Time sub-optimal nonlinear PI and PID controllers applied to longitudinal headway car control

Abstract

Nonlinear proportional-integral and proportional-integral-derivative (PID) controllers combining time-(sub)optimality with linear control robustness and anti-windup properties are proposed for first-order and second-order integrator systems, without assuming that the control lower-bound and upper-bound are the opposite of each other. A complementary contribution is the introduction of an integral action with anti-windup properties into the control law, under the constraint of ensuring global asymptotic stability. For illustration purposes, the proposed PID solution is applied to the longitudinal headway control of a vehicle following another vehicle.

Keywords:

• time (sub)-optimal control
• nonlinear PI/PID
• anti-windup
• conditional integrator
• nested saturation
• longitudinal headway car control