A PD-type iterative learning control algorithm for singular discrete systems

Abstract

Based on a specific decomposition of discrete singular systems, in this paper, we study the problem of state tracking control by using PD-type algorithm of iterative learning control. The convergence conditions and theoretical analysis of the PD-type algorithm are presented in detail. An illustrative example supporting the theoretical results and the effectiveness of the PD-type iterative learning control algorithm for discrete singular systems is shown at the end of the paper.

Iterative Learning Control for V-Shaped Electrothermal Microactuator

“…The simulation results for the displacement of the top of the beam by using the discrete time PD-type learning procedure (16) are given in Figures 8 and 9 for both cases without and with an additional output disturbance. It is exhibited extraordinary here in the obtained results, especially in Figure 8a (without external disturbances) and Figure 9a (with an additional output disturbance), which illustrate the dependence of maximal tracking error on applied learning step number, that the tracking error does not decrease monotonously if the learning number is increased, as proven in [28][29][30][31][32][33][34][35][36][37] by using a mathematical model of VEM. A reason for it could be that an uncertain difference between the mathematical models given in [5,8,9] and the here used Simscape model of VEM has appeared.…”

“…Many of them can be found in [21,22,[29][30][31][32][33]. A good summary of ILC development is presented in [34][35][36][37], in which a few of the following practicably powerful linear ILC algorithms of the alternative structure of Equation (11) are given (see [21,22] for more examples):…”

Discrete Fourier transform based frequency characteristics of iterative learning control for linear discrete-time systems

“…Reviewing the contributions of the ILC convergence for discrete-time systems, the analytical techniques are mainly the time-and frequency-domains. In terms of convergence in a discrete-time domain, the kernel idea is to express the ILC dynamics as an algebraic input-output equation by the lift vector technique, and thus the ILC convergence is equiv-alent to the stability of the transmit matrix as shown [13][14][15][16][17][18][19][20][21][22][23][24][25][26]. The idea is innovative, and the results are progressive.…”

Iterative learning control for a class of discrete-time singular systems

“…On the other hand, it should be pointed out that most of the singular systems studied in the above-mentioned works are based on the assumption that the matrix A 22 is nonsingular (see [16][17][18]), which implies that the systems are impulse-free (for continue-time singular systems) or causal (for discrete-time singular systems). However, in many practical singular system models, the matrix A 22 may be singular.…”

“…Based on the nonsingular transformation method, a PD-type algorithm was designed in [17] to study the state tracking problem for a class of singular systems. Very recently, reference [18] applied the ILC strategy to a class of discrete singular systems, then the convergence analysis of the algorithm was given in detail by using λ-norm.…”