Nonminimum-phase (NMP) control is a control system configuration that control engineers regularly encounter in their work. Nonminimum-phase control typically occurs when the sensors and actuators are placed at different locations of the dynamic system (plant) to be controlled. As a result, the plant transfer function contains right-half plane (RHP) zeros and time delays. The presence of RHP zeros and delays can make a stable plant to represent properties such as severe undershoots and overshoots, which are not suitable for a desired output. Thus, a closed-loop system is always recommended to remedy the dissatisfactions in output responses. However, as it is well-known, the closed loop weakens the stability properties. The principals of the common configurations, such as internal model control (IMC) and generalized Smith’s principle (GSP), to cope with NMP plants, have been proposed for years since 1975. Most of these configurations borrow their main ideology from the Smith’s predictor configuration that handles plants with singly delayed with left-half plane (LHP) zeros and stable transfer function. However, by the recent works of the authors of this paper, those configurations were argued to have an unnecessary complicacy that can degrade the robustness properties of the closed-loop system. The main concern is that the characteristics of the complicated model in the parallel feedforward branch can deviate from the real plant. In the situations that the mathematical dynamic model, upon which the whole control system is built, is not perfect, those proposed configurations can perform poorly and, sometimes, not even quite advantageous compared to the feedforward control models.

In the previous works by the authors of this paper, it is shown that a parallel feedforward compensator such as parallel feedforward compensation with derivative (PFCD) can stabilize any stable nonminimum-phase plant in a closed-loop system with ease. For that matter, one could simply follow the closed-loop poles in the root-locus plane while they cross the right-half plane to the left-half plane and conclude the closed-loop system stability. The theorems related to the PFCD stability were brought and proven in the previous works. Also, some of the nominal stability results were verified by applying the PFCD methodology on different NMP transfer function examples. Herein this work, the performance characteristics of the PFCD configuration is examined. Also, the robustness properties of such a configuration, i.e., the robust stability and robust performance of the closed-loop system, are evaluated using the H-infinity framework. Then, through an example that exhibit noise and disturbance, the claimed robustness properties are verified.

 


Robustness Analysis of Parallel Feedforward Control With Derivative (PFCD) Method

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Aerospace, Bioengineering, Applied Mechanics, Design Engineering Division, Advanced Energy Systems, Manufacturing Engineering Division, Noise Control and Acoustics, Nondestructive Evaluation, Diagnosis, and Prognosis (NDPD), Nuclear Engineering Division, Process Industries Division, Fluids Engineering, Heat Transfer, Materials, Microelectromechanical Systems, Safety Engineering and Risk Analysis, Computers & Information in Engineering


Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2020/volume/84478

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