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## Hot answers tagged optimal-control

5

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 that can be programed via computer. These tend to be expensive. I would suggest following web sites similar to the ones listed below. They tend to have blogs, ...

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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 digging into linear control theory first if you have not done so. Depending on the course you take, concepts such as Lyapunov stability are discussed here, which ...

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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 $p_i = \lambda + i\omega$, with $i = \sqrt{-1}$. The real part ($\lambda$) of this pole will determine the convergence rate towards zero, while the imaginary part $\... 1 Im going to step out of the comment section as it is fairly limited. The quickest answer to the question: Is it possible to somehow form a transient process (with given properties) if the steady state is not known in advance, but it is known that in the steady state f(x,t)=0? Given the proposed conditions is simple: no. And the explanation boils down to ... 1 Taking the time derivative of$y$yields: $$\dot{y}=\frac{\partial f}{\partial x}(f(x)+u)$$ We need$y(t)=y(0) e^{-\beta t}$but this is possible if and only if$\dot{y}=-\beta y $, if the hessian is invertible then this is possible if and only if$u=-f(x)-\left(\frac{\partial f}{\partial x}\right)^{-1}\beta y$. To get an intuition on why the hessian must ... 1 Adding to the other answers. I just so happen to have done exactly this. I used a windshield wiper motor and a potentiometer but the principal is the same. Here's my arduino source code: https://pastebin.com/0ezsmi4y And a short video I took of it in action. This is an alternate version that takes RC PWM input instead of serial. I think all the talk about ... 1 You are at the right track. As the DC motor is rather fast for a potential slow microcontroller, using a discrete controller will improve the reliability and stability of the closed-loop system. Even though a DC motor is rather easy to model (speaking of the basic dynamics upto the 3rd order), using system identification can improve parameter estimation ... 1 I would think that this refers to using mathematical and physical principles and equations to predict the behaviour of a control system. The opposite would be to empirically design a control system, by implementing it and measuring it. 1 What you need to do is use Laplace transform to$U(t)$so you would get$\mathcal{L}(U(t))=U(s)$for example, if you are rusty on Laplace transforms (or their inverse), you can use wolfram alpha multiply$H(s)*U(s)$that will get you a function of s$Y(s)$use the inverse laplace transform to Y(s) to get the$y(t) = \mathcal{L}^{-1}(Y(s))$1 MPC finds the optimal input$u^*$which is the input that minimizes the cost function$J$or$c$. This means that regardless of what this actual value is, its proven to be its minimum. As such, multiplying the cost function with any constant value does not change this minimum, it just scales the value. Therefore,$\frac{t_{hor}}{N}$does not affect the ... 1 I think I have found an answer and please correct me if there are any other reasons apart from the following justification. Since$x^{*}(t)=\{x(t)\in\Omega|J(x)<\min J(y), \forall { y \in \Omega}\}$is optimal between all admissible trajectories$x(t)\in\Omega$for$t\in[t_0,t_1]$with$x^{*}(t_0)=x(t_0)=x_0$and$x^{*}(t_1)\neq{x(t_1)}\$, it is still ...

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