PID Tuning by Optimization

This repository contains Python scripts to optimize PID controller gains (proportional, integral, and derivative) using optimization techniques. The optimization aims to minimize the step response characteristics: overshoot, rise time, and settling time.

Introduction

This repository provides two approaches to optimize PID controller gains:

1. Gradient Descent
2. Quadratic Programming

Explanation

Both scripts perform the optimization of PID controller gains for a given state-space model. The gradient descent script uses a simple finite difference approach to estimate the gradient, while the quadratic programming script uses the minimize function from scipy.optimize with the SLSQP method to find the optimal PID gains.

Gradient Descent Script: Defines the PID controller and closed-loop state-space model. Computes the cost function as a combination of overshoot, rise time, and settling time. Updates PID gains iteratively using the gradient descent algorithm.

Quadratic Programming Script: Similar to the gradient descent script but uses the minimize function for optimization. Defines bounds for the PID gains and optimizes the cost function using quadratic programming.

Requirements

• Python 3.x
• NumPy
• SciPy