Static output‐feedback controller design for vehicle suspensions: an effective two‐step computational approach

Abstract

In this paper, a novel two-step methodology is applied in designing static output-feedback controllers for a class of vehicle suspension systems. Following this approach, an effective synthesis of static output-feedback controllers can be carried out by solving two consecutive linear matrix inequality optimization problems. To illustrate the main features of the proposed design strategy, two different static output-feedback H ∞ controllers are designed for a quarter-car suspension system. The first of those controllers uses the suspension deflection and the sprung mass velocity as feedback information, while the second one only requires the sprung mass velocity to compute the control actions. Numerical simulations indicate that, despite the restricted feedback information, the proposed static output-feedback H ∞ controllers exhibit an excellent behavior in terms of both frequency and time responses, when compared with the corresponding state-feedback H ∞ controller.

A New SSUKF Observer for Sliding Mode Force Tracking H∞ Control of Electrohydraulic Active Suspension

“…In order to design the demanded force controllers, the robust H∞ performances for a static output‐feedback system can be realized by introducing the following lemmas .Lemma Given a positive scalar η , the closed‐loop system with H∞ state feedback controller is asymptotically stable and satisfies the condition for all w if and only if there exists symmetric positive‐definite matrix X i ( i = 1, 2)and general matrix Y i such that the matrix inequality is satisfied. …”

“…Then , the matrix R i can be defined as in which T i is a constant matrix. A detailed introduction of some relevant properties of the matrix T i can be found in . In this paper, the matrix is suggested as where X si is an optimal solution of the matrix variable X i in Lemma , Q † = ( QQ T ) ‐1 Q T is the Moore–Penrose pseudoinverse of Q .Lemma Considering the symmetric matrix X i > 0 in Lemma , the matrix inequality QX Qi Q T + R i X Ri R T i >0 is satisfied if and only if there exists symmetric matrices X Qi >0 and X Ri >0.Lemma In the static output‐feedback system, combining the equality and equation , the gain matrix K i is computed as .Remark Substituting equation into the matrix inequality , and combining Lemma with Lemma 2 and Lemma 3, the closed‐loop system is asymptotically stable and satisfies the condition for all w if there are symmetric matrices X Qi >0, X Ri >0 and general matrix Y Ri satisfying the matrix inequality .…”

“…In order to design the demanded force controllers, the robust H∞ performances for a static output-feedback system can be realized by introducing the following lemmas [29,30]. Lemma 1.…”

“…in which T i is a constant matrix. A detailed introduction of some relevant properties of the matrix T i can be found in [29,30]. In this paper, the matrix is suggested as…”

Predictor Feedback Stabilization of Stochastic Linear Delayed Systems with Both Additive and Multiplicative Noises

“…There are many results concerning static control of active suspension systems with different structures and configurations [23,[36][37][38]. There are many results concerning static control of active suspension systems with different structures and configurations [23,[36][37][38].…”