Perfect tracking control based on multirate feedforward control with generalized sampling periods

Abstract

In this paper, a novel perfect tracking control method based on multirate feedforward control is proposed. The advantages of the proposed method are that: 1) the proposed multirate feedforward controller eliminates the notorious unstable zero problem in designing the discrete-time inverse system; 2) the states of the plant match the desired trajectories at every sampling point of reference input; and 3) the proposed controller is completely independent of the feedback characteristics. Thus, highly robust performance is assured by the robust feedback controller. Moreover, by generalizing the relationship between the sampling period of plant output and the control period of plant input, the proposed method can be applied to various systems with hardware restrictions of these periods, which leads to higher performance. Next, it is shown that the structure of the proposed perfect tracking controller is very simple and clear. Illustrative examples of position control using a dc servomotor are presented, and simulations and experiments demonstrate the advantages of this approach.

Short Trajectory Control between Focusing and Tracking Based on Two-Dimensional Equivalent-Perfect Tracking Control for Optical Disk

“…These coefficient matrices and the state variable are as shown in (7) to (10), respectively. A is a n × n regular matrix.…”

“…The perfect tracking control (PTC) (10)- (12) system is a perfect inverse system composed of a multi-rate system. Multi-rate is a particularly effective technique for systems where the sampling frequency is limited.…”

Perfect Tracking Control Method by Multirate Feedforward and State Trajectory Generation based on Time Axis Reversal

“…In Case 2, there is one stable zero, Case 3 has one real stable zero and one real unstable zero, and Case 4 is the case having one real unstable zero. In the perfect tracking control method using the conventional multirate feedforward (13) , perfect tracking is possible only in the cases where there was no unstable zero in the continuous time system (Case 1, 2). Whereas, in the proposed method with the extended state variable trajectory generation, it is demonstrated that perfect tracking is possible even in cases having continuous time unstable zeros (Case 3, 4).…”

“…Therefore, we have proposed the Perfect Tracking Control (PTC) method (13) using multirate feedforward, which is a method of designing a stable inverse system without approximating to the unstable discretization zeros. This method is applied to high-precision stages (14) (15) , HDD (7) , Atomic Force Microscope (AFM) (16) , machine tools (17) , etc.…”

“…The proposed method can be applied to any reference trajectory as long as the (n − 1)th derivative of the reference trajectory is given (where n denotes the order of the nominal plant). Next, stable inversion for unstable discretization zeros is performed by the multirate feedforward control (13) . In this paper, simulation is performed using the model of an experimental stage in which actuators and sensors are arranged redundantly for rigid body mode.…”