Abstract
This paper presents the design of a linear quadratic analog tracker (LQAT) based on the observer–Kalman-filter identification (OKID) method and the design of a modified functional observer-based equivalent input disturbance (EID) estimator for unknown square–non-square singular analog systems with unknown input and output disturbances. First, an equivalent mathematical model of the singular analog system is presented to simulate the time response of continuous-time linear singular analog systems to arbitrary inputs via the model conversion method. Then, for the unknown singular analog system, it constructs a linear quadratic analog tracker with state feedback and feed-forward gains based on the off-line OKID method. Furthermore, it extends the design methodology of the EID estimator for strictly proper regular systems with unknown matched–mismatched input and output disturbances to proper regular systems. It is important to mention that the newly developed modified functional observer for proper systems is used to estimate the unknown EID of singular analog systems and that the constraints on the dimensions of unknown disturbances can be eliminated by using the newly proposed EID estimation method. The contributions of this paper can be listed as follows: (1) based on both the OKID method and the discrete-to-continuous model conversion, the simulation of the time responses of the continuous-time linear singular models (which are not feasible using existing MATLAB toolboxes) become feasible; (2) for effective control of the unknown singular analog system, an off-line OKID method is proposed to design an LQAT with state feedback and feed-forward gains; and (3) based on the newly developed modified functional observer for the reduced-order proper regular system, the original EID estimator in the literature is newly extended to estimate the EID from the unknown strictly proper singular analog system, without the original dimensional constraints of the disturbances. It is important to mention that the disturbances of interest can be unknown matched–mismatched input and output disturbances.
Highlights
Singular analog system models naturally arise in describing large-scale systems, such as interconnected power systems
This paper provides more details on improving the disturbance rejection performance based on a net equivalent input disturbance (EID) estimation approach for a system with li unknown input disturbances and lo output disturbances imposed simultaneously, where li, lo > p, with p representing the number of outputs
The main objective of this paper is to propose a new functional observer-based EID estimator for the unknown square–non-square singular continuous-time systems subject to unknown input and output disturbances
Summary
Singular analog system models naturally arise in describing large-scale (complex) systems, such as interconnected power systems. An approach for solving the tracker-based generalized algebraic Riccati equation for the singular system has not yet been developed in the literature. It was proven in [4] that the tracker-based generalized algebraic Riccati equation cannot be directly solved for a singular system, even with an impulsive model-free and strictly proper transfer function. To overcome this issue, in [4] the singular system is converted into an equivalent regular model with a direct transmission term from input to output
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