This letter proposes an iterative learning control with advanced output data (ADILC) scheme using an estimation of the impulse response for non-minimum phase (NMP) systems, whose model is unknown, except for the relative degree and the number of NMP zeros. Although the ADILC has a simple learning structure that can be applied to both minimum phase and NMP systems, at least a partial model should be known in order to apply ADILC. Considering this fact, in this letter, we propose a new ADILC method based on the estimation of the impulse response for NMP systems whose model is unknown. An estimation method for the learning matrix and an ADILC scheme are presented for NMP systems.

This letter investigates an iterative learning control with advanced output data (ADILC) scheme for non-minimum phase (NMP) systems when the number of NMP zeros is unknown. ADILC has a simple learning structure that can be applied to both minimum phase and NMP systems. However, in the latter case, it is assumed that the number of NMP zeros is already known. In this paper, we propose an ADILC scheme in which the number of NMP zeros is unknown. Based on input-to-output mapping, the learning starts from the relative degree. When the input becomes larger than a certain upper bound, we redesign the input update law which consists of the relative degree and the estimated value for the number of NMP zeros.

In this paper, we propose a method capable of shortening the distance from a noise detection microphone to a loudspeaker in active noise control system with non-minimum phase secondary path. The distance can be basically shortened by forming the noise control filter, which produces the secondary noise provided by the loudspeaker, with the cascade connection of a non-recursive filter and a recursive filter. The output of the recursive filter, however, diverges even when the secondary path includes only a minimum phase component. In this paper, we prevent the divergence by utilizing MINT (multi-input/output inverse theorem) method increasing the number of secondary paths than that of primary paths. MINT method, however, requires a large scale inverse matrix operation, which increases the processing cost. We hence propose a method reducing the processing cost. Actually, MINT method has only to be applied to the non-minimum phase components of the secondary paths. We hence extract the non-minimum phase components and then apply MINT method only to those. The order of the inverse matrix thereby decreases and the processing cost can be reduced. We finally show a simulation result demonstrating that the proposed method successfully works.

Disturbance attenuation for a class of time-delay systems is performed by a combined simple adaptive control (SAC) with a new configuration of disturbance observer (DOB). The nominal system results from the Pade approximation, which is in the form of a non-minimum phase LTI system. For the implementation of SAC and DOB, two parallel feedforward compensators (PFC) are designed with the inverses of PD- and PID-controller, respectively. Simulation results show the effectiveness of the proposed controller to compensate the disturbance response and uncertain delay time.

This letter investigates an ADILC (Iterative Learning Control with Advanced Output Data) scheme for nonminimum phase systems using a partially known impulse response. ADILC has a simple learning structure that can be applied to both minimum phase and nonminimum phase systems. However, in the latter case, the overall control time horizon must be considered in the input update law, which makes the dimension of the matrices in the convergence condition very large. Also, this makes it difficult to find a proper learning gain matrix. In this letter, a new sufficient condition is derived from the convergence condition, which can be used to find the learning gain matrix for nonminimum phase systems if we know the first part of the impulse response up to a sufficient order. Based on this, an iterative learning control scheme is proposed using the estimation of the first part of the impulse response for nonminimum phase systems.

We deal with LTI nonminimum phase (NMP) systems which are difficult to control with conventional methods because of their inherent characteristics of undershoot. In such systems, reducing the undesirable undershoot phenomenon makes the response time of the systems much longer. Moreover, it is impossible to control the magnitude of undershoot in a direct way and to predict the response time. In this paper, we propose a novel two sliding mode control scheme which is capable of stably determining the magnitude of undershoot and thus the response time of NMP systems a priori. To do this, we introduce two sliding lines which are in charge of control in turn. One is used to stabilize the system and achieve asymptotic regulation eventually like the conventional sliding mode methods and the other to stably control the magnitude of undershoot from the beginning of control until the state meets the first sliding line. This control scheme will be proved to have an asymptotic regulation property. The computer simulation shows that the proposed control scheme is very effective and suitable for controlling the NMP systems compared with the conventional ones.

In this paper, we study the problem of perfect tracking control of nonminimum phase systems in magnetic levitation system. Generally, perfect tracking control schemes cannot be applied to nonminimum phase plants because of unstable pole-zero cancellations. Although the method of state matching using multirate feedforward control to realize perfect tracking control have been proposed, the oscillation restraint and the feasibility in nonminimum phase system cannot be satisfied at same time. We propose a method using the difference of state variables to generate a smooth desired state variable trajectory in the discrete-time systems. The techniques we proposed are applicable to nonminimum phase discrete-time systems and the oscillations between the sampling points are well restrained. We will show that the structure of the proposed perfect tracking controller is very simple and clear. Finally, computer simulations and experiment results based on magnetic levitation apparatus are presented.

In this paper, we present a numerical method for the equiripple approximation of minimum phase FIR digital filters. Many methods have been proposed for the design of such filters. Many of them first design a linear phase filter whose length is twice as long, and then factorize the filter to obtain the minimum phase. Although these methods theoretically guarantee its optimality, it is difficult to control the ratio of ripples between different bands. In the conventional lowpass filter design, for example, when different weights are given for its passband and stopband, one needs to iteratively design the filter by trial and error to achieve the ratio of the weights exactly. To address this problem, we modifies well-known Parks-McClellan algorithm and make it possible to directly control the ripple ratios. The method iteratively solves a set of linear equations with controlling the ratio of ripples. Using this method, the equiripple solutions are obtained quickly.

