Mixed H<inf>2</inf>/H<inf>∞</inf> Data-Driven Control Design for Hard Disk Drives

Abstract

A frequency based data-driven control design considering mixed H2/H∞ control objectives is developed for multiple input-single output systems. The main advantage of the data-driven control over the model-based control is its ability to use the frequency response measurements of the controlled plant directly without the need to identify a model for the plant. In the proposed methodology, multiple sets of measurements can be considered in the design process to accommodate variations in the system dynamics. The controller is obtained by translating the mixed H2/H∞ control objectives into a convex optimization problem. The H∞ norm is used to shape closed loop transfer functions and guarantee closed loop stability, while the H2 norm is used to constrain and/or minimize the variance of signals in the time domain.The proposed data-driven design methodology is used to design a track following controller for a dual-stage HDD. The sensitivity decoupling structure[16] is considered as the controller structure. The compensators inside this controller structure are designed and compared by decoupling the system into two single input-single-output systems as well as solving for a single input-double output controller.Index Terms-Data-driven control design, Mixed H2/H∞ norms, Multiple input-single output systems, Hard disk drives, Trackfollowing controller, Sensitivity decoupling.

Application of Mixed H2/H∞ Data Driven Control Design to Dual Stage Hard Disk Drives

“…One of the most important advantages of the data driven control methodology presented in this paper is that it solves the mixed H 2 /H ∞ synthesis problem and the controller is synthesized directed based on the frequency response measurements of the actuators. Moreover, in the cases when multiple frequency response data is used and are sufficient to represent plant variations and the resonant modes of the system, the stability margins and performance specifications achieved during the design stage are assured to be met during implementation on the actual dual-stage HDD [12,13]. There are several reasons for having multiple frequency response measurements of a given actuator.…”

“…The data driven H ∞ control problem for single-input single-output (SISO) systems was addressed in [11], where the H ∞ norm condition was transformed into a necessary and sufficient convex condition. This H ∞ control design methodology is extended to multiinput single-output (MISO) controlled plants in [13], which is the most frequently encountered situation in the design of track -following controllers for dual-stage actuators. A sufficient convex constraint for the H 2 norm condition for multi-input multioutput (MIMO) systems was presented in [10].…”

“…The H ∞ norm and H 2 norm control conditions can be simultaneously considered as a mixed H 2 /H ∞ norm control problem [10,13,14]. Also, [13] presents an approach which considers multiple data measurements simultaneously. This problem formulation is used to design a feedback controller for dual-stage HDDs.…”

“…Hence, the controllers for the two SISO systems can be obtained sequentially by considering two mixed H 2 /H ∞ optimization problems. This strategy is the sequential SISO design strategy [13]. Another viable strategy is to directly design a single-input doubleoutput controller for the dual-stage HDD.…”

“…In this strategy, the SIMO control block will be obtained directly in a single step. This strategy is called the SIMO design strategy [13]. The main advantage of the SIMO design strategy is that both the controllers are designed in one step rather than having one controller fixed while the second controller is being designed.…”