Questions tagged [control-theory]

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$\mathcal H_2$ norm for LTV system

Preliminary: Consider a stable, strictly causal discrete-time LTI system with state-space model $\left[\begin{array}{c|c} A & B\\ \hline C & \pmb{0} \end{array}\right]$. ...
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Controlling a system in a particular direction

In Discrete-time Control Engineering by Katsuhiko Ogata, it is stated that "A necessary and sufficient condition for complete state controllability is that no cancellation occurs in the pulse ...
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What is the original source of the common Ziegler-Nichols PID tuning coefficients?

In many places, including but not limited to the Wikipedia page about PID controllers, I see the following PID coefficients: $K_P = 0.6K_U$, $K_I = 1.2 K_U / T_U$, and $K_D = 0.075 K_UT_U$. When were ...
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What causes an EUC to propel forwards when leaned forwards?

If this question belongs to physics stack exchange, please let me know and I will transfer it as soon as I can. Please also let me know if a diagram is neccessary of the model (I have not made digital ...
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How to develop the the Backward Euler method for a State Space

I have been trying to develop to solve a state space model in discrete time. I have the following equation for my state space: $$\dot{x} = Ax + Bu, $$ I am developping the equation, but I do not ...
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Real-life examples of linear dynamical systems with nonzero D matrix

Which systems that are controlled in real applications are modeled as linear systems $$ \dot x = Ax + Cu\\ y = Cx + Du $$ with a nonzero $D$ matrix? I myself have only been stumbling over systems that ...
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Transfer function with disturbance

I would like to know how do I find the system transfer function below. I don't know how to find it due to disturbance. I need the transfer function to find the state space. if it were a closed loop ...
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State Space Modeling nonlinear terms of vehicle’s longitudinal motion

My project is to build a software to help drivers achieve ecodriving thanks to optimal control based advices. Consequently, to feed a linear quadratic regulator, vehicle longitudinal equation of ...
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What would the dynamics and measurement operators be in this control theory problem/code, and where can I generate them from?

I'm working on something slightly outside of my scope of work, and I can't figure out if I fully understand what these things mean. Could someone help explain what the dynamics operator and ...
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What is the difference between mathematical and process/control degrees of freedom?

Taking mathematical DOF as: $$ DOF= N_{vars}-N_{eqs} $$ How would process, or control degrees of freedom be defined as? Thanks!
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What does this variable stand for in this energy balance equation?

I'm trying to model a two basic transfer functions for temperature and humidity in a room in order to simulate a control algorithm I designed in Simulink. I have gathered this equation from this ...
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1 answer
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Sensor fusion for IMU

I'm working with MPU-6050 sensor with Raspberry Pi 4. I can read acceleration and gyroscope raw data from the sensor. However I want to get yaw, pitch and roll angles from these data. I tried to ...
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How do you find the gains for a PI controller with a first order plant and 2nd order low pass filter?

How can analytically work out the gains knowing the required bandwidth and damping? The plant to be controlled is first order. The low pass filter is 2nd order in the feedback path.
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Can there be more than one gain margin?

Why would that be the case? How does one determine stability in this case?
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Real examples of complex PID regulators

I am currently developing the C library for easy implementation of PID controllers. Can you give some examples of complex PID controllers from real life? I don't mean a simple DC motor with a speed ...
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Lag compensation with the forth order system

The control system below is with lag compensation. The question asks to find a and T so that the characteristic equation of the ...
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Boeing 747 Autopilot Vertical Speed Function (PID Controller)

I originally asked this over at the math stack-exchange but was told I might have better luck here. I have simply copy-pasted the question. I am working on a Boeing 747 autopilot control system for an ...
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How to show that the infinity norm obtained in the problem given below is correct?

I found the following example problem in page 178 of the book "Nonlinear System" by Hassan K. Khalil, Third Edition. The objective of this problem is to show whether a system is input-to-...
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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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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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