Least squares based self‐tuning control of dual‐rate systems

Abstract

A polynomial transformation technique is used to obtain a frequency-domain model for a dual-rate system in which the output sampling period is an integer multiple of the input updating period. Based on this model, a self-tuning control algorithm is proposed by minimizing output tracking error criteria from directly the dual-rate input-output data. Convergence properties of the algorithm are analysed in detail in the stochastic framework. The output tracking error at the output sampling instants has the property of minimum variance. It is shown that the control algorithm can achieve virtually optimal control asymptotically, ensuring the closed-loop systems to be stable and globally convergent. A simulation example illustrates the self-tuning scheme presented.

Parameter and State Estimator for State Space Models

“…The simulation results show that the proposed algorithms are effective. The method in this paper can combine the multiinnovation identification methods [ 80 – 92 ], the iterative identification methods [ 93 – 100 ], and other identification methods [ 101 – 111 ] to present new identification algorithms or to study adaptive control problems for linear or nonlinear, single-rate or dual-rate, scalar or multivariable systems [ 112 – 117 ].…”

Direct model reference adaptive control using K p = LDU factorization for multivariable discrete-time plants

“…The stability and convergence properties of the discrete-time MRAC scheme are analyzed rigorously in a systematic fashion as in the continuous-time case. There are some remaining problems for MIMO discrete time systems to be further considered, e.g., how to design and analyze discrete-time indirect adaptive control schemes [21], how to deal with discrete-time MRAC with the unmodeled dynamics and disturbances as [15], and how to extend the result to time-varying systems as the continuous case [22] and to the dual-rate or multi-rate [23,24] discrete-time MRAC scheme. The optimal steady state tracking controller for MIMO systems is to deal with the SISO discrete time plant as in [25].…”

Least‐squares parameter estimation for systems with irregularly missing data

“…Using (A9) and (A10), we haveû(t) → 0 from (15). As A(z) is stable, we can obtainx(t)− x(t) → 0 from (A7).…”