Black-Box Identification of a High-Order Time-Delay System

A system identification project focused on modeling a high-order industrial process with time delay under limited black-box access.

The project uses step-response identification, relay-feedback testing, PRBS excitation, and least-squares estimation to obtain continuous and discrete models of the unknown process.

Project Overview

In many industrial applications, the internal structure and physical parameters of a process are not completely available.

Under these conditions, the process can be treated as a black-box system and modeled using measured input-output data.

In this project, a high-order system with time delay was implemented in Simulink. Band-limited white noise was added to represent measurement and process disturbances.

Three identification approaches were then applied:

1. Two-point step-response identification
2. Relay-feedback analysis
3. PRBS-based discrete ARX identification

Project Objectives

• Simulate a high-order industrial process with time delay
• Add band-limited white noise to the simulated process
• Analyze the step response of the unknown system
• Identify an FOPDT model using the two-point method
• Perform relay-feedback testing
• Determine critical frequency-domain parameters
• Generate a PRBS input signal
• Estimate a discrete ARX model using least squares
• Compare identified models with the original process
• Evaluate model accuracy and dynamic similarity

Black-Box Identification

Black-box identification develops a mathematical model using only measured input and output signals.

The internal equations and physical parameters of the process are assumed to be unavailable.

The general identification workflow includes:

1. Applying a suitable excitation signal
2. Recording the process output
3. Preprocessing the measured data
4. Selecting a model structure
5. Estimating model parameters
6. Validating the identified model
7. Comparing the model with the original process

Original Process

The studied process is characterized by:

• High-order dynamics
• Time delay
• Limited internal information
• Band-limited white noise
• Industrial process behavior
• Continuous- and discrete-time representations

The original system was implemented in the Simulink environment.

FOPDT Identification

A First-Order Plus Dead-Time model was extracted from the process step response using the two-point method.

The identified model has the general form:

             K
G(s) = ------------- e^(-Ls)
           Ts + 1