Questions tagged [control-theory]
The control-theory tag has no usage guidance.
347
questions
0
votes
0answers
29 views
Additive perturbation
consider the following transfer functions:
$$
G(s)=\frac{1}{\tau s+1}G_0 \quad \tau_{min}<\tau<\tau_{max}
$$
show that this system equal to model with additive perturbation as follow
$$
G(s)=...
0
votes
0answers
26 views
Limitations to consider when picking a cut-off frequency low-pass filter for PID control?
Considering a first-order low-pass filter transfer function:
$$ \frac{\omega_c}{s + \omega_c} $$
Where $\omega_c$ is the cut-off frequency. Are there any limitations on where to place this pole?
For ...
0
votes
0answers
25 views
Block-diagram combining two controlled subsystems
I have two subsystems which are shown in the picture below.
One of them is a system of stable and controlled differential equations of a mechanical system.
Second is a block that implements a function ...
1
vote
0answers
30 views
(Dominant) Poles very close to zeros in PID control
I have a plant transfer function $G(s)$:
$$ G(s) = \frac{1}{s^2(0.1s + 1) } $$
I want to control this with practical PID control:
$$ C(s) = k_p + k_i \frac{1}{s} + k_d \frac{N}{1 + N \frac{1}{s}} $$
...
0
votes
2answers
62 views
How to tune a PID controller when plant's step response looks like a ramp?
The system is a boat and I want to specify a yaw angle and the PID controller would operate the rudder of the boat in order to reach the desired yaw angle. So, the step response of the plant (boat) ...
0
votes
0answers
28 views
What is residual oscillation and critically damped oscillation in the context of a controller's performance?
What do these terminology "residual oscillation" and "critically damped oscillation" mean when evaluate a controller's performance? How are they related to the stability of the ...
0
votes
0answers
24 views
How to determine time constant/cutoff frequency of the filters in the controlled loop
I was told to be careful to use filters in the control loops as it will add extra time delays in the system and degrade the system dynamic response, but I also saw there are lots of filters in ...
1
vote
2answers
56 views
How could I verify the stability of a real system with non-linearities?
For a closed loop system, I could do the stability margin analysis using linear method like bode diagram, but in reality there are non-linear elements in the system like saturation/rate limits inside ...
0
votes
1answer
51 views
Could someone explain how a compensator shifts the root locus?
I'm reading a root-locus course note from MIT. However, I can't understand this part:
How does adding a compensator with a pole at origin remove the plant pole on the right half-plane into the left ...
1
vote
0answers
31 views
Sliding-mode control is a model-based technique?
The sliding mode control can be considered a model-based control? In my opinion yes since takes the information of the mathematical model of the system to be controlled handling with possible ...
0
votes
1answer
61 views
Controls System experiment
We performed an experiment in which we turned a bicycle on its side and placed a piece of green tap on one of the spokes. We spun the wheel and recorded the wheel spinning until it came to a complete ...
2
votes
1answer
61 views
What should be the sample frequency to test the response of a filter?
I am testing the frequency response as a filter as below, what should be the sample rate of the chirp signals, someone told me it should be at least 2 times of the input signals frequency, someone ...
0
votes
0answers
39 views
Stability from Gain and Phase Margin
I know that a system with positive gain and phase margin is a stable system. And the one with a negative gain and phase margin is unstable. What will a system with negative phase margin and positive ...
1
vote
1answer
53 views
Is It Possible to Have a Continuous-Time System Controllable but Discrete-Time System Uncontrollable?
I have a continuous-time state-space system $\dot{x} = Ax + Bu$ with
$A = \begin{bmatrix}0 & 0 & 0 & 1.0000 & 0 & 0\\
0 & 0 & 0 & 0 & 1.0000 & 0 \\
0 & 0 &...
0
votes
0answers
20 views
Is it possible to calculate Over Shoot percentage and settling time of an Underdamped 2nd order system with Ramp input?
Most of the books derive Over Shoot percentage, settling time for 2nd order underdamped it for unit step response. Do these parameters exist for 2nd order underdamped system for Ramp response too?
If ...
1
vote
1answer
33 views
Excluding the transient in computing RMSE in control algorithm implementation
I have implemented a control algorithm and I would like to study its performance by looking at the trend of the tracking error and then algebraically transpose what I visualize, I have thought to use ...
