controlSim 0.1.0

Delay Control System Simulation with PID Controller

ControlSim

A Python package for simulating delay control systems with PID controller implementation.

Overview

ControlSim provides tools to simulate control systems with input delays using state-space representations and transfer functions. It includes:

• ProcessDefinition: Simulates a plant model with configurable delays
• PIDController: Implements a PID controller with derivative filtering
• Tuning Methods: IIMC (Indirect-IMC-PID) and IDA2 controller tuning algorithms

Features

• Support for transfer function and state-space representations
• Input delay simulation using circular buffer
• PID controller with filtered derivative action
• Gain and phase margin calculations
• IIMC and IDA2 automatic controller tuning methods
• Marginal stability checking

Installation

Install from PyPI:

pip install controlSim

Or install from source:

git clone https://github.com/vkbharatv/controlSim.git
cd controlSim
pip install -e .

Quick Start

import control as ctrl
from controlsim import ProcessDefinition, PIDController
import numpy as np

# Define a transfer function
s = ctrl.TransferFunction.s
G = 1 / ((s + 1) * (0.7 * s + 1))

# Create process with 2-second delay
process = ProcessDefinition(G, delay_time=2.0, dt=0.01)

# Create and tune PID controller
pid = PIDController(dt=0.01)
Kp, Ki, Kd = pid.IIMC_tuning(process, theta=2.0, l=0.5)

# Simulate for 100 seconds
setpoint = 1.0
for _ in range(10000):
    output = process.y[-1][0]
    control_signal = pid.compute(setpoint, output)
    process.step(control_signal)

# Analyze margins
gain_margin, phase_margin, wgc, wpc = process.gain_phase_margin()
print(f"Gain Margin: {gain_margin} dB")
print(f"Phase Margin: {phase_margin}°")

API Reference

ProcessDefinition

Represents a continuous-time process with input delay.

ProcessDefinition(tf, delay_time, dt=0.01, Total_time=10)

Parameters:

• tf: Control system transfer function
• delay_time: Input delay in seconds
• dt: Simulation step size (default: 0.01)
• Total_time: Total simulation time (default: 10)

Methods:

• step(u): Advance simulation by one step with input u
• reset(): Reset simulation state
• marginal_stability(): Check if system is marginally stable
• gain_phase_margin(omega): Calculate gain and phase margins

PIDController

Implements a discrete-time PID controller with derivative filtering.

PIDController(Kp=1.0, Ki=0.0, Kd=0.0, dt=0.01, N=100)

Parameters:

• Kp: Proportional gain
• Ki: Integral gain
• Kd: Derivative gain
• dt: Sampling time
• N: Derivative filter coefficient

Methods:

• compute(setpoint, measurement): Calculate control output
• reset(): Reset integral and derivative states
• update_gains(Kp, Ki, Kd): Update controller gains
• IIMC_tuning(process, theta, l): IIMC-based automatic tuning
• IDA2_tuning(rho): IDA2-based automatic tuning

Requirements

• Python 3.8+
• control >= 0.9.4
• numpy >= 1.20.0
• scipy >= 1.7.0
• matplotlib >= 3.3.0

Citation

If you use this package in your research, please cite:

@software{controlsim2026,
  author = {Bharat Verma},
  title = {ControlSim: Delay Control System Simulation},
  year = {2026},
  url = {https://github.com/vkbharatv/controlSim},
  orcid = {0000-0001-7600-7872}
}

License

This project is licensed under the MIT License - see the LICENSE file for details.

Author

Dr. Bharat Verma
The LNMIIT, Jaipur, India
ORCID: 0000-0001-7600-7872

Contributing

Contributions are welcome! Please feel free to submit a Pull Request.

Disclaimer

This software is provided for educational and research purposes. The authors are not responsible for any damages or losses resulting from the use of this software.