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Engineering Stack Exchange

Questions tagged [optimal-control]

58 questions
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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 conditions for $x(t)$. I want to solve a problem that…
Daniel Wills
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11
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1 answer

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 the EKF state estimate appears to drift. Since the…
krisdestruction
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7
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2 answers

How to optimise feed-forward control of a process based on a prediction using the prediction confidence?

I'm looking for a control method for a production process with the following characteristics: 1 control variable many process parameters (+-50) 1 resulting variable continuous measurement of resulting variable with 30-90 second delay complex…
marqram
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5
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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, sometimes this PDE has no strong solution, and the deep…
Isley
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4
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1 answer

what's wrong with this robust control scheme?

I'm learning how to control a double integrator with $H_\infty$. my model is simply $$\begin{gather} \dot{r} = v \\ \dot{v} = F/m \\ r(t_0) = 0\text{ m}, $v(t_0) = 0\text{ m/s}, m = 1000\text{ kg} \end{gather}$$ so I want to be able to track a step…
venom
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4
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2 answers

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 help me develop the model further. From the…
JeffR1993
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1 answer

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 vector.I'm asking about stability,is the optimal…
Imad Eddine Mokhtari
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4
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1 answer

Optimising driving speed of stepper motor for maximum acceleration by trial and error

I'm writing code for a microcontroller that will ramp up the speed of a stepper motor as quickly as possible, for a jig that I'm building, that moves a workpiece from one position to another along a linear rail. This question is not about modifying…
CL22
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3
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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: %% Continuous Time clear all; close all; clc; % Parameters n = 2; m = 1; A = [1 1; 0 1]; B = [0.5; 1]; C = [1 0]; Q = eye(2); QT =…
Josh Pilipovsky
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3
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1 answer

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 try respecting them?
Adams
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3
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How to solve LMIs with equality constraints using MATLAB?

I would like to find n by n matrices P and Q that minimize J = norm(P) + w*norm(Q), where w is a given weight, subject to P>=0, Q>=0, and f(P,Q)=0, where f(P,Q)=0 is a given function of P and R. I tried to solve this problem using the lmi solver of…
David
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3
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2 answers

Replacing PID with Lead–lag compensator?

I have a vehicle (I bought it and it proprietary and I have no information about any internals) which I want to integrate into my simulation environment. So far I have a physical model of it which I gained by driving around recording data and…
Westranger
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Multiple solutions in optimal control

Consider a control problem of the form: $\frac{d \vec{x}}{dt} = F(\vec{x}, \vec{u})$ where $\vec{u}$ is the control inputs and $\vec{x}$ is the state variables, and all we want to do is drive the system from $\vec{x}_0$ to $\vec{x}_1$ in some given…
iamasecretadgent
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LQR control effort / control bandwidth relationship

I'm working with a linear system, having given matrices A and B $$A = \left[\begin{array}{cc} 0 & 1 \\ -0.9 & 0 \end{array}\right]$$ $$B = \left[\begin{array}{c} 0 \\ 2 \end{array}\right]$$ assume we have full state and no feedtrough matrix $D$…
venom
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2
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3 answers

How to convert a DC motor into a servo motor using a rotary encoder and a microcontroller?

Operating/ Rated Voltage: 24V No load Speed: 350 rpm No load Current: 150mA (max) Max efficiency: 1.4 Kg-cm/300 rpm/ 14.2W/ 0.87A Max power: 4.5 Kg-cm/180 rpm/28.2W/1.4A Stall Current: 2.9 A (max) Stall/ max Torque: 8 Kg-cm Gear Ratio: 1:34 1496…
Samm Flynn
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