Lecture #10: Routh-Hurwitz Stability & Steady State Error | Fundamentals of Control Eng. (Part 2)

This lecture was delivered at East China University of Technology, Nanchang, China, during the Winter 2025 semester (September 2025) as part of the Fundamentals of Control Engineering course.

In this lecture, we study the Routh-Hurwitz Stability Criterion and Steady State Error analysis, two fundamental concepts in control engineering used to determine system stability and evaluate system accuracy under different input signals. The lecture explains stability analysis of higher-order systems, construction of Routh arrays, special cases in Routh tables, and the evaluation of static error constants for different system types.

📘 Topics Covered:

Stability of Higher Order Systems
Stable and unstable systems
Pole locations and system stability
Introduction to Routh-Hurwitz Stability Criterion
Determining stability without solving characteristic equations
Relationship between sign changes and right-half plane poles
Generating the Routh Table
Construction of the first two rows
Calculation of remaining rows
Interpretation of Routh arrays
Routh Stability Conditions
Conditions for system stability
Determining the number of poles in the right-half plane
Solved Examples on Routh Arrays
Stability determination of higher-order systems
Analysis of characteristic equations
Special Cases in Routh-Hurwitz Criterion:
Case-I: Zero in the first column
Use of epsilon (ε) method
Case-II: Entire row of zeros
Auxiliary equation method
Handling even polynomial factors
Introduction to Steady State Error
Transient vs steady-state performance
Dependence of steady-state error on system type
Classification of Control Systems:
Type-0 systems
Type-1 systems
Type-2 systems
Effect of system type on accuracy and stability
Steady State Error Analysis:
Final Value Theorem
Error transfer function
Static error constants
Static Position Error Constant (Kp)
Static Velocity Error Constant (Kv)
Static Acceleration Error Constant (Ka)
Steady-state errors for:
Step input
Ramp input
Parabolic input
Solved examples on static error constants and steady-state error calculations

🎯 What You Will Learn:

By the end of this lecture, you will:

Understand the concept of stability in control systems
Apply the Routh-Hurwitz criterion to determine system stability
Construct and interpret Routh arrays
Handle special cases in Routh stability analysis
Understand steady-state error and system accuracy
Classify control systems based on system type
Calculate static error constants (Kp, Kv, Ka)
Evaluate steady-state errors for standard test inputs
Apply Final Value Theorem in control system analysis

👨‍🎓 Who is this for?

Mechanical Engineering students
Electrical & Electronics Engineering students
Control Systems beginners
Students interested in automation, robotics, and dynamic system analysis

🔗 Course:

Fundamentals of Control Engineering
📍 East China University of Technology, Nanchang, China
👨‍🏫 Lecturer: Md Rayhan Tanvir

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#ControlEngineering #RouthHurwitz #SteadyStateError #ControlSystems #SystemStability #MechanicalEngineering #ElectricalEngineering #EngineeringLectures #LaplaceTransform #CircuitsAndCosmos

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