🚀 PID Full Stack Design with Root Locus & Python

Описание: This comprehensive tutorial walks through the "full stack" design of a PID controller, bridging analytical root locus methods with practical Python implementation. Starting from a third-order plant, we define specific performance requirements for overshoot, peak time, and steady-state error.  

The session is divided into two major phases:

Analytical Design: We use root locus techniques on the board to translate performance goals into desired closed-loop pole locations. We then calculate the necessary PD zero placement for transient improvement and specify the integral action required to eliminate steady-state error.  

Computational Implementation: Using Python and the control library, we verify our manual calculations, perform root locus plotting, and simulate the step responses of the uncompensated (P), transient-improved (PD), and final PID systems.  

By the end of this video, you will see how the theoretical 180° angle condition and second-order approximations translate directly into functional code that achieves precise control objectives.

00:00 Session Introduction and Problem Statement  
01:10 Controller Structure: Decomposing PID into Transient (PD) and Steady-State (I) Parts  
02:11 Translating Performance Goals: Overshoot to Damping Ratio (Zeta)  
03:34 Root Locus Analysis for the Uncompensated Third-Order System  
05:00 Second-Order Approximation and Peak Time Calculations  
07:31 Determining Target Closed-Loop Pole Locations  
09:56 PD Zero Placement: Applying the 180-Degree Angle Condition  
14:14 Adding Integral Action: Zero/Pole Placement for Zero Steady-State Error  
15:58 Python Implementation: Setting up the Control Toolbox and Environment  
16:45 Computational Root Locus Plotting for Gain Selection  
18:59 Verifying the Complete PD Design in Python  
20:41 Final PID Tuning and Gain Verification  
22:10 Step Response Comparison: P vs. PD vs. PID Performance  
23:43 Final Results Analysis and Design Summary