This paper deals with the problem of synthesizing feedforward control to aid the regulation of output of a nonlinear system in the presence of partially known exogenous inputs. Currently known methods for this problem either require the solution of a constrained partial differential equation or the preview information of the signal to be tracked. The novelty of this paper lies in synthesizing feedforward control as the solution of an algebraic - differential equation, which is considerably less complex. The techniques developed in this paper generalize very directly to nonlinear systems governed by differential-algebraic equations. In this paper, we consider two separate problems: the problem of tracking reference signals and the problem of regulating the output while rejecting the disturbances. We assume that the disturbance and the reference signals are outputs of known exogenous systems. Furthermore, we assume that the initial conditions for the exogenous system corresponding to the reference signals are known while those for the exogenous system corresponding to disturbances are unknown. We develop a parameter identification scheme to estimate the unknown initial conditions for the exogenous system in the case of output regulation. We illustrate the effectiveness of the control schemes for tracking problem with the example of a ball and beam system, and for the disturbance attenuation problem with two examples, nonlinear vibration absorber and a rotational translational actuator.
- Dynamic Systems and Control Division
Output Regulation of a Class of Nonlinear Systems Using Differential-Algebraic Equations
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Manyam, SG, Darbha, S, & Rajagopal, KR. "Output Regulation of a Class of Nonlinear Systems Using Differential-Algebraic Equations." Proceedings of the ASME 2012 5th Annual Dynamic Systems and Control Conference joint with the JSME 2012 11th Motion and Vibration Conference. Volume 2: Legged Locomotion; Mechatronic Systems; Mechatronics; Mechatronics for Aquatic Environments; MEMS Control; Model Predictive Control; Modeling and Model-Based Control of Advanced IC Engines; Modeling and Simulation; Multi-Agent and Cooperative Systems; Musculoskeletal Dynamic Systems; Nano Systems; Nonlinear Systems; Nonlinear Systems and Control; Optimal Control; Pattern Recognition and Intelligent Systems; Power and Renewable Energy Systems; Powertrain Systems. Fort Lauderdale, Florida, USA. October 17–19, 2012. pp. 635-643. ASME. https://doi.org/10.1115/DSCC2012-MOVIC2012-8611
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