SPRUHJ1I January 2013 – October 2021 TMS320F2802-Q1 , TMS320F28026-Q1 , TMS320F28026F , TMS320F28027-Q1 , TMS320F28027F , TMS320F28027F-Q1 , TMS320F28052-Q1 , TMS320F28052F , TMS320F28052F-Q1 , TMS320F28052M , TMS320F28052M-Q1 , TMS320F28054-Q1 , TMS320F28054F , TMS320F28054F-Q1 , TMS320F28054M , TMS320F28054M-Q1 , TMS320F2806-Q1 , TMS320F28062-Q1 , TMS320F28062F , TMS320F28062F-Q1 , TMS320F28068F , TMS320F28068M , TMS320F28069-Q1 , TMS320F28069F , TMS320F28069F-Q1 , TMS320F28069M , TMS320F28069M-Q1
Stability of a control system is a safety issue in engineering systems. There are multiple definitions of system stability: Lyapunov stability, bounded-input bounded-output stability, and input-to-state stability. For simplicity, in this document, the criterion of stability is Lyapunov asymptotic stability, which means that the system has the nature to converge to the equilibrium point asymptotically.
In speed control, the equilibrium point is the target speed of a step response, or the speed trajectory while tracking a changing reference speed. In position control, the equilibrium point is either the end position of a step response or the changing position reference during a transition.
One simple way to assess the stability of the system is to see if the step response eventually converges to the setpoint. Typical step responses of stable and unstable systems are illustrated in Figure 13-1.
The figures show the system responses when a unit step input is applied. Top left is the set point input signal. Cases 1 and 2 are stable systems; Cases 3, 4, and 5 are unstable systems. Case 3 is defined as marginally stable in some instances since the response is bounded oscillation.