Demystifying Enigmatic Undershoot in Setpoint Command Following [Focus on Education]

One of the most striking phenomena in systems and control theory is initial undershoot, where the initial direction of the response of a system to a step input or setpoint command is opposite to the direction of the asymptotic response. As mentioned in 'Summary,' initial undershoot represents a fundamental limitation on the performance of a control system, and it has potentially serious consequences, especially when the initially 'wrong' direction violates constraints on the output of the system. For example, in motion control applications, such as robotics or autonomous vehicles, initial undershoot may result in a collision. In any event, initial undershoot is an intriguing, visual example of a system-theoretic phenomenon that occurs in electrical, mechanical, and cyberphysical systems, and it is one of the many deleterious effects of nonminimum-phase zeros on the achievable performance of feedback control systems [1]-[3].