AbstractSimple nonlinear PI and PID controllers combining time-(sub)optimality with linear control robustness and anti-windup properties are presented 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.