Error Feedback Coefficients Research Articles

Study of Generalized Chaotic Synchronization Method Incorporating Error-Feedback Coefficients.

In this paper, taking the generalized synchronization problem of discrete chaotic systems as a starting point, a generalized synchronization method incorporating error-feedback coefficients into the controller based on the generalized chaos synchronization theory and stability theorem for nonlinear systems is proposed. Two discrete chaotic systems with different dimensions are constructed in this paper, the dynamics of the proposed systems are analyzed, and finally, the phase diagrams, Lyapunov exponent diagrams, and bifurcation diagrams of these are shown and described. The experimental results show that the design of the adaptive generalized synchronization system is achievable in cases in which the error-feedback coefficient satisfies certain conditions. Finally, a chaotic hiding image encryption transmission system based on a generalized synchronization approach is proposed, in which an error-feedback coefficient is introduced into the controller.

Fractional-order sliding mode control for a bearingless induction motor based on improved load torque observer

In order to improve the anti-disturbance performance of a bearingless induction motor (BIM) control system, a fractional-order sliding mode control (FOSMC) strategy based on improved load torque observer is proposed on the basis of the sliding mode speed regulation system. Using the information memory and genetic characteristics of the fractional calculus operator, the fractional integral term of the speed error is introduced in the design of the traditional sliding surface, which reduces the influence of disturbance on the speed regulation system. The fractional-order sliding mode control law is derived based on the BIM mathematical model, and the stability of the control law is proved by Lyapunov theorem. An improved observer is constructed based on the BIM state equations, and the real-time observed load torque is introduced into the fractional-order sliding mode controller. To improve the observer's convergence speed, the proportional integral form is used to replace the integral form in the traditional reduced order load observer. And the state error feedback coefficients of the improved load observer are calculated. Both simulation and experimental results verified the effectiveness of the proposed control strategy.

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 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.

Error spectrum shaping in two-dimensional recursive digital filters

This paper treats error spectrum shaping for two-dimensional recursive digital filters, described by a rational transfer function as well as the Roesser local state-space model. For each description of the filter, a technique is developed for obtaining the optimal error-feedback (EF) coefficients that minimize the noise variance at the filter output. The optimal solution can be characterized in a closed form which minimizes a quadratic form subject to constraints such as symmetry, antisymmetry, quadrantal symmetry, or quadrantal antisymmetry of the EF coefficients. In an unconstrained case, the optimal EF corresponds to a special case of the above optimal solution. Finally, two numerical examples are given to illustrate the utility of the proposed technique. In the numerical examples, the discrete sub-optimal coefficients of the EF are obtained by applying an existing procedure for the least-squares discrete-space optimization.

Error spectrum shaping in two‐dimensional digital filters

AbstractA technique for minimizing the normalized noise variance at the output of two‐dimensional (2‐D) recursive digital filters is developed where error spectrum shaping of the filter is performed by means of higher‐order feed‐back. First, the optimal solution of error feedback coefficients is derived. Then suboptimal error feedback coefficients are found in which the error feedback coefficients are symmetric. Here, both the optimal and suboptimal solutions are found analytically by solving the minimization problem of a quadratic form. Finally, a numerical example is given to check the validity of the proposed algorithm and it is shown that the proposed technique is effective even if the optimal or suboptimal coefficients are rounded to a power of 2.

Implementation of a time-varying MIMO system with error feedback

The error feedback method for roundoff noise reduction is applied to a time-varying multiple-input multiple-output (MIMO) system. The optimal error feedback coefficients are derived for a general Mth-order structure, which reduces to M distinct optimization problems. The developed theory is applied to a signal processor implementation of a 4th-order time-varying AC motor model. By employing 2nd-order error feedback, the roundoff noise can be cut down very efficiently with only 8% increase in program execution time, which is only a fraction of the costs of a double-precision implementation. Although the model is time varying, keeping the error feedback coefficients fixed results in almost equal reduction as with time-varying coefficients.

Elimination of limit cycles in direct form digital filters using error feedback

AbstractThe elimination of zero‐input limit cycles in direct form filter sections using either a rounding or a magnitude truncation fixed‐point quantizer is considered. the well‐known criterion of Chang is reformulated for second‐order filter sections in a more practical form using the bilinear transformation. This enables graphical interpretation and quantitative analysis of the possible error feedback solutions for different pole locations.The synthesis of limit‐cycle‐free error feedback for second‐order filter sections is addressed in detail and several solutions are proposed. the error feedback coefficients are constrained to power‐of‐two values or to symmetric values so that the implementation is efficient, e.g. with signal processors. Different limit‐cycle‐free solutions are discussed with design examples and their round‐off noise properties are compared.The absence of limit cycles is related to the round‐off noise properties of the filter section. the main conclusion of the paper is that when the EF coefficients are appropriately chosen, low round‐off noise and the absence of limit cycles can always be accomplished at the same time. A particularly close correlation between limit cycles and roundoff noise is demonstrated with a rounding quantizer: a limit‐cycle‐free implementation always guarantees low roundoff noise. For most complex conjugate pole locations the converse relation also holds, i.e. low round‐off noise implies the absence of limit cycles.

Noise reduction in recursive digital filters using high-order error feedback

The problem of solving the optimal (minimum-noise) error feedback coefficients for recursive digital filters is addressed in the general high-order case. It is shown that when minimum noise variance at the filter output is required, the optimization problem leads to set of familiar Wiener-Hopf or Yule-Walker equations, demonstrating that the optimal error feedback can be interpreted as a special case of Wiener filtering. As an alternative to the optimal solution, the formulas for suboptimal error feedback with symmetric or antisymmetric coefficients are derived. In addition, the design of error feedback using power-of-two coefficients is discussed. The efficiency of high order error feedback is examined by test implementations of the set of standard filters. It is concluded that error feedback is a very powerful and versatile method for cutting down the quantization noise in any classical infinite impulse response (IIR) filter implemented as a cascade of second-order direct form sections. The high-order schemes are attractive for use with high-order direct form sections.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

On error-spectrum shaping in state-space digital filters

A new scheme for shaping the error spectrum in state-space digital filter structures is proposed. The scheme is based on the application of diagonal second-order error feedback, and can be used in any arbitrary state-space structure having arbitrary order. A method to obtain noise-optimal state-space structures for fixed error feedback coefficients, starting from noise optimal structures in absence of error feedback (the Mullis and Roberts Structures), is also outlined. This optimization is based on the theory of continuous equivalence for state-space structures.