11
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 ...
- 10k
9
votes
Accepted
How can I approach the application of control theory to real control systems?
I hope I can help you in some way, your question bounces around a bit so I'm guessing a little on what you are wanting to know. This is how you come up with a controller that is implementable from ...
- 725
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
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) =...
- 907
8
votes
Accepted
How do you set up a PID-Control if the time constants of the controlled system are variable?
One way would be to implement some form of adaptive control. If your range of time constants is small and known, you could use something called "gain scheduling"
where you determine before hand all ...
- 725
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 ...
- 1,643
7
votes
Accepted
Feedback control of two-link planar manipulator
Convert the nonlinear model to state-space form, $x'=f(x,u)$, and linearize it to get a linear state-space or transfer function representation. You can use this to design a PID controller and simulate ...
- 1,911
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
When are overshooting controllers preferred over asymptotic ones?
For some systems, the salient criterion is settling time to within some error band. Sometimes you can get faster settling by allowing earlier overshoot.
If you need a system to get to within some ...
- 11.4k
6
votes
Accepted
In Control Systems Engineering, why do imaginary poles and zeros on the LHP indicate stability?
Only the poles in the LHP are necessary for stability. This is because the transient response of a LTI system will consists of a linear combinations of $e^{p_i t}$. If a pole is complex, $p_i=\rho_i+i ...
- 1,643
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 ...
- 1,863
5
votes
Accepted
Determine the range of values for a PI controller
There is a mistake in your expressions. The coefficient of $s$ is $2+k_p$.
The conditions are: $$\frac{1}{3} \left(3 \left(k_p+2\right)-k_i\right)>0$$ $$k_i>0$$ $$k_p>0$$
This simplifies ...
- 1,911
5
votes
Controllability of $x' = Ax + Bu(t)$ implies controllability of $\left \{ \begin{matrix} x' = Ax + By \\ y'=u(t) \end{matrix} \right.$
The solution is fairly straightforward.
Short answer
The system is controllable without any modifications. You made a small mistake calculating the new controllability matrix: you are missing the ...
- 1,220
5
votes
Why can't proportional gain alone, reduce the error to zero?
To understand why proportional gain won't drive the error point to zero, it is best just to look at the math. Consider the PID loop shown in the image below. The loop algebra in the $s$ domain comes ...
- 6,386
5
votes
Accepted
A stable transfer function which diverges?
Without any more info, I think your problem arises from the values of $a_0$ and $a_1$. The answer is a little involved, so a bit of systems background is necessary.
The short answer
Your system should ...
- 1,220
5
votes
Accepted
Continuous time and Discrete time systems
A controller is built around a physical system. What is the open-loop behavior of the system?
You have to sample the physical (continuous-time!) system in order to provide feedback to your discrete ...
- 3,575
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 ...
- 3,561
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
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$$
There is nice caveat for third order systems which is derived from the Routh-Hurwitz stability criterion. In order ...
- 1,009
5
votes
Accepted
Can someone explain how the output of this control system is derived?
Well as a fresh start: net(n) is the value before the node, this can be seen by equation (1). The value after the node is the following (lets call this $x$ for simplicity):
$$x(n) = net(n) - a_1x(n-1) ...
- 1,069
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 ...
- 1,069
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 ...
- 1,069
4
votes
Accepted
Control theory - Differential equations and state variable description
A professor of mine, long ago, once quipped:
"Give me a word... any word at all... and I'll show you how the root
of that word is a PDE!"
A touch of Philosophy
All physical systems are modeled ...
- 2,539
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
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 ...
- 1,643
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
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