In this dissertation, the modeling and control of time-varying automotive systems is addressed with the use of linear-parameter varying (LPV) control. In practice, many automotive systems with time-varying physical processes are operated with gain-scheduled controllers whose gains are manually calibrated through engine dynamometer and vehicle field tests for the best performance as functions of system operational conditions. However, this approach for gain scheduling is not only expensive and time consuming, but also does not guarantee the stability and performance of the closed-loop system for all time-varying parameters. LPV control techniques, on the other hand, can be used to design gain-scheduled controllers with guaranteed closed-loop stability and performance. The goal of this dissertation is to create a framework to design gain-scheduled controllers using LPV techniques, including, most importantly, the ability to select physically meaningful performance design constraints. As part of this effort, LPV control methods have been applied to the air-to-fuel ratio control of port-fuel-injection systems and the control of hydraulic and electric variable valve timing (VVT) systems.Gain scheduling controllers designed using the LPV method have traditionally included H∞ performance constraints. This is largely due to the fact that H∞ controllers can provide robust stability margins that H2 controllers cannot provide. However, since the H∞ norm is defined as the root-mean-square gain, or l2 to l2 gain, from the exogenous input to the regulated output, controllers designed with only H∞ performance constraints are not suitable for use when hard constraints on responses or actuator signals must be met. When hard constraints on responses or actuator signals must be met, a controller with a guaranteed l2 to l∞ gain is needed, which is a special type of H2 controller. When H2 performance is used to design a controller, normally a quadratic cost function that balances the output performance with the control input needed to achieve that performance is considered. However, unlike the conventional H2 performance criterion, the system l2 to l∞ gain provides a hard constraint (l∞) on the system output for a class of inputs with bounded l2 norm. Many practical control problems in automotive and aerospace systems impose hard constraints (or l∞ norm) on the system output. The existing mixed H2/H∞ LPV control method cannot be used to solve this class of the control synthesis problems. To remedy this gap, this dissertation provides a control synthesis method which provides a guaranteed l2 to l∞ gain on the system output for LPV systems. The result is a gain-scheduled controller that can provide hard constraints on multiple system outputs. To demonstrate the effectiveness of this approach, both a numerical example and a simulation study with an electrical VVT system are presented.
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