Dual-rate Input-output Data Research Articles

A modified stochastic gradient based parameter estimation algorithm for dual-rate sampled-data systems

In this paper, we propose a novel identification algorithm for a class of dual-rate sampled-data systems whose input–output data are measured by two different sampling rates. A polynomial transformation technique is employed to derive a mathematical model for such dual-rate systems. The proposed modified stochastic gradient algorithm has faster convergence rate than stochastic gradient algorithms for parameter identification using the dual-rate input–output data. Convergence properties of the algorithm are analyzed. Finally, illustrative and comparison examples are provided to verify the effectiveness and performance improvement of the proposed method.

Parameter Identification and Intersample Output Estimation for Dual-Rate Systems

In this paper, we derive a mathematical model for dual-rate systems and present a stochastic gradient identification algorithm to estimate the model parameters and an output estimation algorithm to compute the intersample outputs based on the dual-rate input-output data directly. Moreover, we investigate convergence properties of the parameter and intersample estimation, and we test the proposed algorithms with example systems, including an experimental water-level system.

A GRADIENT BASED ADAPTIVE CONTROL ALGORITHM FOR DUAL‐RATE SYSTEMS

ABSTRACTIn this paper, using a polynomial transformation technique, we derive a mathematical model for dual‐rate systems. Based on this model, we use a stochastic gradient algorithm to estimate unknown parameters directly from the dual‐rate input‐output data, and then establish an adaptive control algorithm for dual‐rate systems. We prove that the parameter estimation error converges to zero under persistent excitation, and the parameter estimation based control algorithm can achieve virtually asymptotically optimal control and ensure the closed‐loop systems to be stable and globally convergent. The simulation results are included.

Generalized Yule-walker and two-stage identification algorithms for dual-rate systems

In this paper, two approaches are developed for directly identifying single-rate models of dual-rate stochastic systems in which the input updating frequency is an integer multiple of the output sampling frequency. The first is the generalized Yule-Walker algorithm and the second is a two-stage algorithm based on the correlation technique. The basic idea is to directly identify the parameters of underlying single-rate models instead of the lifted models of dual-rate systems from the dual-rate input-output data, assuming that the measurement data are stationary and ergodic. An example is given.

Convergence analysis of estimation algorithms for dual-rate stochastic systems

Identification is to estimate the unknown parameters of systems by using the measured input–output data { u( t), y( t)}. Most existing identification approaches assume that the input–output { u( t), y( t)} is available at each sampling instant t. This paper focuses on a class of dual-rate sampled-data systems in which all inputs u( t) are available, but only scarce outputs { y( qt)} are available ( q > 1 being an integer). We derive a mathematical model for such dual-rate systems by using a polynomial transformation technique, and present new algorithms for parameter identification and intersample output estimation using directly the dual-rate input–output data { u( t), y( qt)}, and study in detail convergence properties of the algorithms in the stochastic framework by using the stochastic process theory and stochastic martingale theory. We show that (1) the parameter estimation error consistently converges to zero under the persistent excitation condition; (2) the intersample output estimation error is uniformly bounded. Finally, we illustrate and test the proposed algorithms with example systems, including an experimental water-level system.

Parameter estimation of dual-rate stochastic systems by using an output error method

In this note, a new gradient-based recursive algorithm for estimating parameters of dual-rate sampled-data systems is presented. The basic idea is, by using an output error method, to identify the single-rate models and the unknown noise-free outputs (true outputs) directly from dual-rate input-output data. Further, convergence properties of the proposed algorithm in parameter and output estimation are analyzed; and the result is illustrated and tested with an experimental water-level system.

Hierarchical identification of lifted state-space models for general dual-rate systems

This paper is motivated by practical consideration that the input updating and output sampling rates are often limited due to sensor and actuator speed constraints. In particular, for general dual-rate systems with different updating and sampling periods, we derive the lifted state-space models (mapping relations between available dual-rate input-output data), and, by using a hierarchical identification principle, present combined parameter and state estimation algorithms for identifying the canonical lifted models based on the given dual-rate input-output data, taking into account the causality constraints of the lifted systems. Finally, we give an illustrative example to indicate that the proposed algorithm is effective.

Combined parameter and output estimation of dual-rate systems using an auxiliary model

For a dual-rate sampled-data system, an auxiliary model based identification algorithm for combined parameter and output estimation is proposed. The basic idea is to use an auxiliary model to estimate the unknown noise-free output (true output) of the system, and directly to identify the parameters of the underlying fast single-rate model from the dual-rate input–output data. It is shown that the parameter estimation error consistently converges to zero under generalized or weak persistent excitation conditions and unbounded noise variance, and that the output estimates uniformly converge to the true outputs. An example is included.

Application of dual-rate modeling to CCR octane quality inferential control

Octane quality control at Shell Canada's continuous catalytic reforming (CCR) units is typically done manually due to infrequent measurements of the research octane number (RON). The goal of this paper is to study automating the control loop by developing a dual-rate inferential control scheme. In particular, for a dual-rate process with fast input updating and slow output sampling, we propose a polynomial domain method to identify a fast single-rate linear model based on dual-rate input-output data; using the fast model to supply missing samples, we extend a popular model-based predictive control algorithm to the inferential control framework; the identification and control algorithms are applied to a Shell Canada's CCR reactor, and the inferential controller is implemented in real time, resulting in 40% reduction in octane quality variance-a significant improvement.

Application of dual-rate modeling to CCR octane quality inferential control

This paper discusses system identification of dual-rate systems. In particular, a dual-rate system with control interval T and output sampling interval nT is considered. At first the problem of identifying a fast single-rate model with sampling period T based on dual-rate input-output data is studied in the polynomial domain. Then the proposed algorithm is applied to model an industrial process. The estimated fas-rate model is then used in inferential control of the octane quality in a continuous catalytic reformer.