Questions tagged [optimal-control]

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12
votes
2answers
286 views

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
1answer
1k views

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 ...
7
votes
2answers
165 views

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 ...
5
votes
0answers
49 views

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, ...
4
votes
1answer
435 views

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
1answer
512 views

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 ...
4
votes
1answer
206 views

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} \...
3
votes
1answer
279 views

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
2answers
428 views

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 ...
3
votes
2answers
3k views

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 ...
3
votes
0answers
59 views

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: ...
3
votes
0answers
63 views

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 ...
2
votes
3answers
196 views

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) ...
2
votes
1answer
52 views

Is there a concept of gain and phase margin for a strictly open-loop transfer function?

I'm new to control systems, and I'm attempting to analyze the stability of an open-loop transfer function. I know that by checking the locations of the poles (and ensuring all poles are in the LHP) I ...
2
votes
1answer
69 views

Does the controllability of nominal system imply the controllability of the actual uncertain system?

Given a system dynamics \begin{equation} \dot{x}=A(p)x+Bu, \end{equation} where $A(p)$ is the uncertain system state matrix with the nominal matrix being $A(p_0)$. The uncertainty in $A(p)$ ...
2
votes
1answer
41 views

Direct Optimisation - How to Create Time Efficient Study

I made a simulation of this cylinder that is being suspended mid air and held up by 8 rods, 4 on top and 4 on the bottom. The entire model is cooled to 15K I managed to find the forces required for 6 ...
2
votes
2answers
139 views

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 ...
2
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0answers
37 views

avoidance with LQR

I'm interested in using linear quadratic regulators (LQR) to model prey avoidance behaviors. I want to adapt the LQR algorithm to incorporate dynamics and state costs that maximize the distance from a ...
2
votes
0answers
71 views

Is Hamilton Jacobi Bellman optimization used in engineering control? [closed]

Is solving stochastic HJB a practical method for stochastic optimal control in engineering field or it is just a method used in finance?
1
vote
1answer
56 views

Are linear controllers inadequate for nonminimum phase systems?

Based on the following publication: Kouro, S., Perez, M.A., Rodriguez, J., Llor, A.M. and Young, H.A., 2015. Model predictive control: MPC's role in the evolution of power electronics. IEEE ...
1
vote
1answer
53 views

Using place command in MATLAB using different state representation

I had a transfer function $$\frac{10s+20}{s^3+10s^2+24s}$$ and I found the state space representation of the above using MATLAB. Using $place(A,B,[poles])$, I found a gain matrix K that corresponds ...
1
vote
1answer
139 views

Model Predictive Control and Numerical Integration Schemes

When simulating systems of ODEs, I'm used to always using a numerical integration scheme to propagate the equations forward in time, such as simple Euler integration or Runge-Kutta methods. However, ...
1
vote
1answer
26 views

What does “analytical design” mean?

What is meant by "designing analytically" ? Especially in control systems design Does it mean theoretically design?
1
vote
2answers
47 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) = \...
1
vote
1answer
31 views

Fixed end points optimal control problem

Given two points $(t_0,x(t_0)=x^{0})$ and $(t_1,x(t_1)=x^{1})$ in the $(t,x)$ plane, the objective is to find an optimal trajectory $x^{*}(t)$ such that the cost function \begin{equation}\label{eq:1} ...
1
vote
1answer
63 views

Maximum MPC prediction horizon for an unstable plant

In the following book, Model Predictive Control ToolboxTM (User's Guide) Alberto Bemporad Manfred Morari N. Lawrence Ricker At page 1-6, it has been ...
1
vote
1answer
115 views

Layout of a controller for controlling a water pump

I'm currently writing a simulation environment in python/c for heat networks and got to the point where I'm implementing the controls for the environment. The PID controller is already implemented and ...
1
vote
0answers
27 views

Equations of motion in matrix form and energy consumption

I am working on Lagrangian derived high-dimensional motion equations for a robot in matrix form. The structure of such an equation is known: $M(q)\ddot{q}+C(q,\dot{q})\dot{q}+G(q)=0$ In here, $M(q)$, $...
1
vote
0answers
39 views

