Non-minimum Phase Property Research Articles

Strong Structural Non-Minimum Phase Systems

Structural analysis can reveal properties of the investigated systems without knowing the exact parameters of the system, for example masses, geometries or resistor values. Properties that can be determined are for instance controllability and observability. Recently, there have been investigations about structural stability and structural non-minimum phase behavior. In general by considering the structure of a system a precise answer if the mentioned properties hold numerically can not be given. This led to the introduction of strong structural properties, that hold for all admissible numerically realization of the analyzed system. In this paper the strong structural non-minimum phase property is investigated. The representation of a dynamical system as a graph is proposed for the structural analysis. A method to calculate the invariant zeros polynomial from the graph-theoretic representation of a square MIMO systems is introduced. From that method the strong structural non-minimum phase property is derived. An example for the application of the method is given.

Control of fuel cell-based electric power system using adaptive sliding mode control and observation techniques

The paper deals with controlling an autonomous electric power system that comprises of a primary source of power supply, Proton Exchange Membrane fuel cell (PEMFC), DC–DC boost power converter as a power conditioner, and the ultracapacitor for an auxiliary power supply. Relative degree approach is applied for direct control of the output load voltage as well as the fuel cell and ultracapacitor current in the presence of the model uncertainties. The zero dynamics of the studied electric power system is analyzed and appeared to be stable. The non-minimum phase property of the DC–DC boost converter is eliminated by controlling the fuel cell current based on the power balance. The adaptive super-twisting sliding mode observer is employed for identification of the load resistance, which estimated value is used for generating the fuel cell current command profile. The adaptive gain second order (2-SM) super-twisting sliding mode controller is proposed for controlling the current in PEMFC. The conventional Sliding Mode Controllers (SMC) is designed for controlling the output voltage of the converter and the load current of the ultracapacitor. The efficacy and robustness of the proposed decentralized three-fold electric power system controller that consists of two SMCs and one 2-SM adaptive-gain controller are confirmed via computer simulations.

Time waveform replication for electro-hydraulic shaking table incorporating off-line iterative learning control and modified internal model control

In this article, a combined control strategy incorporating off-line iterative learning control and modified internal model control is proposed for improving the time waveform replication performance of electro-hydraulic shaking table. To reduce the modeling error between the estimated inverse model and the actual system, a modified internal model control strategy is first utilized to cope with the modeling error by back absorbing the nominal model and the inverse controller into a direct through block. Due to the non-minimum phase property of the nominal model estimated by the recursive extended least square algorithm, the zero magnitude error tracking controller is exploited to obtain a stable inverse controller. Then, an off-line iterative learning control strategy involving a real-time feedback controller is conducted on the compensated system to further enhance the replication performance. Therefore, the proposed algorithm combines the merits of modified internal model control and off-line iterative learning control and simplifies the conventional iterative control process by eliminating consecutive computation of Fourier and inverse Fourier transforms. The combined strategy is first programmed in MATLAB/Simulink and then compiled to a real-time personal computer with xPC target technology for implementation. Experiment results demonstrate that a better tracking accuracy and a faster convergence rate are achieved with the proposed algorithm than conventional pure iterative learning controller.

Trajectory planning and tracking control for autonomous bicycle robot

Control of the autonomous bicycle robot offers considerable challenges to the field of robotics due to its nonholonomic, underactuated, and nonminimum-phase properties. Furthermore, instability and complex dynamic coupling make the trajectory planning of the bicycle robot even more challenging. In this paper, we consider both trajectory planning and tracking control of the autonomous bicycle robot. The desired motion trajectory of the contact point of the bicycle’s rear wheel is constructed using the parameterized polynomial curve that can connect two given endpoints with associated tangent angles. The parameters of the polynomial curve are determined by minimizing the maximum of the desired roll angle’s equilibrium of the bicycle, and this optimization problem is solved by the particle swarm optimization algorithm. Then, a control scheme that can achieve full-state trajectory tracking while maintaining the bicycle’s balance is proposed by combining a planar trajectory tracking controller with a roll angle balance controller. Simulation results are presented to demonstrate the effectiveness of the proposed method.

