Zero Phase Error Tracking Controllers With Optimal Gain Characteristics

Recently, a digital feedforward controller, called a Zero Phase Error Tracking Controller (ZPETC), has been proposed. In this controller, the overall frequency response between the desired output and the controlled output exhibits zero phase shift for all frequencies by using a few steps of the future desired output data. In this paper, two extensions of ZPETC’s are proposed: a ZPETC with deadbeat tracking performance and an L₂-Optimal ZPETC. These ZPETC’s can provide the overall control system with not only the above phase property but also the excellent tracking performance for a desired output and the superior gain property, respectively. Moreover, a ZPETC with both the excellent tracking performance for a step-type and ramp-type desired output and the superior gain property, called an L₂-Optimal ZPETC with deadbeat tracking performance, is presented.