Lyaponuv stability condition of linear systems for homogenous P in V(x) = x^T P x

I am currently learning about using Lyaponuv functions to find Linear Matrix Inequalities (LMIs) as conditions for stability of a linear time invariant system. i.e. $$ \dot{x}(t) = Ax(t) $$ is stable ...
1
vote
0answers
21 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 ...
1
vote
0answers
38 views

LQR control effort / control bandwidth relationship

I'm working with a linear system, having given matrices A and B $$A = \left[\begin{array}{cc} 0 & 1 \\ -0.9 & 0 \end{array}\right]$$ $$B = \left[\begin{array}{c} 0 \\ 2 \end{array}\right]$$ ...
1
vote
0answers
20 views

Optimal Control Singular Arcs

This is about linear time-invariant, stationary problems. According to Donald Kirk's book Optimal Control Theory, for minimum-fuel problems on page 299, I was told that if there exists a singular arc,...
1
vote
1answer
111 views

simulation of an attitude optimal Backstepping controller based quaternion for a UAV in MATLAB

I'am trying to implement this open access research article Attitude Optimal Backstepping Controller Based Quaternion for a UAV I did not find the same result in this paper Can anyone tell me where my ...
1
vote
0answers
42 views

Does open loop stability guarantee an MPC stability?

In the following publication ...
1
vote
1answer
74 views

Extended Kalman Filter formulation

For a nonlinear system, $$ \begin{align} &{\boldsymbol x}(k+1)={\boldsymbol f}({\boldsymbol x}(k),{\boldsymbol u}(k),{\boldsymbol w}(k)) \\ &{\boldsymbol y}(k)={\boldsymbol h}({\boldsymbol x}(...
1
vote
0answers
159 views

LQR vs. Numerical Optimal Control

I'm a little confused by the differences between LQR control and numerical optimal control (such as direct multiple shooting, direct collocation and pseudospectral optimal control). It seems that LQR ...
1
vote
0answers
231 views

How many controllers of output or state are available? [closed]

Im in daily basis see a lot of controller. Sliding mode PID. Fuzzy, adapttive. Controller based on lyapunov etc. But how many are they that are actually in use in industry and when do we use them? ...
0
votes
2answers
152 views

Which course to take? Optimal control? Nonlinear control? [closed]

I have tried to compare two courses, and there seems to be some overlap, but not as much. Which method is better when controlling a nonlinear system? Also, what is the main difference between the two?
0
votes
2answers
3k views

Open loop versus closed loop Model Predictive Control

I hear a lot about open loop and closed loop Model Predictive Control (MPC). What is the difference between an open loop MPC and a closed loop MPC? Any block diagram demonstrating the difference is ...
0
votes
1answer
40 views

Efficiency of off road vehicles [closed]

Im working on efficienxy of heavy vehicle. Since i never had any experience with this kimd of things ( cars ) i dont have so much insight in what kind of efficiencys are important in vehicle. I have ...
0
votes
1answer
34 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: $$ ...
0
votes
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 ...
0
votes
1answer
57 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\...
0
votes
2answers
591 views

Transfer function with cancellable zero pole and controllability

I have a transfer function (From Ogata's Modern Control Engineering) $$\frac{s+2.5}{(s+2.5)(s-1)}$$ and the theory says the system has a pole zero cancellation and is uncontrollable. They said that ...
0
votes
0answers
30 views

MPC controller unable to control the height of the quadcopter

I am trying to develop a model predictive controller for my quadcopter. As the equations are non-linear in nature, I linearized the quadcopter at a hovering point. After linearizing, I discretized it ...
0
votes
0answers
18 views

Optimizing error for PID based control of Line Following Robot

I am working to find the optimal PID gains of my line following robot. To do this, I need to optimize any performance index dependent on the error (a typical example is the integral absolute error). ...
0
votes
1answer
31 views

What is the meaning of this symbol in Control System Diagram

I was reading the paper "Full-Speed Range Self-Balancing Electric Motorcycles Without the Handlebar" released in March 2016 by Professor Yang and Murakami in Keio University. I couldn't ...
0
votes
0answers
28 views

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 ...
0
votes
0answers
43 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{...
0
votes
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 ...