Real-Time Walking Pattern Generation Method for Humanoid Robots by Combining Feedback and Feedforward Controller

This paper focuses on real-time walking pattern generation for humanoid robots with linear inverted pendulum model (LIPM). In general, there are many issues in generating proper walking patterns of center of mass and zero moment point (ZMP) with the LIPM since the LIPM has two drawbacks such as instability and non-minimum phase property. For resolving these difficulties, the paper proposes a new real-time approach by combining a feedback and a feedforward controller. The feedback controller employs a pole placement method which shifts the poles of the LIPM in order to improve system stability. The feedforward controller utilizes advanced pole-zero cancelation by series approximation method (APZCSA) for reducing non-minimum phase property which occurs by an unstable zero and is not able to be dealt with by the feedback controller. In addition, the APZCSA improves the tracking error induced by finite series approximation. Using the two controllers, the proposed method makes the transfer function of overall walking pattern generation system approximately unity and consequently generates a stable walking pattern which follows a desired ZMP according to walking path. The efficiency of the proposed method is verified by walking pattern planning examples and experiments with the humanoid robot MAHRU-R.

A study of bicycle dynamics via system identification approaches

This study investigates bicycle dynamic properties by using system identification approaches. The non-linear bicycle model with configuration parameters from a previously developed benchmark model is studied. The roll angle of the bicycle is controlled at different speeds to generate input–output data including steering torque, roll, and steering angles. The collected data are then used to identify the one-input two-output linear model by a prediction-error identification method using parameterization in canonical state-space form derived as Whipple's model. Simulations are used to verify the accuracy of the generated linear model. Numerous properties for various speed ranges are discussed from the pole and zero locations of the identified linear model. The system stability, limit-cycle phase portraits of the roll and steering angles, and the non-minimum phase property of the non-linear system are further investigated and compared with the corresponding linearized results from previous studies in the literature.

Complementary PID Controller to Passivity-Based Nonlinear Control of Boost Converters With Inductor Resistance

Since the DC-DC boost converter exhibits highly nonlinear and non-minimum phase properties, it is not an easy task to design a controller that is robust against load perturbations. This paper presents a dynamic output feedback controller for a DC-DC boost converter that has a practical inductor and a series resistance. In order to maintain its robust output voltage regulation, the proposed controller adopts a simplified parallel-damped passivity-based controller (PD-PBC). A complementary proportional-integral-differential (PID) controller to the PD-PBC has been designed for removing the steady state error owing to the parasitic resistance. We present sufficient conditions for the asymptotic stability of the augmented system with an additional dynamic system. Computer simulations and experimental tests under reference step changes and load perturbations confirm the improved performance of the proposed approach.

Designing Type-1 and Type-2 Fuzzy Logic Controllers via Fuzzy Lyapunov Synthesis for nonsmooth mechanical systems

In this paper, Fuzzy Lyapunov Synthesis is extended to the design of Type-1 and Type-2 Fuzzy Logic Controllers for nonsmooth mechanical systems. The output regulation problem for a servomechanism with nonlinear backlash is proposed as a case of study. The problem at hand is to design a feedback controller so as to obtain the closed-loop system in which all trajectories are bounded and the load of the driver is regulated to a desired position while also attenuating the influence of external disturbances. The servomotor position is the only measurement available for feedback; the proposed extension is far from trivial because of the nonminimum phase properties of the system. Performance issues of the Type-1 and Type-2 Fuzzy Logic Regulators that were designed are illustrated in experimental studies.

An internal state decomposition approach to a discrete-time [formula omitted] control problem with irrational input non-minimum phase property

An internal state decomposition approach to a class of discrete-time H2 control problems with irrational non-minimum phase property at the control input is proposed. This is a generalization of the state-variable transformation to derive the discrete-time Smith predictor for a single input-delay system. The H2 optimal controller is derived using the orthogonality principle in H2 space as a direct consequence of the state decomposition. The characterization of the optimal cost by the previous and alternative truncation operators is also discussed.

