Multiple Real Pole Research Articles

Un Nuevo Método de Identificación Basado en la Respuesta Escalón en Lazo Abierto de Sistemas Sobre-amortiguados

In this paper a new process identification method based in open loop step response of overdamped systems is presented. Initially the transient behavior of transfer functions with multiple real poles is analyzed, establishing analytical formulas to estimate the time it takes for these systems to reach certain points of his reaction curve to stimuli of the step type, including settling time for error criteria of 2% and 5%. Subsequently developed a method of identification using 3 points characteristic of the reaction curve (tk, yk), allowing estimate the order process N, the time constant T of multiple poles and delay time L of the approximate model. To evaluate the performance of the proposed method, 3 minimum phase and 1 non mimium phase transfer functions are used to compare the proposed method with other of identification methods found in the literature, as well as also, one model of a non-isothermal chemical reactor; establishing as efficiency index the root mean square error (RMSE) of the transient response and the frequency resposne of the identified models with respect to the original transfer functions with different signal to noise ratio (SNR) values. From the results obtained show that the proposed method achieves excellent approximation of the transient responses and frequency compared to other methods. From the results, it was observed that the proposed method obtains good approximations of the transient and frequency responses, being a simple method and requires a low computational load compared with others methods.

Continuous, saturation, and discontinuous tokamak plasma vertical position control systems

This paper is devoted to the design and comparison of unstable plasma vertical position control systems in the T-15 tokamak with the application of two types of actuators: a multiphase thyristor rectifier and a transistor voltage inverter. An unstable dynamic element obtained by the identification of plasma-physical DINA code was used as the plasma model. The simplest static feedback state space control law was synthesized as a linear combination of signals accessible to physical measurements, namely the plasma vertical displacement, the current, and the voltage in a horizontal field coil, to solve the pole placement problem for a closed-loop system. Only one system distinctive parameter was used to optimize the performance of the feedback system, viz., a multiple real pole. A first-order inertial unit was used as the rectifier model in the feedback. A system with a complete rectifier model was investigated as well. A system with the voltage inverter model and static linear controller was brought into a sliding mode. As this takes place, real time delays were taken into account in the discontinuous voltage inverter model. The comparison of the linear and sliding mode systems showed that the linear system enjoyed an essentially wider range of the plant model parameters where the feedback system was stable.

Closed Form Solutions to L2-Sensitivity Minimization of Second-Order State-Space Digital Filters with Real Poles

This letter proposes closed form solutions to the L2-sensitivity minimization of second-order state-space digital filters with real poles. We consider two cases of second-order digital filters: distinct real poles and multiple real poles. In case of second-order digital filters, we can express the L2-sensitivity of second-order digital filters by a simple linear combination of exponential functions and formulate the L2-sensitivity minimization problem by a simple polynomial equation. As a result, the minimum L2-sensitivity realizations can be synthesized by only solving a fourth-degree polynomial equation, which can be analytically solved.

Closed Form Solutions to L2-Sensitivity Minimization Subject to L2-Scaling Constraints for Second-Order State-Space Digital Filters with Real Poles

This paper proposes closed form solutions to the L2-sensitivity minimization subject to L2-scaling constraints for second-order state-space digital filters with real poles. We consider two cases of second-order digital filters: distinct real poles and multiple real poles. The proposed approach reduces the constrained optimization problem to an unconstrained optimization problem by appropriate variable transformation. We can express the L2-sensitivity by a simple linear combination of exponential functions and formulate the L2-sensitivity minimization problem by a simple polynomial equation. As a result, L2-sensitivity is expressed in closed form, and its minimization subject to L2-scaling constraints is achieved without iterative calculations.

Positive Realizations of Transfer Matrices With Real Poles

In this brief, we prove that any normal transfer matrix with nonnegative impulse response and simple real poles of second order in discrete-time linear systems admits a minimal positive realization. This result can be used to obtain a minimal positive realization of some transfer matrices of any order with simple real poles. In addition, several results obtained for single-input single-output systems are adapted to solve the positive realization problem of transfer matrices with multiple real poles in multiple-input multiple-output systems.

