Questions tagged [control-theory]

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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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32 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
53 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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33 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
28 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
51 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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38 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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37 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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18 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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18 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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18 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
49 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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42 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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57 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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33 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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20 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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37 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
164 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
58 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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30 views

Finding Derivative Gain for PD Controller

I am trying to design a PD controller $G_c(s) = K_d(s+z_c)$ with the following requirements: No overshoot, $\zeta = 1$ Settling time $T_s = 0.0002s$ The transfer function that I am currently working ...
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1answer
24 views

why do we need state feedback in H-infinity concept instead of output feedback

I have faced control of a flexible manipulator which have a zero dynamic related to flexible parts dynamic. the zero dynamic states (generalized states) are not observable in input-output dynamic and ...
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17 views

Scalability in the context of optimization and control systems

I am having a hard time trying to make sense of the phrase "Scalable optimization". I read from a few papers discussing that some global optimization solvers like BARON, ANTIGONE, etc. do ...
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66 views

Stability of a closed loop control system

I have a question regarding control theory. Say I have a closed loop feedback system and I have found the closed loop transfer function, how would I then assess the stability of my closed loop system ?...
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1answer
57 views

Is it possible to solely use a P-controller for velocity control?

Let's say I want a robot to run at a certain speed. I have one motor attached to each robot rear wheel. The feedback value to the controller comes from an encoder, which outputs pulses per time unit, ...
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1answer
43 views

Determine Stiffness (k) and Mass (m) of a system from impulse response

I have a test sample (Piezo Diaphragm) which I am actuating with a voltage supplied to the sample to assess the impulse response. When this voltage is supplied to the sample a deformation per unit ...
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1answer
44 views

How to model this real-world system to define transfer function for stability?

The system shown is an off-axis drive system that rotates the platform to 60° via a substantially-sized NEMA 34 stepper motor. The axial force required by the stepper/ballscrew assembly has already ...
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1answer
29 views

Transfer Function

Hi Guys I am trying to evaluate the following transfer function below can anyone verify if this is correct $$e_i = -d_{r,i} + d_i $$ $$d_i = q_{i-1}-q_i$$ $$d_{r,i} =H_iq_i$$ $$Therefore, e_i = -...
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1answer
44 views

Closed Loop transfer Function

Hi Guys wanted some help for breaking down a block diagram which can be seen below. I know that typically with feedback systems be it negative or positive you would employ using the following:- Close ...
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1answer
53 views

Determine the parameters for this given nyquist plot

I have seen quite many of this type of question and I want to find how to solve them but I haven't cracked it yet. For example this is one: My thoughts so far: Replace $$s \rightarrow j\omega$$, $$G(...
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1answer
48 views

Which way of solving from nonlinear control to choose?

I have a nonlinear system: \begin{cases} x'=f(x)+u \\ y=f(x) \end{cases} where $f(x)$ - gradient of some one-extremal function (for example $f=e^{-(x)^2}$), i.e. $\frac{df}{dx}$. Task: I want ...
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2answers
112 views

Why does accuracy of temperature PID controller drop over time and how to eliminate it?

What am I trying to control? I have a container with approximately 3*2*6 meters (width, height, length). I am controlling through PID the ...
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2answers
54 views

High pass filter and differential equation relationship

Consider the problem stated as follows: A signal y passes through a high pass filter $\frac{s}{s + ω }$. A high pass filter with cutoff frequency ω isolates the variations of this optimized variable ...
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4answers
86 views

PID controller - Counterproductive derivative

I'm having trouble understanding the derivative part of a PID controller, because it sometimes seems to react the opposite way that I would like. Let's use a simple example where : the controlled ...
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1answer
57 views

PID Control: Is adding a delay before the next loop a good idea?

I am implementing PID control in C++ to make a differential drive robot turn an accurate number of degrees, but I am having many issues. Exiting control loop early due to fast loop runtime If the ...
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1answer
84 views

What's the difference between Fuzzy PI, PD and PID controllers?