0
votes
1answer
39 views
Unstable System. Error Trying to model the Red Bull Stratosphere Free Fall
I tried to model a problem months ago and still I can't solve, I don't want forget this problem so I would like to share what I tried and if you know what is happening with my graph.
This is the ...
1
vote
3answers
131 views
If a control system is unstable does it mean it will oscillate?
When a plant is known to be unstable, does it mean it will have an oscillation response?
0
votes
0answers
34 views
Examples of model-based control techniques
I am trying to find out the differences between the model-based control approach and the data-driven one.
Surely the main difference is the latter's independence from the information of the ...
3
votes
0answers
46 views
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 ...
2
votes
1answer
34 views
Full state feedback of a closed loop system
Does Full state feedback gains affect the dynamic or steady state gain of a closed loop system?
0
votes
0answers
26 views
How do I find the gain from the root locus with given perfomance, where I know the real part of the poles?
I have an exercise to draw a root locus plot and determine its gain to make sure that it fulfills the performance requirements.
the given system G(s) is
$$G(s) = \frac{1}{s^2+s}$$
And the given ...
0
votes
1answer
43 views
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).
0
votes
2answers
82 views
Why prefer a discrete-time system because of a practical implementation instead of continuous one
I have previously done this question on math stack, and I think that maybe here is better.
I am studying the theory of discrete-time systems, comparing them with continuous ones in the control theory ...
2
votes
2answers
292 views
How are bode plots drawn for unstable systems with time delay?
All the example of bode plots I see in textbooks are of stable systems without delay. I wanted to know if bode plots can be drawn for unstable systems with time delay.
Using the usual method to draw ...
3
votes
1answer
76 views
Modelling of Ball and Beam System
I'm trying to model a basic ball and beam system using Euler-Lagrange Equation. My system looks something like this
I have come up with this final Euler-Lagrange Equation:
Where JB is the ball's ...
0
votes
0answers
35 views
Phase margin by definition
I'm reading about Gain Margin and Phase Margin in a book and having trouble understanding why they calculate the Phase margin like this:
<G(Wcrossover) - (-180) = PM
Why not: <G(Wcrossover) - (...
0
votes
2answers
51 views
How to simulate open and close and control valve using a simple controller
I have successfully developed a mathematical model for my physical system. My objective is to control the mass of gas in and out of the system.
The mass flowrate is given by:
$V_f = C_d.\sqrt{2.\frac{\...
2
votes
1answer
68 views
How do I study the frequency response of a physical system with Arduino?
I am a control engineering student and I am studying the frequency response of a system, so the Laplace domain, the Bode plot, poles, zeros,etc. ...
I have clear grasp of their meaning, but if I think ...
0
votes
1answer
40 views
What is the meaning of this symbol in Control System Diagram
I was reading the paper "Full-Speed Range Self-Balancing Electric Motorcycles Without the Handlebar" released in March 2016 by Professor Yang and Murakami in Keio University.
I couldn't ...
0
votes
0answers
50 views
Issue with LQR Q matrix for a cart-pendulum model
I am currently trying to develop a controller using LQR for a Segway. The model that I am using is an inverted pendulum on a massless cart. I have made animations of the uncontrolled pendulum and of ...
0
votes
0answers
45 views
Demonstration of Controlability and Observability
After I studied my Control Engineering courses some years ago, although I was able to interpret the results obtained after calculating the observability and controllability, I haven't been able to ...
1
vote
1answer
66 views
Can fullstate feedback control reject a disturbance?
Compare to PID. The part that rejects disturbance is the I-term which integrated from error signal. On the other hand, in full state feedback there are no integral part. How does it reject the ...
1
vote
0answers
37 views
Robustness to Additive Uncertainty Proof using small gain theorem
I am trying to use the small-gain theorem to prove the robust stability condition for additive uncertainty. I have been stuck on it for a while now.
Question: How can I use the small-gain theorem to ...
2
votes
1answer
35 views
Applying PSO for tuning a compensator for double integrator plant
I was reading a book on control systems by Richard Dorf and he lists procedure for designing a lead compensator for a double integrator plant. Using the method I developed models in Matlab and it ...
