  • 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 ...
abc1455's user avatar
  • 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: $f(t)$...
Petrus1904's user avatar
  • 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, ...
Petrus1904's user avatar
  • 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 $x^{*}(t)=\{x(t)\in\Omega|J(x)<\min J(y), \forall { y \in \Omega}\}$...
jbgujgu's user avatar
  • 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 ...
Teo Protoulis's user avatar
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 ...
Josh Pilipovsky's user avatar
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 +...
Josh Pilipovsky's user avatar
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 ...
anshul suri's user avatar

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