Modified optimal control of a nonlinear active suspension system

Abstract

In this paper a new control approach for active vehicle suspensions based on a modified optimal control problem is presented, which considers the nonlinear damper characteristic of a vehicle suspension setup. In this context a new method for the systematic construction of a control Lyapunov function is presented, that is applicable to a class of nonlinear systems. The states that are required by the controller are estimated from the available measurement signals using a nonlinear Kalman filter concept recently presented by the authors. In order to achieve the best possible performance with respect to the conflicting objectives passenger comfort, ride safety and suspension deflection, the controller parameters are determined by means of a multiobjective genetic optimization algorithm. The potential of the controller is demonstrated by comparing it to a conventional linear quadratic regulator. The concept is validated on a quarter-vehicle test rig using measurements of real road profiles as disturbance input.

Passivity-based design of switching controllers for nonlinear systems

“…By Frobenius' Theorem [15] and Theorem 3.1 this requires that dim∆ W = dim∆ W,s = n − m. Together with the special structure of s(x) in (19) it can be concluded that all matrices F ν p (x) must be identical 2 , i.e. F ν p (x) = F ν (x) ∀ p ∈ P. Then, it follows that ∆ W = ∆ F,p and hence (19) is equivalent to…”

“…Since ∆ F,p ∈ ∆ W for all p ∈ P, by Assumption 3.1 it holds that dim∆ W ≥ dim ∆ W ≥ dim ∆ F,p = n − m and hence l = n − dim∆ W ≤ m. In order to gain maximum freedom for the energy shaping it is desired that (19) is solvable with the maximum number of l = m characteristic coordinates. By Frobenius' Theorem [15] and Theorem 3.1 this requires that dim∆ W = dim∆ W,s = n − m. Together with the special structure of s(x) in (19) it can be concluded that all matrices F ν p (x) must be identical 2 , i.e.…”

“…As in [19], its entries η = diag(Q y ) are determined by a numerical optimization. The objective function is chosen as…”

“…The parameter values correspond to a quarter vehicle test rig, which has been designed at the authors' institute (see e.g. [19]). To achieve high comfort the root mean square (rms) value of the chassis acceleration z c rms is to be minimized.…”

Nonlinear control of a semi-active suspension system considering actuator and state constraints using methods of optimal control

“…In [6], the nonlinear dynamics of the actuator are considered, while the suspension elements are still assumed to be linear. A nonlinear spring characteristic is addressed in [7] and in [8], a modified optimal control concept is applied on a nonlinear active suspension. In [9] an existing reference model-based controller concept is amended by an optimal control component, which significantly improves ride comfort in case of suspension All Authors are with the Departement of Automatic Control, Faculty of Mechanical Engineering, Technische Universität München, 85748 Garching, Germany.…”