Questions tagged [control-theory]
The control-theory tag has no usage guidance.
425
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How do I solve an optimal control problem where the dynamics depend on some function of the state?
A typical optimal control problem with state $x(t)$ and control $y(t)$ can be expressed as $$\max_{x(t), y(t)} \int_0^{t_1} f(t,x(t), y(t)) dt$$ subject to $x'(t)= g(t, x(t), y(t))$ and boundary ...
11
votes
1
answer
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Observability using the Discrete Extended Kalman Filter (EKF)
I have built (several) discrete Extended Kalman Filters (EKF). The system model I am building has 9 states, and 10 observations. I see that most of the states converge except one. All except 1-2 of ...
9
votes
2
answers
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Block diagram vs flow chart?
I was studying a book on control systems where I read that a block diagram is a specialized high-level type of flow chart.
What is the difference between a normal flow chart and a block diagram?
9
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2
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How can I approach the application of control theory to real control systems?
I am an engineering student and I took my second dedicated controls class last semester. It was cool math and whatnot, but after all was said and done: I still have no idea how to make an actual ...
9
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1
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How do you set up a PID-Control if the time constants of the controlled system are variable?
The common description for a continous PID-controller is written like this:
$$y(t)=K_p⋅e(t)+K_i\int_0^t e(τ)dτ+K_d\dfrac{de(t)}{dt}$$
The best value of the constants $K_p$, $K_i$ and $K_d$ for a given ...
9
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2
answers
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Writing a filtered derivative term of the PID controller into the C++ code
Everywhere I look, be it a PID, lead, lag control or anything else, there are Simulink schematics with transfer functions. This is all nice for system response simulation, however currently I have to ...
8
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2
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How does one become a control systems engineer?
From what I understand, a control systems engineering job is almost always a senior level position. What kind of entry level jobs do most engineers have before they are qualified to actually design ...
8
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1
answer
585
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Why is it impossible to create an observer for this not fully observable system?
Consider a 1D point-mass moving along an axis. A force $u$ is applied as control. There is no gravity or other forces involved. The system can be described in state space equations as:
$$\begin{align}...
7
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1
answer
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Causal and Non-Causal PD Controller
Why is a Non-causal PD Controller:
$C(s) = K_ds + K_p$
When a causal PD Controller is:
$C(s) = (K_ds + K_p)/(\tau s + 1)$
The difference being the denominator. $\tau$ is the time constant and is "...
7
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3
answers
295
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A clarifying question on Lasalle invariance principle
Given a nonlinear system \begin{equation}
\dot{x}=f(x),~x(0)=x_0 \tag{1}
\end{equation}
where $f\in{\mathcal{C}^{1}}:D\to\mathbb{R}^{n}$. The Lasalle invariance theorem statement goes as follows:
Let $...
7
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1
answer
415
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Computing error dynamics from state space deadbeat observer
I'm trying to solve this problem:
Given the transfer function:
$$ G(z) = \frac{z^{2}+2z+1}{z^{3}-z^{2}-5z+1} $$
Design a deadbeat observer for this transfer function and compute the
...
6
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2
answers
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Quaternion in control applications
In many application, the knowledge of the orientation of a body is essential for control purposes. There are several representations, where one is the Euler Angles and another is the Quaternion ...
6
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2
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Feedback control of two-link planar manipulator
TL;DR: how can I calculate the disturbance at each joint due to coupling forces in a two-link planar robot manipulator actuated by two independent DC motors?
I'm studying control theory and trying to ...
6
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2
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Controllability of $x' = Ax + Bu(t)$ implies controllability of $\left \{ \begin{matrix} x' = Ax + By \\ y'=u(t) \end{matrix} \right.$
Suppose that the system
$$x'(t)=Ax(t)+Bu(t)$$
is controllable in $\mathbb{R}^n$, where $A$ is $n \times n$, $B$ is $ n \times m$ and $u(t)$ is $m \times 1$
Show that the system
$$\left \{ \begin{...
6
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1
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881
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Second order system with additional pole
Why is it that a second order system with an additional pole or zero can be approximated into the general second order system for analysis?
This was asked during our lecture and I am still looking ...
6
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1
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How many states need to be measured for a reduced order observer?