I am investigating fuzzy control and I am a little confused, I have come across 3 models and I can't quite fathom out what is going on. In this PD+I controller, I can see the error signal being ...
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37 views

Controlling the dynamics of nonlinear systems with an unknown steady state

On the one hand, the question is simple, on the other hand, I need the help of specialists in control theory. Let's take a simple gradient dynamical system: $\frac{dx}{dt}=\frac{df}{dx}$ where $f=e^{-(...
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1answer
25 views

What does “analytical design” mean?

What is meant by "designing analytically" ? Especially in control systems design Does it mean theoretically design?
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1answer
36 views

Is it true that points of root locus only satisfiy the angle condition?

So , I was reading a course book : ''Modern Control Engineering '' by Ogata and I came forward this statement that made me skeptical: ''The points of root locus only satisfiy the angle - condition. ...
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1answer
26 views

Complementary filter in MPU_6050 is giving me the wrong answer when the system is accelerating

So I am using a complementary filter to find the attitude in my quadcopter, doing the following $$\text{angle} = 0.98\cdot (\text{angle}+\text{dt}\cdot \text{angle_rate})+0.02\cdot \text{...
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1answer
33 views

Feedback Control Question: Finding compensator numerator (B(s)) and denominator (A(s)) polynomials to satisfy a specific requirement

I wish to find the polynomials B(s) and A(s) in the following compensator equation: A(s)D(s) + B(s)N(s) = F(s) Given, $$N(s) = s - 2$$ $$D(s) = s^2 - 1$$ $$F(s) = s^2 + 3*s + 4$$ Condition The degree ...
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2answers
68 views

Determine the transfer function of a movement equation

The problem is the following. I have to control a spaceship (assuming no gravity, no mass, no friction / no external forces). In other words, the first equation in this question leads to $0 = 0$. My ...
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2answers
41 views

What is the output of a signal in time domain that passed through a High Pass Filter with simple transfer function

If a signal function $ U(t) = 25 – (5 – t)^2$ is passed through a high pass filter with transfer function $\frac{s}{s + ω}$. what is the output signal Y(t). I know that the transfer function $H(s) = \...
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36 views

Evaluating Steady State Error Constant for a Discrete Time Control System with Kronecker Delta Input

Hello there, hope you are doing well. I am working on a Discrete Time Control Systems homework and at a certain part of it, the question asks me to find the steady state error of the system. I ...
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38 views

How to model a double transfer function in Simulink?

I'm trying to model an actuator in Simulink based transfer functions previously derived. One of functions is $$\omega_p=G_2(K_cG_1V_c-c)$$ where $$G_1=\frac{K_e}{\tau_es+1}$$ $$G_2=\frac{1}{c+...
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62 views

Is there any application of control engineering to the study of algorithms stability or computer science theory?

I am an undergraduate student in Electrical and Computer engineering. In our 5th semester we have a obligatory "Introduction to control systems course". I was wondering if these bunch of ...
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1answer
69 views

Feedback loop and zero - error in steady state

I need help with this exercise. I 've tried many times with pen and paper but I'm stuck. I don't want a full answer but some feedback . Here is my progess: $$\frac{dx}{dt} = Ax(t) + Bu(t) \Rightarrow ...
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45 views

Changing the quality of the transient process in a nonlinear system (in Mathematica)

I urgently need advice and help. I have a system of differential equations like this: $\begin{cases} \frac{dx}{dt} = y[t] \cdot \alpha \cdot sin(\omega t) + \frac{d}{dt}(\alpha \cdot sin(\omega t)) ...
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1answer
56 views

Numeric quadrature vs summation of running costs in model predictive control

Usually, an MPC consists of discretizing the optimal control problem in time using some numerical quadrature scheme. So the infinite-dimensional OCP reads $$\begin{aligned}J(\vec{u}) &= \varphi\...
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2answers
70 views

How do I interpret states in the MATLAB System Identification Toolbox?

I am using the MATLAB System Identification Toolbox to estimate a 3rd order state space plant model. More precisely, the plant is a car with an Arduino mounted on it. The car takes in a PWM duty cycle ...

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