Questions tagged [control-theory]
The control-theory tag has no usage guidance.
371
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Derive equation of the lead compensator [closed]
Referring to the closed-loop system shown in Figure below design a lead compensator Gc(s) such that the phase margin is 45°, gain margin is not less than 8 dB, and the static velocity error constant ...
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Linearization about equilibrium point 0 in the presence of unknown input
Consider a SISO non-linear system $$\dot{x} = F(x,u)$$ in which $\vec{0}$ is an equilibrium point. In the process of determining that it is indeed an equilibrium point, the input did not matter at all....
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Control Engineering: Formal vs. Trial-and-Error
At university, my control engineering courses are focused on a more theoretical approach, but the main message from our professors was clear: When designing a feedback controller (PID, H-infinity, MPC,...
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Intuition for blocks and Laplace form for cascading transfert function
I'm failing to understand Blocks in block diagram in control theory. Indeed, the link between transfer function of time and function of Laplace is fuzzy to me. I'm looking for a way to ground my ...
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Which controller is more suitable in this scenario? P, I or PI controller?
Scenario:
A robot has a ultrasonic sensor which measures the distance to the nearest object in centimetres. The robot has two motors, a motor for the left wheels and a motor for the right wheels. The ...
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How can I find characteristic equation of complex systems?
I am working on an Overhead crane, where I am supposed to design a controller that controls the position of the crane while minimizing the load's sway angle. I have derived the transfer functions for ...
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Contradiction of bandwidth and damping
I am studying control theory and mechanical vibrations.
From control theory aspect, I know that bandwidth and response time is inversely proportional, which means bandwidth and damping as well.
But in ...
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What's a real life example of linearization of a system around a fixed point
I'm tasked on finding a example of a real non-linear control system. a real paper or publication on a website like the IEEE thats describes the model of the system so I can then linearizy it around a ...
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Bode plot phase margin concept details
I know a closed-loop system $\frac{G}{1+G}$ is unstable when the open-loop transfer function $G$ equals -1 or $0dB\angle-180^{\circ}$. The denominator becomes 0 so the gain is infinite. This is why ...
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Phase margin concept: why can there be instability when the gain never reaches 0dB?
If the open-loop transfer function is always below 0dB but the phase crosses or approaches 180 degrees, the closed-loop system can still be unstable. Why? Example: open-loop transfer function $\frac{0....
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SMC: Is there a way to control two sliding surfaces with just one control input?
This is a question related to Control Systems.
I've been searching papers all over the internet with very little success. I know that traditionally we want one control per sliding surface but If ...
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Deadbeat gain for system with measurement delay
Say we have SISO system (e.g. the velocity of a permanent-magnet motor) that we're controlling with proportional feedback, with the condition that our measurements of the process variable are delayed ...
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How to control speed of DC Gearmotor with Varying Torque
I have a system where the torque is constantly changing, but I need the speed to remain at 9RPM. I have enough room for error where I can be between 8 and 10RPM. How can I achieve this? All I can find ...
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Modelling an S-shaped Second Order Process Response
I am trying to model an S-shaped second order process response as a transfer function in Simulink, as shown in figure 3 in the linked article. Ideally the response should be overdamped. I have tried ...
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Unexpected uncontrollable double integrator system during reference tracking (augmented state-space)
I'm trying to design a controller that will achieve reference tracking of the second state for the following system.
$$
\begin{aligned}
\dot{x} &=\underbrace{\left[\begin{array}{ll}
0 & 1 \\
0 ...
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Kalman Filter but for control variable from finite horizon controller
I am running a closed loop simulation, using a convex controller that uses simplified linear equations of motion to calculate the control variable w. The controller considers a limited number of ...
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Stability properties of controllers with independent control laws applied in underactuated systems
I am interested in designing a GNC controller for a 3DOF underactuated vehicle that follows a path in 2D space. The two available control inputs are the thrust force in the surge direction and a ...
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How to model the state space matrix of a pendulum?
Here's an image of the problem:
I'm trying to put the following problem in matrix form (state space) but I don't know how would I put -(g/L)sin(x1) in the A matrix since the x1 value is inside the ...
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Full state feedback with integral action - Matlab script
I made this Matlab script to implement a dynamical system with full state feedback and integral action.
Maybe I'm wrong in implementing the integral action because the system diverges.
First I ...
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Dynamical system problem
I have this dynamical system:
A = [ -0.313 56.7 0
-0.0139 -0.426 0
0 56.7 0];
B = [0.232
0.0203
0 ];
C = [0 0 1];
D = 0;
I'm ...
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Finding optimal PID gain values with no Transfer Function or Plant model
Background:
I have a Matlab simulation model with .m files. The functions simulate a speed control system of a vehicle. I can control the vehicle's speed by adjusting the vehicle’s acceleration and ...
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Control scheme for roll compensation
I'm working on an application that rotates a cylindrical mass in a manner to compensate for roll in a boat. The roll of the boat is rather slow so I was thinking it might be possibly to simply use a ...
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Definition of Bandwidth as angular frequency
I am searching for a Formal Definition of bandwidth given the transfer function of a system, or the bode plot.
Is it the frequency $\omega_b$ in which
$$20log|H(j\omega_b)| = -3\text{dB}$$
or
$$20log|...
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Best Techniques to design a cascaded precision position controller
I'm looking to design a cascaded controller to transform a BLDC into a servomotor. The system has a motor current controller in the inner loop, which is controlled by a torque controller, which is ...
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What are disadvantages if increasing the gain Kd for a PD(Proportional Plus Derivative ) controller
What are disadvantages if I increase the gain Kd for a PD(Proportional Plus Derivative) controller, someone told me larger gain for derivative error for will reduce the stability margin, while the ...
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How could I compute the stability margin from a closed loop response?
Why the stability margin is typically computed by the open loop response or transfer function rather than the closed loop response or transfer function, how could I measure/compute the stability ...
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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
$$
G(s)=...
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Limitations to consider when picking a cut-off frequency low-pass filter for PID control?
Considering a first-order low-pass filter transfer function:
$$ \frac{\omega_c}{s + \omega_c} $$
Where $\omega_c$ is the cut-off frequency. Are there any limitations on where to place this pole?
For ...
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Block-diagram combining two controlled subsystems
I have two subsystems which are shown in the picture below.
One of them is a system of stable and controlled differential equations of a mechanical system.
Second is a block that implements a function ...
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(Dominant) Poles very close to zeros in PID control
I have a plant transfer function $G(s)$:
$$ 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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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