Questions tagged [optimal-control]

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What is the relationship between classical control: transfer functions/frequency domain and the swing-up problem of an inverted pendulum

I am still pretty new to control theory, but I have been studying both classical and modern state space/optimal control ideas. I am having trouble understanding what the frequency domain/transfer ...
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Cost/Objective Function Normalization (MPC)

I am trying to develop an MPC. In this MPC, I predict the temperature and try to bring the sensor value to the desired setpoint temperature. I predict the temperature in the next 180 minutes for the ...
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Some questions about model predictive control (MPC)

I have some questions about model predictive control (MPC) How does MPC use a system's model to forecast its future response? How do model uncertainties and mismatches affect the performance of MPC, ...
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Seeking example problems solved using Automated Design Synthesis (ADS) algorithms

Premises. Gary N. Vanderplaats and coworkers at the Naval Postgraduate School in Monterey, California developed the Automated Design Synthesis (ADS) algorithms (software) that have been adapted to ...
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How to implement H-infinity controller in STM32 platform?

I used matlab to simulate some H infinity controllers, and I have some understanding of the related theory. But I don't know how to implement H-infinite controller on STM32 platform using C/C++ code. ...
zymaster's user avatar
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Entire Complex Function for dynamical systems

I am working on my master Thesis and I was going through this Thesis : https://scholarship.rice.edu/bitstream/handle/1911/89289/RICE0327.pdf?sequence=1&isAllowed=y Here, the author computes the ...
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Inverted pendulum LQR controller using motor

In my lab, I am trying to balance an inverted pendulum using simple LQR. To balance the arm I am using a DC motor. Now I have the A,B,C,D matrices. Using those I am able to find the feedback gain 'K' ...
V Adarsh's user avatar
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$\mathcal H_2$ norm for LTV system

Preliminary: Consider a stable, strictly causal discrete-time LTI system with state-space model $\left[\begin{array}{c|c} A & B\\ \hline C & \pmb{0} \end{array}\right]$. ...
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How do I make a attitude trajectory of a satellite so the attitude always points towards a point on earth given its current orbital position?

Let us say there is an antenna on earth and I have a satellite in an orbit how do I make the trajectory (not control, so body velocities of the satellite) to make it point toward the earth when it is ...
Hamzalihi's user avatar
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Modelling an S-shaped Second Order Process Response

I am trying to model an S-shaped second order process response as a transfer function in Simulink, as shown in figure 3 in the linked article. Ideally the response should be overdamped. I have tried ...
phikter's user avatar
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Block-diagram combining two controlled subsystems

I have two subsystems which are shown in the picture below. One of them is a system of stable and controlled differential equations of a mechanical system. Second is a block that implements a function ...
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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, $M(q)$, $...
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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). ...
Rob Christian Caduyac's user avatar
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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 ...
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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 ...
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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 ...
Christopher Li's user avatar
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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 ...
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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{...
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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: $$ ...
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LQR control effort / control bandwidth relationship

I'm working with a linear system, having given matrices A and B $$A = \left[\begin{array}{cc} 0 & 1 \\ -0.9 & 0 \end{array}\right]$$ $$B = \left[\begin{array}{c} 0 \\ 2 \end{array}\right]$$ ...
venom's user avatar
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Why do we need state feedback in the H-infinity concept instead of output feedback?

I have faced control of a flexible manipulator which has a zero dynamic related to flexible parts dynamic. The zero dynamic states (generalized states) are not observable in the input-output dynamic ...
King's user avatar
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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 ...
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Optimal control of the gradient type PDE

I recently encountered the following optimal control problem. The purpose of the system is to find the parameter $x$ at which the maximum or minimum of the function $f$ a is reached. $x$ is unknown to ...
dtn's user avatar
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3 answers
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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) ...
Samm Flynn's user avatar
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What does "analytical design" mean?

What is meant by "designing analytically" ? Especially in control systems design Does it mean theoretically design?
DSP_CS's user avatar
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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) = \...
Tee's user avatar
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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\...
link's user avatar
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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} ...
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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 ...
jgholder's user avatar
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Low accuracy current feedback measurement in motor control

Given a very low accuracy current sensor in a 3 phase inverter (in my case used for motor control) what is the best way to tackle the issue and keep reasonable performance and robustness at the same ...
Nick90's user avatar
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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,...
Superman's user avatar
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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 ...
hritz's user avatar
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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: ...
Josh Pilipovsky's user avatar
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2 answers
330 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?
Superman's user avatar
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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 ...
General Stubbs's user avatar
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When is it necessary to consider digial control rather than directly coding in the gain matrix?

I designed a LQR controller and want to implement it on a microcontroller. I don't know about digital control and don't know when to apply it. After a brief research, I found out that I need to apply ...
ganto's user avatar
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1 answer
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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 ...
James Dilaw's user avatar
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1 answer
298 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} \...
venom's user avatar
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1 answer
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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 ...
aldo's user avatar
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2 answers
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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 ...
aldo's user avatar
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2 answers
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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 ...
JeffR1993's user avatar
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Does open loop stability guarantee an MPC stability?

In the following publication ...
Adams's user avatar
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1 answer
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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 $A(p)$ ...
jbgujgu's user avatar
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1 answer
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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}(...
Adams's user avatar
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1 answer
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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 ...
Adams's user avatar
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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, ...
InquisitiveInquirer's user avatar
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1 answer
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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 ...
Adams's user avatar
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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 ...
Adams's user avatar
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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 ...
Imad Eddine Mokhtari's user avatar
1 vote
2 answers
5k 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 ...
Dormetric's user avatar