Questions tagged [control-theory]

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15 views

Using Integral gain for motor positioning

I'm struggling to see how Integral gain is used for motor positioning. Suppose we have an AC motor (with a 2048PPR encoder on the shaft) connected to a winch which drives an object forwards and ...
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11 views

Passivity in State Space Systems

Suppose I have the state space system $a\dot{x} = -x + \frac{1}{k}h(x) + u$, and output $y = h(x)$, where $a,k > 0$. The only information I'm given about $h(x)$ is that $h\in[0,k]$. I want to show ...
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39 views

Backstepping control of second order nonlinear system

$\dot{x_{1}}=x_{2}^2-3sin(x_{1})x_{2}$ $\dot{x_{2}}=x_{1}^3-3x_{2}cos(x_{1})+u^\frac{1}{2}$ Question: Using the backstepping method and Lyapunov function, design the controller(u) that will make the ...
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26 views

avoidance with LQR

I'm interested in using linear quadratic regulators (LQR) to model prey avoidance behaviors. I want to adapt the LQR algorithm to incorporate dynamics and state costs that maximize the distance from a ...
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2answers
71 views

How to obtain transfer function of control diagram with Internal Model Control?

I want to design a robust control system using the internal model design specifications. The block diagram is the one shown below: I am trying to obtain the transfer function $\ \frac{Y(s)}{R(s)} $ ...
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17 views

Tuning a cascaded attitude and attitude rate PID controller

Assume that I have an object in 3D, and I want to have a controller that stabilizes its orientation (also referred to as "attitude"). To be sure we are clear: attitude is measured in "degrees" or "...
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0answers
18 views

Applying full state feedback on DC motor with torque load

I tried to apply full state feedback on DC motor (with no load) and it works fine in the simulation on Simulink But the question is if I have a load applied on the motor (let’s say constant load or ...
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1answer
19 views

Noise sensitivity transfer function

Consider we have a second order system (plant) described by the following transfer function: $$ P(s) = \frac{b_0}{s^2+a_1*s+a_2} $$ which is controller by a PD-controller: $$ C(s) = K_p+K_ds $$ ...
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1answer
41 views

How to reduce oscillations (rapid changes of control signal) when controlling a real system, which occur due to noise in measurement from sensors?

I have a real mechanical system (ball & beam) which I want to control. The system is approximated by the second order transfer function: $$ T(s) = \frac{b_0}{s^2+a_1s+a_2} $$ and in state-space ...
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2answers
37 views

Chemical engineering equivalancy to the spring-mass-damper/RLC circuit

I understand the equivalency between the MSD and RLC circuits. Mass ~ resistance, spring ~ inductor, damper ~ capacitor. With the equations of the form MSD: $$ m\ddot{x} + c\dot{x}+ kx = F $$ ...
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1answer
70 views

Proportional-Derivative compensator design

I have been struggling with the following problem for a few days now and would greatly appreciate some assistance. I'm new to control systems and have very little experience with PD controllers and ...
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2answers
71 views

Increasing Kd in PID control loop

Why does increasing derivative gain $K_d$ in a PID controller loop lead to a reduction in overshoot and an increase in rise time? This is not a homework question, it is a question to improve my ...
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1answer
99 views

Does this PID-like algorithm make any sense for a solar inverter?

The application I want to implement the control of a photovoltaic inverter. The goal would be to keep the consumption of a microgrid (the power absorbed from the grid) to a constant value. Notes: I ...
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1answer
43 views

Control System; Finding resonant frequency of 3rd order

We've been requested to find the resonant frequencies of a 3rd order plant in class and were presented to the following method to do so: My question is, when using the $\ \omega_r $ formula, to find ...
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0answers
21 views

Kalman Filter by Orthogonal Projection

I'm working through the derivation for the Kalman filter using orthogonal projections. It's pretty intuitive that if we want to generate the best linear estimate for an $n$-vector $x$ using some $m$-...
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1answer
57 views

How to obtain linear parametric model of given system?

