All classes PID & FOPID Metaheuristics Syllabus · Episode 1 of 6

Class PID & FOPID Metaheuristics #1: Control System: Transfer Function, Step Response, and Performance Specifications

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Tutorial on DC motor and AVR generator transfer function with Python: closed-loop, step response, rise time, overshoot, settling time, pole. Episode 1 of the PID and FOPID metaheuristics optimization series.

Software: Python (NumPy, SciPy, Matplotlib)
Level: Intermediate
Duration: ± 10 min
Series total: 52 min · 6 videos
Published: October 25, 2026

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Class PID & FOPID Metaheuristics #1: Control System: Transfer Function, Step Response, and Performance Specifications: Cover: Class PID & FOPID Metaheuristics #1: Control System: Transfer Function, Step Response, and Performance Specifications

Class PID & FOPID Metaheuristics #1: Control System: Transfer Function, Step Response, and Performance Specifications: Before you start, steps list, and Step 1

Class PID & FOPID Metaheuristics #1: Control System: Transfer Function, Step Response, and Performance Specifications: Step 2: DC motor & AVR transfer function

Class PID & FOPID Metaheuristics #1: Control System: Transfer Function, Step Response, and Performance Specifications: Step 3: Closed loop & specifications

Class PID & FOPID Metaheuristics #1: Control System: Transfer Function, Step Response, and Performance Specifications: Step 4: Measuring performance without controller

Class PID & FOPID Metaheuristics #1: Control System: Transfer Function, Step Response, and Performance Specifications: Step 5: Step response & pole map

Class PID & FOPID Metaheuristics #1: Control System: Transfer Function, Step Response, and Performance Specifications: Done: Final Result and Further Practice

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Transcript

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Introduction

Here is the final result, the DC motor model and the automatically regulated voltage generator system, or AVR, that we wrote ourselves with Python. Without a controller, AVR voltage spikes by 65% and takes 7 seconds to settle. This is the problem we will solve in this series. Let's get started. Hello, welcome to the research tutorial series on PID and fractional order PID parameter optimization using new generation metaheuristics. PID is used in more than 90% of industrial control systems, but setting its parameters is not easy. In this 6th episode series, we build everything from scratch. Transfer function, classical Ziegler-Nichols tuning, fractional order PID, whale optimization algorithm, and Harris-Hawks algorithm Optimization for DC motor and AVR, up to robustness testing and statistical analysis. In the first episode, we model the system. We open the terminal through the terminal menu, new terminal, then install numpy, skipi, and matplotlib.

Step 1: Installing the library

We use the Skipi.signal to calculate the transfer function response, While the entire system model and algorithms are written by us.

Step 2: Transfer function of DC motor & AVR

Create the system.py file. Our transfer function is stored as a pair of numerator and denominator polynomial. Series transfer function combines several transfer functions connected in sequence, and close the loop to form the Gepersatu Plus G for unit feedback. A DC motor maps voltage to rotational speed with inertia parameters, friction, motor constant, resistance, and inductance. AVR consists of an amplifier, exciter, and generator in the forward path, As well as voltage sensors on the feedback path, each being a first-order system.

Step 3: Closed-loop & specifications

The AVR loop function places a C controller in front of the plant, so the closed-loop transfer function is C times G1 plus C times G times H. The Response tab function calculates the output for a unit step input. The rise time specification function measures the rise time from 10 to 90 percent, overshoot, settling time 2 percent, and steady-state error. A system is said to be stable if all poles, that is, the roots of the denominator, have negative real parts.

Step 4: Measuring performance without controller

Create a test file named underscore system.py and run it. An open-loop DC motor reaches 0.0999 radians per second per volt, and with unit feedback only 0.0908, the steady-state error is very large. AVR without a controller rises quickly, rise time 0.26 seconds, but overshoot 65.2 percent, settling time 7.02 seconds, and still deviates by 0.088 per unit. Its two poles, minus 0.52 plus minus 4.66G, are very close to the imaginary axis.

Step 5: Step response & pole map

Let's look at the graph. The DC motor rises smoothly but never reaches the target 1. The AVR voltage oscillates for a long time before settling below 1. The pole map explains the cause, complex poles close to the imaginary axis produce slowly damped oscillations. The task of the PI controller is to eliminate the error and dampen these oscillations.

Done!

Done. We have modeled the DC motor and AVR as transfer functions, set up a closed-loop system, calculated the step response, and measured the performance specifications and pole locations. In the next episode, we will install PID and tune it using the classical Ziegler-Nichols method. Currently working on a thesis, dissertation, or research in the field of control systems and optimization? Cerdas Inovasi Digital helps implement control systems, from modeling DC motors and AVR generators, PI tuning in Ziegler-Nichols, fractional order PID, up to meta-heuristic optimization such as whale optimization and Harris-Hawkes, as well as opening Python programming courses for electrical engineering. Want to master the entire series, from transfer functions to statistical analysis and robustness testing? All six episodes, complete with PDF step-by-step guides and source code, are available to premium tutorial subscribers. Subscribe starting at Rp69.000 per month, save 28% with the 12-month package, or pay once Rp999.000 for lifetime access. Want just one class? Buy the single class with lifetime access. Subscribe now on the premium page cerdasinovasidigital.com. Contact us via WhatsApp, or visit cerdasinovasidigital.com. Thank you for watching, see you in the next episode.

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Transcript

0:03Introduction

1:09Step 1: Installing the library

1:18Step 2: Transfer function of DC motor & AVR

3:22Step 3: Closed-loop & specifications

5:15Step 4: Measuring performance without controller

7:03Step 5: Step response & pole map

8:30Done!

Ask the class material

My notes

Questions & answers

Your instructor

▶ Video Lesson

Recommended classes for you

Need more than a video?

Transcript

0:03Introduction

1:09Step 1: Installing the library

1:18Step 2: Transfer function of DC motor & AVR

3:22Step 3: Closed-loop & specifications

5:15Step 4: Measuring performance without controller

7:03Step 5: Step response & pole map

8:30Done!

Ask the class material

My notes

Questions & answers

Your instructor

Introduction

Step 1: Installing the library

Step 2: Transfer function of DC motor & AVR

Step 3: Closed-loop & specifications

Step 4: Measuring performance without controller

Step 5: Step response & pole map

Done!

Introduction

Step 1: Installing the library

Step 2: Transfer function of DC motor & AVR

Step 3: Closed-loop & specifications

Step 4: Measuring performance without controller

Step 5: Step response & pole map

Done!