Design of a memory‐based prefilter supplementing a robust PID control system

For systems with uncertainties, lots of PID parameter tuning methods have been proposed from the view point of the robust stability theory. However, the control performance becomes conservative using robust PID controllers. In this paper, a new two‐degree‐of‐freedom (2DOF) controller, which can improve the tracking properties, is proposed for nonlinear systems. According to the proposed method, the prefilter is designed as the PD compensator whose control parameters are tuned by the idea of a memory‐based modeling (MBM) method. Since the MBM method is a type of local modeling methods for nonlinear systems, PD parameters can be tuned adequately in an online manner corresponding to nonlinear properties. Finally, the effectiveness of the newly proposed control scheme is numerically evaluated on a simulation example. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

A Spatial-Domain Technique for the Design of 3-D Separable-Denominator State-Space Digital Filters

In this paper,a technique for designing 3-D separable-denominator state-spacedigital filters is developed. The design process is divided intotwo phases. First, the coefficient matrices related to stabilityare constructed for the filter to be stable by using alternatingvariable method. Next, the other matrices are obtained by solvinglinear equations. These phases are repeated until there is nosignificant change in the squared error function.     

Design for 2-D error feedback networks with identical coefficient sets

In realization of recursive digital filters with fixed point arithmetic, an error caused by roundoff arises. It is known that the level of the roundoff noise of an IIR filter tends to be high when the poles are close to the unit circle. Error feedback (EF) is an effective method to reduce the roundoff noise. It is desirable to design an EF network using as few parameters as possible in order to keep computational costs low. In this paper, we propose a method for designing a 2D EF network with identical coefficient sets. That is, the EF coefficients are divided into several subsets such that all the elements within each set have the same absolute value. In order to optimize the coefficient sets, we propose an algorithm by using the genetic algorithm. In the numerical example, we demonstrate the effectiveness of the proposed method.     

Separate/joint optimization of error feedback and coordinate transformation for roundoff noise minimization in two-dimensional state-space digital filters

This paper is concerned with the minimization of roundoff noise subject to l/sub 2/-norm dynamic-range scaling constraints in two-dimensional (2-D) state-space digital filters. Two methods are proposed, with the first one using error feedback alone and the second one using joint error feedback and coordinate transformation optimization. In the first method, several techniques for the determination of optimal full-scale, block-diagonal, diagonal, and scalar error-feedback matrices for a given 2-D state-space digital filter are proposed. In the second method, an iterative approach for minimizing the roundoff noise under l/sub 2/-norm dynamic-range scaling constraints is developed by jointly optimizing a scalar error-feedback matrix and a coordinate transformation matrix, which may be regarded as an alternative approach to the conventional method for synthesizing the optimal 2-D filter structure with minimum roundoff noise. An analytical method for the joint optimization of a general error-feedback matrix and a coordinate transformation matrix under the scaling constraints is also proposed. A numerical example is presented to illustrate the utility of the proposed techniques.     

Memory‐based IMC tuning of PID controllers for nonlinear systems

This paper describes a new memory‐based proportional, integral, derivative (PID) controller design. These PID parameters are tuned by the IMC‐PID method, which is derived from the relationship between the internal model control (IMC) and PID control. The IMC‐PID has a user‐specified parameter that greatly influences the control performance. The authors have already proposed a system identification scheme based on the memory‐based approach. In this paper, a new controller design scheme is discussed, whose system parameters and the corresponding suitable user‐specified parameter are simultaneously computed. Finally, the behavior of the newly proposed control scheme is examined in a simulation example. © 2006 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

Separate/joint optimization of error feedback and realization for roundoff noise minimization in a class of 2-D state-space digital filters

Techniques for the separate/joint optimization of error-feedback and realization are developed to minimize the roundoff noise subject to l ₂-norm dynamic-range scaling constraints for a class of 2-D state-space digital filters. In the joint optimization, the problem at hand is converted into an unconstrained optimization problem by using linear-algebraic techniques. The unconstrained problem obtained is then solved by applying an efficient quasi-Newton algorithm. A numerical example is presented to illustrate the utility of the proposed techniques.     

Noise Reduction in Two-Dimensional Recursive Digital Filters with Discrete Optimized Error Feedback Coefficients

This paper treats the minimization problem for roundoff noise in two-dimensional (2-D) recursive digital filters with an error feedback (EF). The EF is known as an available scheme for the reduction of roundoff noise, and this can be achieved by extracting a roundoff error from the quantizer and feeding it back to the adder. Since the EF circuit is an additional device of the digital filter, the bit length of the coefficients should be as short as possible for the fast arithmetic and low-cost realization. In this paper, we propose an algorithm to optimize the EF coefficients in a discrete space. The proposed algorithm is based on the branch and bound method by estimating the lower bound of the optimal solution, and the optimality of the obtained solution can be guaranteed. Finally, we?give?a?numerical example to demonstrate the effectiveness of the proposed method, and show the optimal solution can be found without using the round-robin algorithm.     

Design of Two-Dimensional Adaptive Digital Notch Filters

In this paper, a method for realizing a two-dimensional (2-D) adaptive notch filter is proposed. The obtained 2-D structure contains a pair of one-dimensional (1-D) second-order IIR notch filters and a pair of 1-D first-order allpass filters. The method has been successfully applied for the removal of a sinusoidal interference superimposed on an image.     

Jointly optimized error-feedback and realization for roundoff noise minimization in state-space digital filters

Roundoff noise (RN) is known to exist in digital filters and systems under finite-precision operations and can become a critical factor for severe performance degradation in infinite impulse response (IIR) filters and systems. In the literature, two classes of methods are available for RN reduction or minimization-one uses state-space coordinate transformation, the other uses error feedback/feed-forward of state variables. In this paper, we propose a method for the joint optimization of error feedback/feed-forward and state-space realization. It is shown that the problem at hand can be solved in an unconstrained optimization setting. With a closed-form formula for gradient evaluation and an efficient quasi-Newton solver, the unconstrained minimization problem can be solved efficiently. With the infinite-precision solution as a reference point, we then move on to derive a semidefinite programming (SDP) relaxation method for an approximate solution of optimal error-feedback matrix with sum-of-power-of-two entries under a given state-space realization. Simulations are presented to illustrate the proposed algorithms and demonstrate the performance of optimized systems.