Consider the system: $$ y(s)=b\frac{e^{−sτ}}{s+a}u(s) $$ where a,b are unknown, constant parameters and $\ τ>0 $ is an unknown delay constant. How can I obtain a linear parametric model for this ...
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32 views

LQR Implementation in MATLAB

I am trying to implement a simple LQR controller in MATLAB for a purely deterministic system. The code is shown below: ...
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1answer
39 views

What are the drawbacks of inceasing the bandwidth of the system?

I have a doubt concerning the closed loop frequency responce of a control system. Suppose I have the following situation: in which is plotted the frequency response of a system with different ...
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1answer
40 views

Develop linear parametric model of a third order plant

Consider we have the third order plant described by the equation: $$ y = G(s)u $$ where $\ G(s) = \frac{b_{2}s^{2}+b_{1}s+b_{0}}{s^{3}+a_2s^2+a_1s+a_0} $ If we assume that all parameters $\ a_0,a_1,...
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1answer
39 views

Problem finding value of the gain such that the closed loop is stable

I have the following transfer function: $G(s)=\frac{-s^3 +s}{s^4+3s^3+2s^2}$ and this is a transfer function of a plant with two poles in the origin. So I want to desing a controller with two poles ...
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1answer
21 views

Problem with RHP zero in transfer function

I have a transfer function with a RHP zero in $s=+1$, and I am trying to show in Matlab thath this limitation is present. In particular, initially I had a MIMO system, which I decoupled and then I ...
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1answer
31 views

Doubt on bandwidth of a control system

Consider this image of a loop shaping design: here which is the bandwidth of the system? I have a doubt because until now I have considered as bandwidth to the system the one of the complementary ...
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1answer
22 views

Nyquist stability criterion for positive feedback

it is known that the stability of a system with negative feedback may be analized through the Nyquist stability criterion, which is based on observing the number of turns around the point (-1;0) in ...
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0answers
50 views

How do I add unmodeled dynamics to the system?

I am considering the following paper: Stability‐and performance‐robustness tradeoffs: MIMO mixed‐µ vs complex‐µ design and I am having troubles understanding how to handle the unmodeled dynamics of ...
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1answer
49 views

analysis of PD controller vs static-gain

I have a plant $G(s)$ which gives position and velocity as output $$ G = [G_{ru}(s)\quad G_{vu}(s)]^T $$ where $G_{ru}$ is the integral of $G_{vu}$, and $u$ is the input to the system. Now if I want ...
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2answers
42 views

How to convert output of controller (control signal) into PWM signal?

I am trying to control a mechanical system with some transfer function T (output is position & input is voltage). I have implemented a state feedback controller in order for the output of the ...
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0answers
51 views

Finding coefficients for a PID controller that minimize the integral of the squared error (ISE)

The problem The problem is to find the coefficients for the P, I and D terms of a PID controller used to regulate the object that minimize the the integral of the squared error (ISE): $$Q = \int_0^\...
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1answer
83 views

Is it necessary to use PID control in my use case?

I have a workflow of two functions. Both of them aggregate the items that are receiving and only the first is adjustable. I mean that I can decide how many items to aggregate on the first function <...
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1answer
53 views

what is the physical interpretation of poles and zeros of a mechanical system?

what is the physical interpretation of poles and zeros of a mechanical system? I'm asking things like the meaning if I have only 0 or only complex numbers. And about the number of the poles and zeros, ...
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1answer
63 views

Optimal control vs. nonlinear control

I have tried to compare between two courses, and there seems to be some overlap, but not as much. Which method is better when controlling a nonlinear system? Also, what is the main difference between ...
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1answer
33 views

Aircraft Longitudinal and Lateral Transfer Function Terms

The figure shows input and output variables for both longitudinal and lateral stability transfer functions. I completely understand what each term stands for but I was wondering what would be the ...
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1answer
29 views

Doubt on zero pole cancellation

I am looking at a control system which has an unstable pole in the process. The transfer functions of process and controller are the following: ...
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0answers
41 views

Why a zero too close to the imaginary axis gives bad berformances?