Robust stabilization of systems with multiple real pole uncertainties

The robust stabilization of systems with several uncertain real poles is discussed. Necessary and sufficient conditions of existence of a controller in terms is obtained of an interpolation problem are given. The interpolating function is obtained directly for a particular case. Two examples are shown for the synthesis of a controller. An explicit solution of the controller for plants without zeros in the right hand plane (RHP) and without known poles in the RHP is given. This shows the practical utility of the method to the design of robust stabilizers.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

An alternative design for a multiple-real-pole/multiple-critical-pole all-pole equiripple RC active low-pass filter

A design technique for a class of all-pole transfer functions with multiple real poles and multiple critical poles and equiripple pass-band magnitude response is described. It is seen as an alternative design which is mathematically simpler than the generalized method previously proposed [8]. It is useful for the designer who is more familiar with the simultaneous linear equations than the optimization using linear programming.

An auditory spectral analysis model using the chirp z-transform

In this paper we discuss a new signal-processing approach to implementing an auditory processing model. The model is based on auditory physiology and psychophysics; it uses constant-bandwidth analysis below 500 Hz and constant-Q analysis above 500 Hz, with the analysis filters being implemented with multiple real poles. The constant-Q analysis is performed using the chirp z-transform (CZT). We review the evidence for the auditory model and the properties of constant-Q analysis, and derive the CZT formulation for both causal and linear-phase analysis filters. The paper concludes with an example of speech illustrating the use of the auditory model.

Multiple real‐pole equal‐ripple rational (MRPER) approximation for lowpass RC‐active filters

AbstractA new class of lowpass rational transfer functions is defined, with equal‐ripple behaviour both in the passband and in the stopband. The proposed functions have a multiple real pole, which allows the realization of lowpass RC‐active filters by cascading more (than one) 3rd‐order blocks.These new functions, called multiple real‐pole equal‐ripple rational (MRPER), improve the attenuation performance with respect to a classical solution employing the same number of 2nd‐order blocks and hence may allow a reduction in the required number of active elements and, eventually, in power consumption and in noise‐to‐signal ratio. However, even if the number of active blocks cannot be reduced, the better attenuation performance, which results, allows component tolerances to relax.

Various approximating functions for cascade or ladder simulating RC active networks

The use of m.r.p.e.r. (multiple real pole equal ripple) and m.c.p.e.r. (multiple critical pole equal ripple) approximating functions for the design of RC active filters is shown. A study of various LC ladder structures using Cauer,3 m.r.p.e.r. or m.c.p.e.r. solutions has been performed. The results indicate that no significant difference can be expected if either of these solutions is used. It is shown that more components are required for m.r.p.e.r. or m.c.p.e.r. solutions, and that no improvement over coupled sections of lower order can be observed.

Transitional Murromaf–Murroer filters

A new class of lowpass filters with all transmission zeros at infinity, having equal-ripple behaviour in the passband, is described. The transfer function of these filters, referred to as transitional Murromaf-Murroer filters, is obtained by adding the multiple real poles and reducing the number of complex pole pairs to realise a lowpass RC active filter with a reduced number of amplifiers with respect to the classical transitional Butterworth-Chebyshev filters.

Design of low-pass maximally flat RC-active filters with multiple real pole: The MURROMAF polynomials

A new class of low-pass all-pole transfer functions is defined, with maximally flat behavior at the origin. The main feature of this class is the introduction of a multiple real pole, in order to realize RC-active filters by cascading third-order sections and, if necessary, second-order sections. This solution yields a reduction in the number of OA's and, consequently, in power consumption and in SNR.

Maximally flat approximation of lowpass RC active filters with multiple real pole

A new maximally flat approximation criterion is proposed to realise lowpass RC active filters with a reduced number of amplifiers with respect to the classical Butterworth polynomials. This improvement is obtained by adding a multiple real pole and reducing the number of the complex pole pairs. The cascade connection of 3rd-order blocks allows the realisation of filters with fewer sections (fewer o.a.s) with respect to the commonly used cascade connections of 2nd-order blocks.

Extended interpretation of a Steiglitz–Zemanian lemma on positive real functions

The easy recognisibility of positive reality, contained in a lemma due to Steiglitz and Zemanian for the case of rational functions consisting of a multiple real pole and multiple real zero, will be extended so as to include possible multiple complex poles and zeros. The emphasis will therefore be on multiplicity and complexity, such as may be exhibited by the poles and zeros of immittance functions.