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

Abstract

Nonlinear PI and PID controllers combining time-(sub)optimality with linear control robustness and antiwindup 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.

Nonlinear feedback control of Quadrotors exploiting First-Order Drag Effects

“…By applying the same attitude controller (23), we can show (with similar proofs to those proposed in Hua and Samson (2011)) the asymptotic stabilization of the equilibrium (ξ,ξ) = (0, 0) in case of a slowly time-varying perturbation term.…”

“…Among different possibilities, the bounded integrator I p complemented with anti wind-up capabilities defined in Hua and Samson (2011) is chosen. It is the solution of the following differential equation (with I p (0) =İ p (0) = 0):…”

Hardware and Software Architecture for Nonlinear Control of Multirotor Helicopters

“…Then, applying the inner-loop control (8) ensures the asymptotic stability of (ξ z , η) = (0, η d ). Finally, it is easy to show that the convergence ofξ z to zero also ensures the one ofξ to zero (see, e.g., [17] for a detailed proof).…”

“…To further add robustness with respect to the imprecise knowledge of γ e and other unmodeled dynamics, an integral term should be incorporated into the control law. To this end and also to limit the integral wind-up effects largely discussed in the literature (e.g., [14], [17], and [37]), we propose the following bounded nonlinear integrator ofξ: . Defining a new tracking error variableξ z :=ξ + z and using (9), one obtains…”

Implementation of a Nonlinear Attitude Estimator for Aerial Robotic Vehicles

“…Consequently, one may choose a very small value for the integral gain k I to reduce overshoots, but this in turn degrades the estimation performance. In fact, this issue is well-known as the so-called "integral wind-up effects" and has been well studied in the literature, particularly in the context of control systems [13], [15], [17], [32]. However, in the context of attitude estimation design, to our knowledge, there are no standard references for anti-windup for observers.…”