control_tutorial_code

0 Content

• Open Loop Control
• Closed Loop Control
• Control use case
• Twiddle optimization for best parameters
• How to use code

1 Open Loop Control

Open-loop control, also known as an open-loop control system, is a control system where the output is not fed back to influence the input. In an open-loop control system, the input can affect the output, but the input is not influenced by the output. The signal from the input to the output is unidirectional.

2 Closed Loop Control

Closed-loop control, also known as a closed-loop control system, refers to a control system where the output can influence the input through a feedback loop, thereby affecting the control process of the system.

3 Control use case

• Lane correction
• Speed control
• UAV altitude control
• ...

4 Twiddle optimization for best parameters

To avoid the manual guesswork and trial-and-error process for obtaining better PID values, we can design an automated tuning logic loop. By aiming to minimize a specified objective function, we can obtain a more optimal parameter set.

A more intelligent and automated approach is to use the gradient descent algorithm.

• The prerequisite is to start with an initial guess vector of three gains. Typically, a small nonzero value is used for P, while I and D are set to 0.
• Then, each gain is incrementally adjusted, and the objective function is tested for a decrease. If it decreases, the parameters are continuously modified in the same direction. Otherwise, an attempt is made to adjust the parameters in the opposite direction.
• If neither increasing nor decreasing the gain values reduces the cost function, the magnitude of the gain increment is reduced, and the process is repeated.
• The entire loop should continue until the magnitude of the increment decreases below a certain threshold.

5 How to use code

5.1 Set up environment

conda create -n control python=3.7
pip install -r requirements.txt 

5.2 Understand PID tunning

For different models, PID controller needs to be fine-tune accordingly.

Change the robot.py, locate the following lines of code, and change the length to 20.

From:

class Robot(object):

    def __init__(self, length=4.5):

To:

class Robot(object):

    def __init__(self, length=20):

5.3 For code detail usage

Please check the following README

6 MCP control

The MPC controller minimize this cost function defined as: $$ J = x^TQx + u^TRu $$ subject to:

• Linearized Inverted Pendulum model
• Initial state

For more detailed code implementation, please check this README

Here is the results:

Reference

[1] Controls in Robotics - Robotics Nanodegree by Udacity (Term1)