6
votes
Accepted
Advantage of anti-windup
Anti-windup is a concept for feedback controllers with integral terms, e.g. PID, to keep the integral term from „overcharging“ when regulating a large set point error. It basically saturates the ...
- 1,808
5
votes
Accepted
Which course to take? Optimal control? Nonlinear control?
In nonlinear control theory, you will recognize most concepts such as controllability and observability where the linear case is often a special case of the nonlinear case. I would highly recommend ...
- 98
5
votes
How to convert a DC motor into a servo motor using a rotary encoder and a microcontroller?
At the very high level you will need
24V Power supply or a method to generate 24V
24V Motor controller
Microcontroller - Arduino is a good place to start
There are also prebuild motor controllers ...
- 7,105
5
votes
Open loop versus closed loop Model Predictive Control
I think the other answer is not complete. Model predictive control (or 'receding-horizon control' is a technique in which a predictive system model is used to evaluate a sequence of future control ...
4
votes
Stability of the optimal control law
So, just to formally repeat your question, we consider an infinite horizon continuous-time optimal control problem
$J^*(x_0) = min \int_0^{\infty} x(t)^TQx(t)+u(t)^TRu(t)dt$
which is subject to ...
- 1,808
3
votes
Accepted
Is there a concept of gain and phase margin for a strictly open-loop transfer function?
The transient response (or homogeneous solution) of a linear ODE is
$$y_h(t) = \sum_{i=1}^N C_i e^{p_i\cdot t} $$
where $p_i$ is the i-th pole of your system.
Assume you have a pole at location $p_i = ...
- 884
3
votes
Accepted
Are linear controllers inadequate for nonminimum phase systems?
A LTI system is nonminimum phase if it has one or more zeros in the right half plane. When using a LTI controller for feedback also then the bandwidth of this controller will be limited to roughly to ...
- 1,633
3
votes
How do I solve an optimal control problem where the dynamics depend on some function of the state?
Why would $z$ need to be external to $g$?
$$g'(t,x(t),y(t))=g(t,x(t),y(t),z(x(t)))$$
now use $g'$ as $g$
$g$ can be any arbitrary function, so any function $z$ could just be incorporated into $g$.
...
- 1,305
3
votes
LQR control and system dynamics linearization
The idea that you describe is basically Model Predictive Control with successive linearization (the optimization problem that is solved in MPC is finite-horizon while LQR is infinite-horizon, but the ...
- 1,808
3
votes
Accepted
Does the controllability of nominal system imply the controllability of the actual uncertain system?
You can prove it using the PBH test for controllability. It states that $rank \left(
\begin{array}{cc}
\lambda I -A & B \\
\end{array}
\right) = n$ for all values of $\lambda$.
For the ...
- 1,901
3
votes
Accepted
Open loop versus closed loop Model Predictive Control
In short: it is both. Model Predictive Control is a repeated open-loop control in a feedback fashion.
The explanation comes not from the general concept of open-loop and closed-loop, but from how ...
- 1,808
3
votes
$\mathcal H_2$ norm for LTV system
LTV systems don't have a transfer function associated with them, so the integral of the squared 2-norm of the transfer function does not exist. However, according to Parseval's theorem in the ...
- 1,633
2
votes
Efficiency of off road vehicles
There are a few issues to consider.
Dedicated off road vehicles tend to have ladder or in some cases space-frame chassis. There are robust and make it easier to add specialist bodies but tend to be ...
- 15.1k
2
votes
Accepted
Optimising driving speed of stepper motor for maximum acceleration by trial and error
One way might be to try to model and understand the physical problem. You are however clear in your question that you would prefer an empirical approach where constants are tuned to experience data.
...
- 386
2
votes
Using place command in MATLAB using different state representation
Using a different state space model, which is equivalent to the same transfer function, means that you are applying a similarity transformation. The new state vector will therefore have a different ...
- 1,633
2
votes
Model Predictive Control and Numerical Integration Schemes
The first equation you wrote is called discrete-time system. They are often also written as
$$x_{k+1} = Ax_k + Bu_k$$
Recall that MPC solves an optimization problem every time-step, so you need your ...
- 1,808
1
vote
How to convert a DC motor into a servo motor using a rotary encoder and a microcontroller?
Adding to the other answers. I just so happen to have done exactly this. I used a windshield wiper motor and a potentiometer but the principal is the same.
Here's my arduino source code: https://...
- 1,858
1
vote
How to convert a DC motor into a servo motor using a rotary encoder and a microcontroller?
You are at the right track. As the DC motor is rather fast for a potential slow microcontroller, using a discrete controller will improve the reliability and stability of the closed-loop system. Even ...
- 1,069
1
vote
What does "analytical design" mean?
I would think that this refers to using mathematical and physical principles and equations to predict the behaviour of a control system.
The opposite would be to empirically design a control system, ...
- 24k
1
vote
What is the output of a signal in time domain that passed through a High Pass Filter with simple transfer function
What you need to do is
use Laplace transform to $U(t)$ so you would get $\mathcal{L}(U(t))=U(s)$
for example, if you are rusty on Laplace transforms (or their inverse), you can use wolfram alpha
...
- 24k
1
vote
Accepted
Numeric quadrature vs summation of running costs in model predictive control
MPC finds the optimal input $u^*$ which is the input that minimizes the cost function $J$ or $c$. This means that regardless of what this actual value is, its proven to be its minimum. As such, ...
- 1,069
1
vote
Accepted
Fixed end points optimal control problem
I think I have found an answer and please correct me if there are any other reasons apart from the following justification.
Since $x^{*}(t)=\{x(t)\in\Omega|J(x)<\min J(y), \forall { y \in \Omega}\}$...
- 215
1
vote
Which course to take? Optimal control? Nonlinear control?
In control systems, the main focus is the design of a controller for machines or robots, here we mainly deal with linear systems application of linear control theory.
While non-linear systems is an ...
- 84
1
vote
Accepted
Direct Optimisation - How to Create Time Efficient Study
Found out about Response Surfaces and using all the points that I already created, created a Response Surface Optimization which let me easily find the answer without a significant amount more ...
- 193
1
vote
simulation of an attitude optimal Backstepping controller based quaternion for a UAV in MATLAB
That is quite the wall of text. You don't need to rewrite an entire academic paper to ask a question (please don't). You failed to show what it is you thought you were supposed to get or what you ...
- 3,565
1
vote
Transfer function with cancellable zero pole and controllability
Normally state space models who are equivalent to the same transfer function are also equivalent to each other, such that there exists a similarity transformation between them. However if the ...
- 1,633
1
vote
Accepted
Maximum MPC prediction horizon for an unstable plant
I think the book is using "infinite" to mean "a number that is too big for the computer software to represent", not in the strict mathematical sense. See near the top of page 1-6:
Open-loop ...
- 12.4k
1
vote
Accepted
Layout of a controller for controlling a water pump
Control problems are usually easier if you specify
The measured variables, I assume $T_{in}$ and $T_{out}$
The manipulated variables, I assume the pump speed according to your description
The ...
- 335
1
vote
Replacing PID with Lead–lag compensator?
Without knowing the transfer function of the plant you try to control it might be that a PID-controller would suffice, but for now I will assume this is not the case. Assuming that your graph is a ...
- 1,633
1
vote
Multiple solutions in optimal control
I assume that you also want to minimize some function of $t$, $T$, $\vec{x}(t)$ and $w(t)$. In this case it depends on how you define a solution to this problem. If you define a solution as ...
- 1,633
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