Questions tagged [optimal-control]
The optimal-control tag has no usage guidance.
63
questions
1
vote
1
answer
16
views
Optimizing Kp Value in P Control
I have a question about a control-related problem I'm facing.
Problem:
I have a total of 10 furnaces, each equipped with hoses for injecting water to lower the temperature. These 10 furnaces need to ...
- 11
0
votes
0
answers
25
views
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, ...
- 101
0
votes
0
answers
20
views
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 ...
user42076
0
votes
0
answers
30
views
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.
...
- 19
0
votes
0
answers
22
views
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 ...
- 1
0
votes
0
answers
17
views
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' ...
- 1
0
votes
0
answers
20
views
Dynamic optimization through orthogonal collocation
I am having difficulties wrapping my head around when exactly does the manipulated variable act in orthogonal collocation.
I have the following problem:
$$ \min x_2(tf) \\ \frac{dx_1}{dt}=u\\\frac{...
- 13
1
vote
2
answers
73
views
$\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]$. ...
- 21
0
votes
0
answers
24
views
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 ...
0
votes
0
answers
32
views
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 ...
- 1
0
votes
0
answers
42
views
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 ...
- 226
1
vote
0
answers
48
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)$, $...
- 226
0
votes
0
answers
24
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
1
answer
128
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 ...
- 3
1
vote
0
answers
46
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)
$$
is stable ...
- 141
0
votes
0
answers
131
views
Issue with LQR Q matrix for a cart-pendulum model
I am currently trying to develop a controller using LQR for a Segway. The model that I am using is an inverted pendulum on a massless cart. I have made animations of the uncontrolled pendulum and of ...
1
vote
0
answers
27
views
Increasing convergence rate using Optimal Control and Pontryagin Maximum Principle
My question is in addition to Tuning the optimal control synthesized according to the Pontryagin maximum/minimum principle and choosing the cost function, but requires help from the mathematical side ...
- 226
0
votes
0
answers
59
views
Nonlinear system with time-optimal control
Given nonlinear system:
\begin{cases} \dot{x_1}=x_3+u \\ \dot{x_2}=-x_2+\dot{f} \\ \dot{x_3}=-x_3+x_2 \cdot \alpha \sin(\omega t) \\ \dot{x_4}=-x_4+x_2 \cdot (\frac{16}{\alpha^2}(\sin(\omega t)-\frac{...
- 226
0
votes
1
answer
56
views
Zero overshoot criterion from the initial point $x_0$ to the final $x_*$, $x_*$ unknown in advance
Suppose a system is described by the following ODE:
$$\dot{x} = f(t,x)+u$$
where
$x$ denotes the state of the system
$f(x,t)$ is an unknown nonlinear function which meets the following condition:
$$ ...
- 226
2
votes
0
answers
142
views
LQR control effort / control bandwidth relationship
I'm working with a linear system, having given matrices A and B
$$A = \left[\begin{array}{cc} 0 & 1 \\ -0.9 & 0 \end{array}\right]$$
$$B = \left[\begin{array}{c} 0 \\ 2 \end{array}\right]$$
...
- 183
0
votes
1
answer
71
views
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 ...
- 53
0
votes
1
answer
53
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 ...
- 226
0
votes
0
answers
42
views
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 ...
- 226
2
votes
3
answers
439
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)
...
- 71
0
votes
1
answer
31
views
What does "analytical design" mean?
What is meant by "designing analytically" ?
Especially in control systems design
Does it mean theoretically design?
- 253
1
vote
2
answers
88
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) = \...
- 33
0
votes
1
answer
76
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\...
- 98
1
vote
1
answer
54
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}
...
- 215
2
votes
1
answer
144
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 ...
- 133
0
votes
0
answers
35
views
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 ...
- 1
1
vote
0
answers
49
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,...
- 123
2
votes
0
answers
42
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 ...
- 21
3
votes
0
answers
93
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:
...
- 461
0
votes
2
answers
285
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?
- 123
2
votes
1
answer
49
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 ...
- 193
0
votes
1
answer
47
views
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 ...
- 37
1
vote
1
answer
134
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 ...
- 11
4
votes
1
answer
278
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}
\...
- 183
1
vote
1
answer
83
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 ...
- 21
0
votes
2
answers
1k
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 ...
- 21
4
votes
2
answers
735
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 ...
- 41
1
vote
0
answers
62
views
2
votes
1
answer
79
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 $A(p)$ ...
- 215
1
vote
1
answer
134
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}(...
- 115
1
vote
1
answer
99
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 ...
- 115
1
vote
1
answer
228
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
1
answer
61
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 ...
- 115
3
votes
1
answer
954
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 ...
- 115
4
votes
1
answer
806
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 ...
1
vote
2
answers
4k
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 ...
- 13