Fuzzy logic control with genetic membership function parameters optimization for the output regulation of a servomechanism with nonlinear backlash

The paper presents a hybrid architecture, which combines Type-1 or Type-2 fuzzy logic system (FLS) and genetic algorithms (GAs) for the optimization of the membership function (MF) parameters of FLS, in order to solve to the output regulation problem of a servomechanism with nonlinear backlash. In this approach, the fuzzy rule base is predesigned by experts of this problem. The proposed method is far from trivial because of nonminimum phase properties of the system. The simulation results illustrate the effectiveness of the optimized closed-loop system.

Analysis and optimal design of delayless subband active noise control systems for broadband noise

Active control of wide-band noise presents certain unique challenges many of which can be addressed using delayless subband adaptive filtering techniques. The performance of a delayless subband active noise control (DSANC) system depends on a complex interplay between the (1) choice of adaptation algorithm, (2) number of subbands, (3) weight stacking scheme, (4) input noise spectrum, and (5) primary, secondary paths. This interplay is studied in this paper for two different kinds of broadband noise. Distortion introduced by the weight stacking methods is investigated and quantified. It is shown that the computational complexity decreases and the stacking distortion increases with the number of subbands. The performance limiting effect of the non-minimum phase property of secondary path on the system performance is evaluated and analytically formulated. An upper bound for the obtainable noise attenuation level (NAL) is derived. A step by step optimal design procedure for the best performance is developed taking computational complexity into consideration. Simulation results support the analytical development and the proposed approach for optimal design of DSANC systems.

Physical-model-based control of a piezoelectric tube for nano-scale positioning applications

Piezoelectric tubes exhibit a highly resonant mode of vibration which, if uncontrolled, limits the maximum scan rate in nano-scale positioning applications. Highly resonant systems with collocated sensor/actuator are often controlled using resonant shunt dampers. Unfortunately, in the configuration used here, this approach is not possible due the non-minimum phase property arising from the presence of a right-half plane zero. This problem is solved by: (i) interpreting the resonant shunt damper in the context of physical-model-based control (PMBC) and (ii) extending the PMBC approach to handle non-minimum phase systems. The resultant controller combines the physical insight of the resonant shunt damper with the ability to control the non-minimum phase piezoelectric tube. A digital implementation of the controller was experimentally evaluated and found to successfully eliminate the resonant mode of vibration during an accurate and fast scan using a piezoelectric tube actuator.

A new expression for the [formula omitted] performance limit based on state-space representation

This paper aims to clarify the performance limit via state-space representation, in order to handle multiple-input-multiple-output systems in a transparent way. To this end, by applying some results on infinite-dimensional control theory, a closed formula for the H 2 performance limit is derived for systems with a special structure described in terms of a rational transfer matrix and a scalar inner function. This formulation is capable of dealing with various control problems, including H 2 control of a class of infinite-dimensional systems. The resulting formula, given as a functional of the inner function, helps us to understand how achievable H 2 performance deteriorates due to non-minimum phase properties or unstable modes of plants.

Control por Modos Deslizantes y Planitud Diferencial de un Convertidor de CD/CD Boost: Resultados Experimentales

This paper is concerned with control of the DC/DC boost converter. Specifically, we propose a solution for output voltage trajectory tracking. Because of the non-minimum phase property of this converter when voltage is the controlled output we design an indirect control strategy based on a combination of sliding modes and differential flatness. This means that we achieve output voltage trajectory tracking by means of a controller which is designed for output current trajectory tracking. We also present some experimental results using the proposed control strategy which show that satisfactory performance is achieved. We use the National Instruments TM PCI-6025E electronic card together with MATLAB®–Simulink®

Direct neural network-based self-tuning control for a class of nonlinear systems

Most self-tuning control algorithms for nonlinear systems become invalid when the controlled systems have nonminimum phase property. In this article, a direct neural network-based self-tuning control strategy is developed to deal with this problem under the certainty equivalence principle. Based on an equivalent linearized model from the local linearization, the controller structure is designed using a modified Clarke index with the guaranteed closed-loop stability and without the traditional requirement of the globally boundedness. For the system with unknown parameters, the controller is self-tuned by an on line RBF neural network identifier. Satisfactory simulations illustrate the effectiveness and adaptability of the proposed strategy even under system parameter variations.

