Andrew White

Linear Parameter-Varying Control for Engineering Applications

Introduction.- Linear Parameter-Varying Modeling and Control Synthesis Methods.- Weight Selection and Tuning.- Gain-Scheduling Control of Port-Fuel-Injection Processes.- Mixed H2/H-infinity Observer-Based LPV Control of a Hydraulic Engine Cam Phasing Actuator.

Mixed

In this paper, a family of linear models previously obtained from a series of closed-loop system identification tests for a variable valve timing cam phaser system is used to design a dynamic gain-scheduling controller. Using engine speed and oil pressure as the scheduling parameters, the family of linear models was translated into a linear parameter varying (LPV) system. An observer-based gain-scheduling controller for the LPV system is then designed based on the linear matrix inequality technique. A discussion on weighting function selection for mixed H2/H∞ controller synthesis is presented, with an emphasis placed on examining various frequency responses of the system. Test bench results show the effectiveness of the proposed scheme.

{\cal H}_{2}/{\cal H}_{\infty}

In this paper, an event-based sampled discrete-time linear system representing a port-fuel-injection process based on wall-wetting dynamics is obtained and formulated as a linear parameter varying (LPV) system. The system parameters used in the engine fuel system model are engine speed, temperature, and load. These system parameters can be measured in real time through physical or virtual sensors. A gain-scheduling controller for the obtained LPV system is then designed based on the numerically efficient convex optimization or linear matrix inequality (LMI) technique. A hardware-in-the-loop (HIL) simulation is performed to validate the gain-scheduling controller on a mixed mean-value and crank-based engine model. The HIL simulation results show the effectiveness of the proposed gain-scheduling controller.

Observer-Based LPV Control of a Hydraulic Engine Cam Phasing Actuator

In this paper, the output covariance constraint (OCC) control problem is cast as a convex optimization with linear matrix inequality (LMI) constraints. The OCC control problem is an optimal control problem that is concerned with minimizing control effort subject to multiple performance constraints on output covariance matrices. The contribution of this paper is the characterization of the control synthesis LMIs used to solve the OCC control problem. To demonstrate the effectiveness of the proposed approach a numerical example is solved with the control synthesis LMIs. The LMI solutions are then compared to results obtained when using the original iterative OCC algorithm. Both discrete and continuous-time problems are considered.Copyright

Hardware-in-the-Loop Simulation of Robust Gain-Scheduling Control of Port-Fuel-Injection Processes

In this paper, the input covariance constraint (ICC) control problem is solved by convex optimization subject to linear matrix inequalities (LMIs) constraints. The ICC control problem is an optimal control problem that is concerned to obtain the best output performance subject to multiple constraints on the input covariance matrices. The contribution of this paper is the characterization of the control synthesis LMIs used to solve the ICC control problem. Both continuousand discrete-time problems are considered. To validate our scheme in real-world systems, ICC control based on convex optimization approach was used to control the position of an electronic throttle plate. The controller performance compared experimentally with a well-tuned base-line proportional-integralderivative (PID) controller. Comparison results showed that not only better performance has been achieved but also the required control energy for the ICC controller is lower than that of the base-line controller. [DOI: 10.1115/1.4030525]

A Linear Matrix Inequality Solution to the Output Covariance Constraint Control Problem

In this paper, the input covariance constraint (ICC) control problem is solved by a convex optimization with linear matrix inequality (LMI) constraints. The ICC control problem is an optimal control problem that is concerned with finding the best output performance possible subject to multiple constraints on the input covariance matrices. The contribution of this paper is the characterization of the control synthesis LMIs used to solve the ICC control problem. To demonstrate the effectiveness of the proposed approach a numerical example is solved with the control synthesis LMIs. Both discrete and continuous-time problems are considered.Copyright

Linear Matrix Inequalities Approach to Input Covariance Constraint Control With Application to Electronic Throttle

In this paper, a discrete-time electronic throttle model was developed based upon the parameters obtained through system identification. To design gain-scheduling controllers using LPV (linear parameter varying) scheme, the throttle was modeled as an LPV system, where the vehicle battery voltage and the non-linear friction coefficient are the measurable time-varying parameters. Gain-scheduling H2 controller was designed for the LPV throttle system using the linear matrix inequality (LMI) convex optimization approach. The designed controller is validated through simulations and show that the proposed controller provides improved performance over the baseline fixed gain controller.Copyright

A Linear Matrix Inequality Solution to the Input Covariance Constraint Control Problem

This paper considers the optimal control of polytopic, discrete-time linear parameter varying (LPV) systems with a guaranteed ℓ₂ to ℓ_∞ gain. Additionally, to guarantee robust stability of the closed-loop system under parameter variations, ℌ_∞ performance criterion is also considered as well. Controllers with a guaranteed ℓ₂ to ℓ_∞ gain and a guaranteed ℌ_∞ performance (ℓ₂ to ℓ₂ gain) are mixed ℌ₂/ℌ_∞ controllers. Normally, ℌ₂ controllers are obtained by considering a quadratic cost function that balances the output performance with the control input needed to achieve that performance. However, to obtain a controller with a guaranteed ℓ₂ to ℓ_∞ gain (closely related to the physical performance constraint), the cost function used in the ℌ₂ control synthesis minimizes the control input subject to maximal singular-value performance constraints on the output. This problem can be efficiently solved by a convex optimization with linear matrix inequality (LMI) constraints. The contribution of this paper is the characterization of the control synthesis LMIs used to obtain an LPV controller with a guaranteed ℓ₂ to ℓ_∞ gain and ℌ_∞ performance. A numerical example is presented to demonstrate the effectiveness of the convex optimization.

LPV control of an electronic throttle

In this paper, a discrete-time, linear parameter-varying (LPV) system representing the electric variable valve timing (VVT) system is developed with engine oil viscosity as the time-varying parameter. A gain-scheduled, dynamic, output-feedback controller is then designed such that the closed-loop system will have a guaranteed ℓ2 to ℓ∞ gain, which is very closely related to the physical performance hard constraints. This is done by first constructing a set of linear matrix inequality constraints and then performing a convex optimization to obtain the controller matrices which satisfy the constraints. Simulation study results demonstrate the effectiveness of the proposed scheme.

Guaranteed ℓ 2 to ℓ ∞ control for discrete-time polytopic LPV systems

In this paper, an event-based dynamic gain-scheduling controller was designed by employing a standard control structure of observer-based state feedback with integral control. The dynamic gain-scheduling controller was applied to an LPV system representing the air-to-fuel ratio control of a port-fuel-injection process. The system parameters used in the engine fuel system model are engine speed, temperature, and load. The static gains of the dynamic gain-scheduling controller for the obtained LPV system were then designed based on the numerically efficient convex optimization (or LMI) technique. The simulation results demonstrate the effectiveness of the proposed scheme.