The objective of this chapter is to study the problem of vibration control analysis and synthesis in a vehicle engine-body vibration structure. It is assumed that the actuator is subject to a time-varying delay for control of bounce and pitch vibrations. Based on a Lyapunov-Krasovskii functional and using some free weighting matrices, delay-dependent sufficient conditions for designing desired state- and output-feedback controllers are given in terms of linear matrix inequalities (LMIs). The state- and output-feedback controllers, which guarantee asymptotic stability with a prescribed γ-level L₂-gain (or H_∞ performance), are then developed directly instead of coupling the second-order model to a first-order system. The controller gains are determined by convex optimization over LMIs. Simulation results are included to demonstrate the validity and applicability of the technique.

Chapter Contents:

• Abstract
• 12.1 Introduction
• 12.2 The vehicle engine-body system
• 12.3 Problem formulation
• 12.4 Main results
• 12.4.1 State-feedback control design
• 12.4.2 Output-feedback control design
• 12.5 Simulation results
• 12.6 Conclusion
• References

Inspec keywords: automobiles; control system synthesis; convex programming; linear matrix inequalities; time-varying systems; vibration control; Lyapunov methods; asymptotic stability; state feedback; actuators; internal combustion engines; delays

Other keywords: vibration control synthesis; Lyapunov-Krasovskii functional; linear matrix inequalities; output-feedback controller design; asymptotic stability; vibration control analysis; γ-level L₂-gain; convex optimization; H_∞ performance; LMI approach; state-feedback controller design; vehicle engine-body vibration structure; actuator; delay-dependent sufficient conditions; bounce control; pitch vibration control; vehicle engine-body systems; free weighting matrices; time-varying delay

Subjects: Optimisation; Engines; Road-traffic system control; Mechanical variables control; Algebra; Control system analysis and synthesis methods; Stability in control theory; Algebra; Vibrations and shock waves (mechanical engineering); Distributed parameter control systems; Time-varying control systems; Actuating and final control devices; Optimisation techniques