An efficient adaptation technique of the delay is introduced for accomplishing more accurate adaptive linear equalization of nonminimum phase channels. It is focused that the filter structure and adaptation procedure of the adaptive Butler-Cantoni (ABC) equalizer is very suitable to deal with a variable delay for each iteration, compared with a classical adaptive linear transversal equalizer (LTE). We derive a cost function by comparing the system mismatch of an optimum equalizer coefficient vector with an equalizer coefficient vector with several delay settings. The cost function is square of difference of absolute values of the first element and the last element for the equalizer coefficient vector. The delay adaptation method based on the cost function is developed, which is involved with the ABC equalizer. The delay is adapted by checking the first and last elements of the equalizer coefficient vector and this results in an LTE providing a lower mean square error level than the other LTEs with the same order. We confirm the performance of the ABC equalizer with the delay adaptation method through computer simulations.

Nonminimum phase systems are difficult to be controlled with a conventional PID-type controller because of their inherent characteristics of undershooting. A neuro-controller combined with a PID-type controller has been shown to improve the control performance of the nonminimum phase systems while maintaining stability. In this paper, we apply a multiobjective evolutionary optimization method for training the neuro-controller to reduce the undershooting of the nonminimum phase system. The computer simulation shows that the proposed multiobjective approach is very effective and suitable because it can minimize the control error as well as reduce undershooting and chattering. This method can be applied to many industrial nonminimum phase problems with ease.

We present a new method for the adaptive control of nonminimum phase continuous-time systems based on the pole-zero placement using approximate inverse systems to avoid the unstable pole-zero cancellations. Using this method effect of the unstable zeros cab be compensated approximately. We show how unstable pole-zoro cancellations can be avoided, and that this method has the advantage of being able to determine an approximate inverse system independently of the plant zeros. The proposed scheme uses only the available input and output data and the stability using approximate inverse systems is analyzed. Finally, the results of computer simulation are presented to illustrate the effectiveness of the proposed method.

A new method is proposed for recovering an unknown source signal ,which is observed through two unknown channels characterized by non-minimum phase FIR filters. Conventional methods cannot estimate the non-minimum phase parts and recover the source signal. Our method is based on computing the eigenvector corresponding to the smallest eigenvalue of the input correlation matrix and using the criterion with the multi-channnel inverse filtering theory. The impulse responses are estimated by computing the eigenvector for all modeling orders. The optimum order is searched for using the criterion and the most appropriate impulse responses are estimated. Multi-channel inverse filtering with the estimated impulse responses is used to recover the unknown source signal. Computer simulation shows that our method can estimate nonminimum phase impulse responses from two reverberant signals and recover the source signal.

A new method to obtain the coefficients of Daubechies's scaling functions is given, in which it is not necessary to find the complex zeros of polynomials. Consequently it becomes easier to obtain the coefficients of arbitrary order from 2 to 40 with high accuracy.

This paper presents a new method for the selftuning control of nonminimum phase discrete-time stochastic systems using approximate inverse systems obtained from the leastsquares approximation. Using this approximate inverse system the gain response of the system can be made approximately unit and phase response exactly zero. We show how unstable polezero cancellations can be avoided. This approximate inverse system can be used in the same manner for both minimum and nonminimum phase systems. Moreover, the degrees of the controller polynomials do not depend on the approximate inverse system. We just need an extra FIR filter in the feedforward path.

This paper is devoted to a new design method for infinite impulse response approximate inverse system of a nonminimum phase system. The design is carried out such that the convolution of the nonminimum phase polynomial and its approximate inverse system can be represented by an approximately linear phase all-pass filter. A method for estimating the time delay and order of an approximate inverse system is also presented. Using infinite impulse response approximate inverse systems better accuracy is achieved with reduced computational complexity. Numerical examples are included to show the effectiveness of the proposed method.

This paper presents a new blind identification method of nonminimum phase FIR systems and an adaptive blind equalization for PAM/QAM inputs without employing higher-order statistics. They are based on the observation that the absolute mean of a second-order white sequence can measure whether the sequence is higher-order white or not. The proposed methods are new alternatives to many higher-order statistics approaches. Some computer simulations show that the absolute mean is exactly estimated and the proposed methods can overcome the disadvantages of the higher-order statistics approaches.

We present a new method for the self-tuning control (STC) of nonminimum phase continuous-time systems based on the pole-zero placement. The long division method is used to decompose a polynomial into a stable and unstable polynomials. It is also shown that the effect of unstable zeros on the magnitude of the desired output can be cancelled. Finally, the results of computer simulation are presented to illustrate the effectiveness of the proposed method.

This letter presents a new design method for approximate inverse systems using all-pass networks. The efficacy of approximate inverse systems for input and parameter estimation of nonminimum phase systems is well recognized. in the previous methods, only time domain design of FIR (finite impulse response) type approximate inverse systems were considered. Here, we demonstrate that IIR (infinite impulse response) type approximate inverse systems outperform the previous methods. A nonlinear optimization technique is adopted for designing the proposed system in the frequency domain. Numerical examples are also presented to show the effectiveness of the proposed method.

This letter presents a new method for adaptive control of nonminimum phase discrete-time systems with disturbances based on the technique of pole-zero placement. The long division method is used to decompose apolynomial into a stable polynomial and an unstable one. Finally, the results of computer simulation are presented to illustrate the effectiveness of the proposed method.