This paper focuses on the design of a low order robust stabilizer for the tracking/disturbance rejection problem based on the internal model principle in the time-varying setting and its application to the hydraulic pressure tracking with varying frequency. The problem of this kind known as output regulation generally consists of two major parts: internal model unit construction and stabilizer design. While the construction of the time-varying internal model unit is non-trivial by itself and a very recent research outcome enables its synthesis for a class of linear time-varying systems, the effective stabilization of the augmented system (internal model unit and plant) for practical applications remains a challenge. This is due to the need to stabilize the high order time-varying augmented system using a low order stabilizer in a robust fashion and with desirable transient performance. While directly applying the stabilization approaches for a general LTV system will result in a high order stabilizer, a new method is proposed in this paper that overcomes this bottleneck by taking advantage of the unique structure of the internal model based control system. Instead of using a dynamic stabilizer with high order, this approach uses a sequence of time-varying gains that are directly injected into the internal model unit. A critical issue addressed is how to avoid the non-convex optimization associated with the time-varying gain synthesis and then convert the stabilizer design into a series of Linear Matrix Inequalities (LMIs). The proposed control approach is then demonstrated on an electrohydraulic system.
Bibliographical noteFunding Information:
The material in this paper was partially presented at the 2012 American Control Conference (ACC 2012) ( Song, Wang, & Sun, 2012 ), June 27–29, 2012, Montréal, Canada. This paper was recommended for publication in revised form by Associate Editor Kyung-Soo Kim under the direction of Editor Toshiharu Sugie. More systematic derivation of the proposed control methodology, detailed dynamics modeling/controller design for an electro-hydraulic system, together with more comprehensive experimental results are presented in this paper. The work is supported in part by NSF under grant CMMI-1150957 .
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- Internal model principle
- LPV system stabilization
- Time-varying output regulation
- Time-varying repetitive control