Questions tagged [control-theory]

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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)=...
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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 ...
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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 ...
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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: $$ C(s) = k_p + k_i \frac{1}{s} + k_d \frac{N}{1 + N \frac{1}{s}} $$ ...
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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) ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 &...
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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 ...
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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 ...
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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 ...
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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?
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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 ...
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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 ...
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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?
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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 ...
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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).
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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 ...
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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 ...
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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 ...
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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) - (...
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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{\...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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}{...
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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 ...
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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 ...
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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 ...
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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{...
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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 ...
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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: $$ ...
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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 = ...
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45 views

LQR control effort / control bandwidth relationship

I'm working with a linear system, having given matrices A and B $$A = \left[\begin{array}{cc} 0 & 1 \\ -0.9 & 0 \end{array}\right]$$ $$B = \left[\begin{array}{c} 0 \\ 2 \end{array}\right]$$ ...
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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. ...
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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 ...

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