I have a DC motor system with three states.
The states are:
$x_1$ = position (degrees),
$x_2$ = velocity (degrees per second)
$x_3$ = current (Amps).
My plant input $u(t)$ is measured in volts.
...
6
votes
2
answers
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Calculating a transfer function from a block diagram
I've been having trouble doing this school assignment. My professor has not taught the class how to read control block diagrams so I assumed that we were supposed to research on it. I've watched a few ...
5
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2
answers
426
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Minimal realization of a MISO system
Given the following system:
$$\dot{x} = \begin{bmatrix}1 & 1 & 0 \\ 0 & 1 & 0 \\ 0 & 1 & 1 \end{bmatrix}x + \begin{bmatrix}0 & 1 \\ 1 & 0 \\ 0 & 1 \end{bmatrix} u$$...
5
votes
2
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524
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A stable transfer function which diverges?
This question might sound stupid as I'm more of a software guy and never really had to do control engineering (besides the 101 classes).
So I have a second order system I could approximate, with the ...
5
votes
1
answer
187
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When are overshooting controllers preferred over asymptotic ones?
Disclaimer
Designing the behavior of controllers is an important task for many applications. Every application needs its own requirements fulfilled. For example a CNC machine needs a controller with ...
5
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4
answers
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Why can't proportional gain alone, reduce the error to zero?
I was told that the proportional gain alone cannot the drive the error signal to zero in a feedback loop. Why is that? If there is a tiny error, there will be a tiny or larger (depending on the number ...
5
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1
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Determine the range of values for a PI controller
This is a basic control theory question, since Control Theory is a part of applied mathematics but also of engineering I was unsure whether to ask this here.
The question says:
Given the transfer ...
5
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2
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363
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Linearization of dynamic equations/transfer function in control theory
I've gone through a control theory course, and after looking back at what we covered and how the subject was taught to us, I still have quite a few questions (which I unfortunately did not ask in ...
5
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2
answers
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Why are negative frequencies included in the nyquist plot?
What is the physical meaning of using negative frequencies while making Nyquist plots?
I know that we do a mapping from $s-$ plane to $f(s)$ plane, and we move along a contour. What I don't get is ...
5
votes
2
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what is a quarter wave decay response after Ziegler–Nichols tuning?
Ziegler–Nichols tuning creates a "quarter wave decay". What does that mean? I cannot find anything online!
5
votes
1
answer
133
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Square shaped position error
I got a position error measured by a linear encoder like in the picture below.
Could anyone explain some possible reasons for this kind of shape to occur in control theory?
My system looks like ...
5
votes
1
answer
160
views
How does the DERIVATIVE term slow down the signal?
I look at PID controler and do not understand derivatve term. I know it's used in order to not let the signal to overshoot the set value. BUT when the sigal is arising, its derivative is positive. So ...
5
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0
answers
59
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Is the viscosity solution of Hamilton-Jacobi equation of practical use in optimal control?
My understanding is, given an optimal control problem, one can show that the optimal cost satisfies a Hamilton-Jacobi PDE and use dynamic programming to figure out the optimal control. However, ...
5
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1
answer
407
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PI-Controler: Comparison of characteristic equations
I have to design a PI-controller with zero order hold for the plant
$G_s(s) = \frac{0.24}{(s+4)(s+12)}$ to meet the specifications of $\omega_n=5\,s^{-1}$ and $\zeta = 0.6$.
I choose a $T=0.12\,s$ ...
4
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2
answers
169
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What is the best method to model the input of an electro-mechanical system for control design and simulations?
In particular, say I have a dynamic model of the inverted pendulum / cart as described here. Instead of using the error difference in force to input into my controller, I want to take into ...
4
votes
1
answer
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Stability of the optimal control law
in linear optimal control,linear quadratic regulator,we have a system of the form: x=Ax+Bu,the optimal control law U is a state feedback,it's a function of the riccati equation solution and the state ...
4
votes
1
answer
80
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Steady state value, a possible shortcut?
I have this differential equation:
$\dot{\eta (t)}=\frac{-2\eta(t)}{C(\widehat{R}+\Delta R)}+\frac{K^2 L}{C E^2 (\widehat{R}+\Delta R)}+K$
which, my book says, correspond to a LTI system, ...
