12
votes
Accepted
Block diagram vs flow chart?
Use Google's define:<item to look up> feature.
block diagram
noun: block diagram; plural noun: block diagrams
a diagram showing in schematic form the ...
- 11.1k
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 ...
- 11.5k
9
votes
If a control system is unstable does it mean it will oscillate?
An example of control system with non oscillatory response.
$$
\frac{d x}{d t} = 0 + u\\
u = x
$$
Closed loop equation of this unstable system is
$$
\frac{d x}{d t} = x
$$
and its response is
$$
x(t) =...
- 1,252
8
votes
Minimal realization of a MISO system
One way of doing this is using the Kalman decomposition. For this you need the reachable and unobservable subspaces. These subspaces can be constructed using the image of the controllability matrix ...
- 1,663
7
votes
Accepted
Why is it impossible to create an observer for this not fully observable system?
Observability means that you can estimate the complete state using only the output, without knowing the initial state. In other words, you have to figure out where you are without knowing where you ...
7
votes
How are bode plots drawn for unstable systems with time delay?
You are absolutely right. Since the magnitude is the absolute value of the complex function $F(j\omega)$ the plot does not change with the sign of the pole or zero. The Phase on the other hand does ...
- 71
6
votes
Accepted
Advantage of anti-windup
Anti-windup is a concept for feedback controllers with integral terms, e.g. PID, to keep the integral term from „overcharging“ when regulating a large set point error. It basically saturates the ...
- 1,943
5
votes
Anomaly in viscous force - vs - velocity relationships
The examples you mentioned both occur due to turbulent flow of a gas. However in a lot of mechanical systems damping often occurs due visco-elastic deformation or due to shearing of the lubricant ...
- 1,663
5
votes
Accepted
Square wave transfer function?
I thought I would expand a little on the answer offered by Karlo.
Long story short, I would not try to calculate the analytical time response of a system to a square wave. That would be a serious ...
5
votes
Quaternion in control applications
Euler angles are easier to understand and use. Imagine a airtrafic controller getting a aircraft heading info as quaternion data. Euler angles are significantly easier to understand interpret and ...
- 3,684
5
votes
Open loop versus closed loop Model Predictive Control
I think the other answer is not complete. Model predictive control (or 'receding-horizon control' is a technique in which a predictive system model is used to evaluate a sequence of future control ...
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
5
votes
Accepted
Root Locus and Routh–Hurwitz stability criterion
Suppose we have a third order polynomial in the form :
$$ s^3+a_2s^2+a_1s+a_0 = 0$$
There is nice caveat for third order systems which is derived from the Routh-Hurwitz stability criterion. In order ...
- 819
5
votes
Accepted
Can someone explain how the output of this control system is derived?
Well as a fresh start: net(n) is the value before the node, this can be seen by equation (1). The value after the node is the following (lets call this $x$ for simplicity):
$$x(n) = net(n) - a_1x(n-1) ...
- 1,099
5
votes
Accepted
How do I interpret the following Bode, Nyquist and Nichols diagrams?
Your systems shows extremely close pole-zero cancellation. So much even that it nearly removes 4 poles and zeros. Lets look at why, starting with the Bode plot:
The magnitude plot is constantly ...
- 1,099
5
votes
Full state feedback of a closed loop system
Let me phrase this a bit more elaborate.
Suppose we have a state space system, ie:
$$\dot{x} = Ax + Bu$$
Where the dynamics of the system are presented through $A$. For instance, the poles of the ...
- 1,099
4
votes
Difference between PI and PD controller?
PI - Proportional - Integral
The output is a combination of how far you are from the goal and the integral of your distance from the goal (total error over time). This means that it will track small ...
- 766
4
votes
Accepted
What do actually control engineers do?
In short, 'systems' refers to a combination of components that act together and perform a certain objective. A system can span across different physical and virtual domains.
Controls engineers ...
- 56
4
votes
How to determine the region in a state plane where the equilibrium state is asymptotically stable
As you might already know your system is nonlinear, which means that it is not trivial at all. See below for the plot of the system. The linearization around $(0,0)$ gives you the information that the ...
- 1,036
4
votes
Accepted
Nyquist plot - what is the meaning of circles with dB values on complex plane
See doc nyquist:
The nyquist function has support for M-circles, which are the contours of
the constant closed-loop magnitude. M-circles are defined as the ...
- 540
4
votes
Accepted
How to execute trajectory?
You have to choose a controller that best fits the system you are trying to control. You have to take into consideration the variables you are trying to control when deciding on the controller. ...
- 596
4
votes
Accepted
Time constant - formula
Does the book not give you the mathematics? The underlying expression is:
$$parameter = 1-e^{ -t/ \tau }$$
so you see at $t = \tau$
$$parameter = 1 - e^{-1} = 0.63$$
Now the second sentence says ...
- 939
4
votes
Accepted
Why does a proportional controller have to have a steady state (offset) error?
If you open your drain valve, and then close it again, then you're correct, the tank will refill back up to 50, leaving you with no offset. If, however, the valve is left open, then the water may not ...
- 7,771
4
votes
Simple examples to illustrate the utility of the Laplace Transform
Consider $s$ as a derivative operator.
Therefore,
$$\frac{Y}{X}=\frac{s+2}{s^2+0.5s+3}$$
looks like
$$\frac{Y}{X}=\frac{\frac{d}{dt}.+2}{\frac{d^2}{dt}.+0.5\frac{d}{dt}.+3}$$
$$(\frac{d^2}{dt}.+0.5\...
- 253
4
votes
Stability of the optimal control law
So, just to formally repeat your question, we consider an infinite horizon continuous-time optimal control problem
$J^*(x_0) = min \int_0^{\infty} x(t)^TQx(t)+u(t)^TRu(t)dt$
which is subject to ...
- 1,943
4
votes
LQR control and system dynamics linearization
The idea that you describe is basically Model Predictive Control with successive linearization (the optimization problem that is solved in MPC is finite-horizon while LQR is infinite-horizon, but the ...
- 1,943
4
votes
Accepted
PI controller for second order system
Step 1: Draw the root locus of the system.
Here you can see the two poles of your plant $G(s)$ (marked with an x), at $p_1=-9$ and $p_2=-1$, the pole of your controller $C(s)$ at $p_c = 0$ and the ...
- 884
4
votes
Root locus: ambiguity on which branch goes where?
I think you're over-analyzing. The root locus is an abstraction. While it usually makes it easier to think of the poles as "moving", you don't want to get too married to that thought.
It works ...
- 2,767
4
votes
Accepted
Problem with performances of a control scheme
Your closedloop crossover frequency (when the magnitude of $P(s)\,C(s)$ is equal to one) lies at roughly 1 rad/s. This means that the feedback controller already causes the system to track reference ...
- 1,663
4
votes
Accepted
what is the physical interpretation of poles and zeros of a mechanical system?
The poles and zeros of a LTI plant or system in relation to their eigenvalues determine how quickly a system will stabilize or destabilize and if it oscillates.
When looking at these in the complex ...
- 729
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