A Smith-Like Control Design for Performance Enhancement of Systems with RHP Zeros

Motivated by the common non-minimum phase property of dead time and right-half-plane (RHP) zero, this paper presents a Smith-like scheme for control of systems with RHP zeros. It is shown that RHP zeros and possible dead time can be removed from the characteristic equation of the scheme so that the control design is greatly simplified, and enhanced performance is achievable. By model reduction, a unified design with a single tuning parameter is presented for processes of different order. The relationships between the time domain specifications and the tuning parameter are developed to ease the design trade-off. Simulation examples are presented to demonstrate the effectiveness of the proposed scheme. For robustness, it is shown that our design ensures a gain margin of 2 and phase margin of π/3, as well as 100% perturbation of the RHP zero or uncertain time delay of |ΔL| ≤ τ/0.42.

離散時間系における最適<I>H</I><SUP>2</SUP>制御性能の非最小位相特性による特徴付け

離散時間系における最適<I>H</I><SUP>2</SUP>制御性能の非最小位相特性による特徴付け

Nonlinear H∞-Output Regulation of a Nonminimum Phase Servomechanism With Backlash

Nonlinear H∞ control synthesis is extended to an output regulation problem for a servomechanism with backlash. The problem in question is to design a feedback controller so as to obtain the closed-loop system in which all trajectories are bounded and the load of the driver is regulated to a desired position while also attenuating the influence of external disturbances. Provided the servomotor position is the only measurement available for feedback, the proposed extension is far from trivial because of nonminimum phase properties of the system. Performance issues of the nonlinear H∞-output regulator constructed are illustrated in an experimental study.

An Accurate Model for the DC-Side Voltage Control of the Neutral Point Diode Clamped Converter

This paper presents an in depth analysis to show that the conventional power balance model for the dc-side control of the Neutral Point Diode Clamped (NPC) converter is not adequately accurate for all operating conditions. The inaccuracy is due to the fact that the instantaneous power of the ac-side inductors is assumed to be negligible in the power balance equation. This paper shows that this assumption obscures (i) the impact of operating point which is a direct consequence of the inherent nonlinear nature of the problem and (ii) the nonminimum-phase property of the plant in the rectifying mode of operation. Thus, the conventional dc-side control model may lead to unsatisfactory performance or even instability. To overcome the shortcoming, this paper also develops accurate nonlinear and linearized models for the dc-side controller design, including the impact of the ac-side interface reactors. The analytical results and the conclusions are validated by digital time-domain simulation of a study system in the PSCAD/EMTDC environment. The mathematical developments and conclusions of the paper are equally applicable to the conventional two-level VSC.

Blind Separation and Deconvolution for Convolutive Mixture of Speech Combining SIMO-Model-Based ICA and Multichannel Inverse Filtering

We propose a new two-stage blind separation and deconvolution strategy for multiple-input multiple-output (MIMO)-FIR systems driven by colored sound sources, in which single-input multiple-output (SIMO)-model-based ICA (SIMO-ICA) and blind multichannel inverse filtering are combined. SIMO-ICA can separate the mixed signals, not into monaural source signals but into SIMO-model-based signals from independent sources as they are at the microphones. After the separation by the SIMO-ICA, a blind deconvolution technique for the SIMO model can be applied even when each source signal is temporally correlated and the mixing system has a nonminimum phase property. The simulation results reveal that the proposed algorithm can successfully achieve separation and deconvolution of a convolutive mixture of speech, and outperforms a number of conventional ICA-based BSD methods.