Final answer:
The Nyquist stability criterion is used to determine the stability of a closed-loop control system given an open-loop transfer function. The Nyquist plot must be drawn, and the range of K for stability is found by ensuring the plot does not encircle the critical point (-1, 0) in an undesirable manner. Specific knowledge of control system principles is required to perform this analysis.
Step-by-step explanation:
The question at hand involves the use of the Nyquist stability criterion to analyze the stability of a closed-loop control system with a given open-loop transfer function. According to the Nyquist criterion, one must plot the Nyquist locus of the open-loop transfer function and examine how it encircles the critical point (-1,0). The system is stable if the number of encirclements matches the number of right half-plane poles of the open-loop transfer function.
To draw the Nyquist plot for the given transfer function G(s), we should consider its polar plot as the frequency changes from 0 to infinity, and also from -infinity to 0 in the negative frequency axis to complete the Nyquist path. The specific characteristic of G(s), such as its poles and zeros, governs the shape of the plot. To determine the range of K for system stability, one must adjust the gain K such that the Nyquist path does not encircle the critical point an unwanted number of times, which would imply instability for the closed-loop system.
For thorough analysis, the mathematical details of drawing the Nyquist plot, which includes finding and plotting points, and analyzing the stability of closed-loop control systems, need to be studied. This process involves complex calculus and control system principles such as phase margin, gain crossover frequency, and the transfer function's phase and gain characteristics.