4
votes
2
answers
807
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LQR control and system dynamics linearization
I recently finished a project that simulated the dynamics and control of a 6DOF quadcopter model using a state-space LQR control approach, but I had a few questions that I wanted to ask that might ...
4
votes
2
answers
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How to determine the region in a state plane where the equilibrium state is asymptotically stable
I have a non-linear system shown:-
$$\dot{x}_1 = x_2$$
$$\dot{x}_2 = -(1-\vert x_1\vert)x_2 - x_1$$
How do I determine the region in the state plane where the equilibrium state at the origin is ...
4
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2
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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):
$$Q = \int_0^\...
4
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1
answer
511
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What benefits does loopshaping have over other control design methods?
I just finished my first controls course (on linear control systems) and we learned about 3 types of controllers: PID, State Space, and Frequency Response/Loopshaping. From what I understand, PID has ...
4
votes
1
answer
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How can I check whether a nonlinear system is zero-state observable?
Given a nonlinear system, such as:
$$\begin{align}
x_1' &= x_2 \\
x_2' &= −x_1^3 + u \\
y &= x_2
\end{align}$$
How can I check the zero-state observability of the system?
4
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1
answer
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How to design a PID controller for MIMO systems in which there are more outputs than inputs?
How do you design a PID controller for MIMO systems in which the outputs outnumber the inputs?
It's typical to design a PID controller for MIMO industrial process with the same number of inputs and ...
4
votes
1
answer
170
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How to design the right input to obtain a desired output for a linear system?
If I have a state-space model, so that matrices $A$, $B$, $C$ and $D$ are known, how can I design the right input $u$, so that $y$ is a desired signal, say, a sine wave with constant amplitude?
$$\...
4
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1
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Using python to send automated commands through a serial-usb-cable adapter
I have an old peristaltic pump with a 9 pin male sub-d socket labeled Gilson Serial Input Output Channel (GSIOC) that connects a master device to devices with RS422A specifications, or RS485 ...
4
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2
answers
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Analog PID controller - settings wrt $V_{err}$ - setpoint always higher than room temp
I designed from scratch an analog PID controller to mantain a temperature selected in the range of 60 to 80ºC with a room temp say = 20ºC. The "plant" is a simple 4R7 5 W resistor heated by a PWM-...
4
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1
answer
6k
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Matched and unmatched uncertainties
In control theory, according to the definition of matched uncertainty, the uncertainty enters the system through the same channel as the control.
If we consider the system:
$$\dot x = F(x)+G(x)u+Δ(x,...
4
votes
1
answer
290
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what's wrong with this robust control scheme?
I'm learning how to control a double integrator with $H_\infty$.
my model is simply
$$\begin{gather}
\dot{r} = v \\
\dot{v} = F/m \\
r(t_0) = 0\text{ m}, $v(t_0) = 0\text{ m/s}, m = 1000\text{ kg}
\...
4
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3
answers
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Control theory: Closed loop zeros, Root locus and its dynamic response
Why the closed loop dominant poles of the root locus can show the response of the system? Wont it neglect the effect of the closed loop zeros?
As I read on the books, root locus method deal with the ...
3
votes
2
answers
3k
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Square wave transfer function?
I made a mathematical model (transfer function) of a rlc circuit. I simulated it in matlab simulink with step input and square wave input and observed the result. I can also calculate this system with ...
3
votes
1
answer
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Advantage of anti-windup
What is the definition of anti-windup? How does it impose the constraints?
What are the advantages of MPC and anti-windup over each other?
Does anti-windup guarantee the constraints or does it just ...
3
votes
2
answers
797
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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. ...
3
votes
3
answers
373
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Determining the transfer function of cruise control given characteristic equations
During my time revising for my control engineering module, i've come across this question
The automatic cruise speed control for a vehicle is described by the following equations
$\bigl( 1\bigl)$ $...
3
votes
1
answer
72
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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 ...
3
votes
1
answer
292
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System model for motor controlled inverted pendulum with rotating motor body (used in camera stabilizer application)
I'm planning to build a head-mounted camera stabilizer for pro GoPro camera. The idea is that when I tilt my head the camera would stay at a user-set angle.
I'm using an accelerometer and a gyro to ...