0
votes
2answers
55 views
Do I need a feedback loop while testing PID controller?
This is a homework for my university course control theory.
The task is simple: Test the P, the I and the D controllers separately to see the effect.
We don't have to connect the controllers to a ...
0
votes
0answers
41 views
State space representation of a product of transfer functions?
In short, I suppose the question boils down to: If we are asked to find the state space representation of $C(s) \cdot G(s)$, where C(s) and G(s) are both transfer functions, then do we treat them as ...
0
votes
0answers
43 views
Controller to maintain a stable amplitude
I am recording a channel before and after injecting current into that channel. I control the current injection using a switch, when the switch is on current goes to the channel, when the switch is off ...
1
vote
0answers
24 views
Increasing convergence rate using Optimal Control and Pontryagin Maximum Principle
My question is in addition to Tuning the optimal control synthesized according to the Pontryagin maximum/minimum principle and choosing the cost function, but requires help from the mathematical side ...
0
votes
0answers
32 views
steady state errors of a control system
I was reading that for a type-2 system the value of acceleration constant
$$K_a = \omega^2$$ where $\omega$ is the gain cross over frequency. This means that the units for $K_a$ should be $(\frac{rad}{...
0
votes
0answers
23 views
Control Partitioning in presence of external disturbance force
I am simulating the dynamics of a control system that has been designed using the control partitioning technique (model-based control + servo control).
I am having a query for the case when an ...
1
vote
0answers
21 views
Find same modulus z plane poles of over damped system
I am asked to find two poles of a second order discrete over damped system that have the same magnitude (0.4, to be exact) in the Z plane. From what I understand, that is not possible since over ...
0
votes
1answer
51 views
Input signal rescaling block [closed]
The input signal is limited and lies in range $[-U;+U]$. $U$ - unknown.
The output signal must be rescaled to be in the range $[-1;+1]$, i.e. is $+1$ if the input is at steady-state $+U$, and $-1$ if ...
0
votes
0answers
48 views
Nonlinear system with time-optimal control
Given nonlinear system:
\begin{cases} \dot{x_1}=x_3+u \\ \dot{x_2}=-x_2+\dot{f} \\ \dot{x_3}=-x_3+x_2 \cdot \alpha \sin(\omega t) \\ \dot{x_4}=-x_4+x_2 \cdot (\frac{16}{\alpha^2}(\sin(\omega t)-\frac{...
0
votes
2answers
62 views
Why shooting precision improves using two hands in opposing directions?
I wonder if someone knows a control theory model that explains the reason why using our two hands (typically in opposing directions) improves gun shooting precision. A similar situation seems to ...
0
votes
1answer
37 views
Zero overshoot criterion from the initial point $x_0$ to the final $x_*$, $x_*$ unknown in advance
Suppose a system is described by the following ODE:
$$\dot{x} = f(t,x)+u$$
where
$x$ denotes the state of the system
$f(x,t)$ is an unknown nonlinear function which meets the following condition:
$$ ...
0
votes
0answers
28 views
Mixed Sensitivity Problem
I have plant,
$$P(s) = \frac{1-s/5}{(s^2 + s/4 +1/4)}$$
I am taking a mixed sensitivity approach for that I have chosen $V$,$W_1$ and $W_2$ as follows:
For bandwidth, $\omega$ =1 so I chose M as,
$M = ...
1
vote
0answers
45 views
LQR control effort / control bandwidth relationship
I'm working with a linear system, having given matrices A and B
$$A = \left[\begin{array}{cc} 0 & 1 \\ -0.9 & 0 \end{array}\right]$$
$$B = \left[\begin{array}{c} 0 \\ 2 \end{array}\right]$$
...
2
votes
2answers
262 views
How do I interpret the following Bode, Nyquist and Nichols diagrams?
I am working with an arbitrarily complicated and long-winded transfer function that looks something like this:
$$
H(s) = \frac{as^4+\cdots+b}{cs^6+\cdots+ds^2}
$$
where letters represent constants. ...
0
votes
1answer
61 views
Examples of situations where using classical control methods are better than modern methods
I'm doing some reading on control systems at the moment and when reading pages on classical control methods, some sites state that they are preferred in industrial applications.
I've read that simple ...
