Control Systems: Nyquist Plots and Stability Analysis

Determining whether a feedback control system is stable is one of the most critical challenges in engineering. Nyquist and polar plots provide a powerful frequency-response framework to evaluate stability without solving for complex system roots. In this written course, you will develop a strong intuitive and mathematical understanding of frequency domain analysis. You will learn to construct plots manually, interpret stability criteria, and apply these concepts to practical engineering scenarios. What you will learn: Understand the foundational mathematics of frequency response, transfer functions, and polar coordinates; Sketch polar plots step-by-step for various open-loop transfer functions; Apply the Nyquist stability criterion to determine closed-loop system stability; Calculate critical stability metrics, including gain margin and phase margin; Analyze complex systems with poles on the imaginary axis using modified Nyquist paths; Compare analytical plotting techniques with modern computational verification methods. The course begins with essential terminology, basic definitions, and the mathematical foundations of the frequency domain. From there, you will progress through structured written explanations and step-by-step solved problems that build your confidence in manual plotting and stability analysis. This course is designed for engineering students, hobbyists, and beginning professionals who want a clear, accessible introduction to control system stability. No advanced background in control theory is required, though a basic familiarity with complex numbers and transfer functions is helpful. Start reading today to master the essential principles of Nyquist plots and control system stability.