I am studying control systems, and I have found that if I consider I control scheme where I filter the reference , if the zero of the pre-filter is too close to the imaginary axis, we have a ...
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1answer
26 views

Predict egg drop outcome in random container

What elements affect the outcome of a raw egg drop in a random container? I’ve considered friction, mass, size of container, size and type of padding. Are there other elements?
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1answer
21 views

Control each axis separately - quadcopter

I would like to know why axis can be controlled independently in a quadcopter. I mean, I was told that you can control $x$ and $y$ independently but I couldn't find a demonstration Edit: the ...
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1answer
44 views

Limitations on the control effort

I am studying the mixed sensitivity design for control systems, and I have seen that the control effort has limitations given by the bandwidth of the process and by the bandwidth of the sensitivity ...
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0answers
29 views

Design compensator to improve yaw rate control performance for aircraft

I am trying to design a compensator to improve the yaw rate ($\dot{r}$) control performance of an aircraft. The lateral dynamics for this aircraft is given in steady space form as following: where A (...
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0answers
21 views

Control effort in mixed sensitivity design

I am dealing with mixed sensitivity controller design in SISO systems and I am comparing this approch with the classic approch. In particular, I have placed a weight for the sensitivity function in ...
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1answer
30 views

Stability with eigenvalues' real part equal to zero

I know, from Lyapunov criteria, that a system is stable (not asymptotically) if the system has eigenvalues with negative real part or it has eigenvalues with real part equals to zero, but in this case ...
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21 views

Relationship between conjugate poles and resonance peak in frequency response

I have two root locus of two closed loop transfer fuctions, which differ just by a different value of the gain. I have that the one with a larger gain has a reasonance peak bigger in the frequency ...
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15 views

Gradient-free optimal control solver?

I have a dynamics simulation that provides the state derivative $\dot x = f(x,u)$, implemented in C. I'd like to solve the optimal control problem (given an initial state and cost function). Because ...
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1answer
45 views

Time constant of second order system

I have a second order system with open-loop transfer function $G(s)={a\over(s+b)(s+c)}$, $a,b,c$ are already known. This system has unity feedback. I am interested in the time consant of this system, ...
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1answer
21 views

Design the equivalent electric circuit (using op-amps) describing open loop transfer function G(s)

How can I convert the Standard form of the second –order system transfer function into op-amp circuit ? G(s) = wn^2 / (s^2 + 2ζwns + wn^2)
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Problem reading control effort frequency response plot

I am trying to plot the frequency response control effort of a control scheme in Matlab, and in particular I want to do this for different values of tau, which is a constant used to add a pole at high ...
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1answer
58 views

Problem with performances of a control scheme

I am trying to prove with Matlab that if I have an improper system and I place poles at higher and higher frequencies the performances of the system improves. In particular I am considering the ...
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1answer
25 views

Transfer function for a quadcopter with linear velocity inputs

I found the control for a quadcopter using the angular velocities or thrust power as the input, but I need a model where I can set the initial and final position (for example, from (0,0,1) to (0,1,1))....
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25 views

H infinity control problem - changing eigenvalues of plant

I'm applying $H_\infty$ approach to control a system with a given input $u$, and I can measure and feedback position and velocity errors. The plant is described by the following transfer function $$...
3
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1answer
48 views

Controls Project: Help needed finding 3rd order system

I'm in need of help finding a third-order or higher system in which I can derive a transfer function. We have a class project in which we need to find a real-life example of the system that equates to ...
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23 views

Zero-state observability and strictly passive systems

I'm currently studying passivity theorems of nonlinear systems, and I find it difficult to understand the difference between the different kinds of strict passiveness. Are there any intuitive ...
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44 views

Offline Parameter Estimation for second order system - Ordinary Least Squares

I have a second order system which is described by the following differential equation: $\ \ddot{y}+α_{1}*\dot{y}=b_{0}*u $ where $\ y $ is the output of the system and $\ u $ is the input of the ...

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