Stability Robustness of LQ and LQG Active Suspensions

Abstract

A two-degree-of-freedom quarter-car model is used as the basis for linear quadratic (LQ) and linear quadratic Gaussian (LQG) controller design for an active suspension. The LQ controller results in the best rms performance trade-offs (as defined by the performance index) between ride, handling and packaging requirements. In practice, however, all suspension states are not directly measured, and a Kalman filter can be introduced for state estimation to yield an LQG controller. This paper (i) quantifies the rms performance losses for LQG control as compared to LQ control, and (ii) compares the LQ and LQG active suspension designs from the point of view of stability robustness. The robustness of the LQ active suspensions is not necessarily good, and depends strongly on the design of a backup passive suspension in parallel with the active one. The robustness properties of the LQG active suspension controller are also investigated for several distinct measurement sets.

Combined design and robust control of a vehicle passive/active suspension

“…The ground motion w(t) =ẋ 0 (t) is a hypothetical zero-mean, white and Gaussian disturbance of variance 2πA 0 V , where A 0 is a ground motion amplitude scaling factor and V is the vehicle forward velocity (Ulsoy et al, 1994). In addition, this ground motion w(t) is acted upon by a first-order low-pass filter with cutoff frequency ω f = 20.91 to produce a coloured ground disturbance velocity input (Fathy et al, 2003).…”

“…Many active suspension control approaches have been proposed, utilising various modern control techniques, such as Linear-Quadratic (LQ) (Ulsoy et al, 1994), Linear-Quadratic-Gaussian (LQG) (Ulsoy et al, 1994;Ulsoy and Hrovat, 1990), adaptive control (Chantranuwathana and Peng, 2004), and nonlinear control (Fialho and Balas, 2000). However, in practice the total mass of the vehicle is uncertain due to changes in passenger and cargo loads, and the damping of the vehicle is uncertain due to approximating the nonlinear model with a linear one, etc.…”

Adaptive robust control for active suspensions

“…The stability of LQG con~ollers for quarter car models with ideal actuators was studied by Ulsoy et al (1994). This study shows that LQG controllers have small stability margins, especially when suspension stroke is the sole measured signal.…”

The Future Development and Analysis of Vehicle Active Suspension System

“…So far, many control approaches such as Linear Quadratic Regulator (LQR) [23], Linear Quadratic Gaussian (LQG) control [24], Adaptive sliding control [25], H∞ control [26], sliding mode control [27], fuzzy logic [28], preview control [29], optimal control [30] and neural network methods [31] have been used in the area of active suspensions. The performance of the active suspension system can be improved by control methods.…”