Impact of Feedback Delay on Closed-Loop Stability in Semiconductor Optical Amplifier Control Circuits

Semiconductor optical amplifiers (SOAs) are attractive for integrated photonic signal processing, but because their response is so fast, delays in a controller feedback path can jeopardize performance and stability. Using state-space methods, we quantify the constraints imposed on feedback controllers by closed-loop delay. We first derive a complete nonlinear state-space control model of a SOA with an equivalent circuit containing parasitics and dynamic impedance; the analytical state-space model agrees well with a validated photonic-only control model. Using a linearized version of the model we demonstrate that time delay in the feedback path can destabilize the SOA through phase accumulation. We then apply linear system theory to calculate the best-case stable delay margin for a given controller norm, and find a potentially severe inverse relationship between delay margin and controller norm. Finally, guided by the delay-controller relationship we design a hybrid feedforward-feedback controller to illustrate that good transient and steady-state regulation is obtained by carefully balancing the feedforward and feedback components. Our state-space modeling and design methods are general and are easily adapted to the design and analysis of more complex photonic circuits.     

A DSP-based implementation of a new nonlinear control for a three-phase neutral point clamped boost rectifier prototype

This work presents the design and implementation of a nonlinear control strategy for a three-phase three-level neutral-point-clamped boost rectifier. The adopted control consists of nonlinear feedback linearization technique. The nonlinear state-space model of the rectifier was obtained in the dq0 reference frame. The input/output feedback linearization is then applied and the linearizing control law is derived. Therefore, the resulting model is linearized and decoupled in three independent subsystems. Afterwards, the stabilizing controllers are designed based on linear techniques to control line currents, output, and neutral point voltages. The control law is designed using Simulink/Matlab and applied to the converter via a 1.8-kHz pulsewidth modulator (PWM). Both control law and PWM signals are executed in real time using the DS1104 DSP of dSPACE. A 1.2 kW laboratory prototype is built for validation purposes. The proposed control law robustness is validated for diverse severe load and system parameter variations. It shows robust performance in terms of high power factor, low total harmonic distortion and output voltage ripples, small overshoot, and short settling time.     

Analysis and design of a multiple feedback loop control strategyfor single-phase voltage-source UPS inverters

This paper presents the analysis and design of a multiple feedback loop control scheme for single-phase voltage-source uninterruptible power supply (UPS) inverters with an L-C filter. The control scheme is based on sensing the current in the capacitor of the load filter and using it in an inner feedback loop. An outer voltage feedback loop is also incorporated to ensure that the load voltage is sinusoidal and well regulated. A general state-space averaged model of the UPS system is first derived and used to establish the steady-steady quiescent point. A linearized small signal dynamic model is then developed from the system general model using perturbation and small-signal approximation. The linearized system model is employed to examine the incremental dynamics of the power circuit and select appropriate feedback variables for stable operation of the closed-loop UPS system. Experimental verification of a laboratory model of the UPS system under the proposed closed-loop operation is provided for both linear and nonlinear loads. It is shown that the control scheme offers improved performance measures over existing schemes, It is simple to implement and capable of producing nearly perfect sinusoidal load voltage waveform at moderate switching frequency and reasonable size of filter parameters. Furthermore, the scheme has excellent dynamic response and high voltage utilization of the DC source     

Coherent-state optical amplifier: a proposal

A new kind of phase-insensitive optical amplifier is proposed whose output is in the coherent state (ideal laser light) if the input is in the coherent state. In-phase and quadrature modulations are preserved in absolute values. Both modulations can be tapped off. The amplifier employs conventional optical amplifiers, electrical feedback, and all-pass filters. Remarkably, these properties hold when either linear or nonlinear optical amplifiers are employed.<>     

Nonlinear control of a series DC motor: theory and experiment

The control problem for a series DC motor is considered. Based on a nonlinear mathematical model of a series-connected DC motor, it is shown that the combination of a nonlinear transformation and state feedback (feedback linearization) reduces the nonlinear control design to a linear control design. To demonstrate its effectiveness, an experimental study of this controller is presented. These experimental results are also compared with a simulation of the closed-loop system. Finally, it is shown that a nonlinear observer (with linear error dynamics) for speed and load torque can be constructed based only on measurements of the motor current. Experimental results of this speed and load-torque estimator are also presented     

Control characteristics and speed controller design for a highperformance permanent magnet synchronous motor drive

The theory of vector control is applied to the nonlinear model of a permanent magnet synchronous motor to develop a linear model for controller design purposes. The operation and relevant mathematics of a pseudo-derivative feedback controller are presented. Controller designs for three different speeds are then considered, and a comparative evaluation is made on the basis of their large and small-signal behavior. In order to test the large-signal response, the detailed nonlinear model of the machine and a real-time model of the inverter switches are used. Results indicate that a critically damped design done so as to ensure that all control and power signals never saturate gives an extremely poor result. Much better small and large-signal responses are achieved by avoiding this constraint and using Zener diodes instead to limit the commanded input into the inverter. Two designs using this technique are presented, an underdamped design with low speed overshoot and an overdamped design with no speed overshoot. The response of the underdamped design was much quicker than that of the overdamped. However the overdamped design has application when speed overshoot is intolerable     

Extension of state-space averaging to resonant switches and beyond

It is shown that the state-space averaging method can be extended by linear network theory from the domain of pulse-width-modulated converters to a much larger class, including resonant switches and current-programmed mode. The canonical model concept is also extended, and it is shown that the effect of resonant switching is to introduce a feedback block into the generalized canonical model. These results are applied to linear zero-current and zero-voltage resonant switches, a new class of nonlinear resonant-switch converters, and the current-programmed mode. Equivalent circuit models are developed for both full and half-wave operation, and experimental verification is presented     

Small signal analysis of the LCC-type parallel resonant converterusing discrete time domain modeling

Discrete state-space modeling of the LCC-type parallel resonant power converter is presented. Using these large signal equations, small signal modeling of the power converter is obtained. Multiple loops have been used for the closed loop operation. State variable feedback control has been integrated with the linear small signal state-space model and the associated control aspects are studied. The small signal state-space model has been used to study the small signal behavior of the power converter for open loop and closed loop operation for parameters like control to output transfer function, audio-susceptibility and output impedance. Key theoretical results have been experimentally verified     

Buck converter small-signal models and dynamics: comparison ofquasi-resonant and pulsewidth modulated switches

The generalized canonical model obtained from extended state-space averaging is used as a design tool for the evaluation of the buck converter dynamics in different switching schemes. Designs are given at a specified constant conversion ratio and load for the pulse width modulated, zero current, zero voltage, and nonlinear resonant switch full- and half-wave converters. The small signal equivalent circuit model is discussed, and the feedback effects introduced by resonant switching on line and control transfer functions are evaluated. The small signal transfer functions of half-wave converters are heavily load-current dependent, and exhibit significant damping at light loads, which can result in two real poles in the converter response instead of a complex conjugate pair. This damping effect is evaluated over the entire normalized load current range for the linear and nonlinear zero-current switching converters. Simple approximate expressions are given for the real poles. Experimental verification of the half-wave analysis is presented, and the effects of converter efficiency on model accuracy are discussed     

一类非线性时滞离散系统模糊H∞滤波器的设计

本文针对一类非线性、多时滞、干扰有界未知的离散系统进行H_∞模糊滤波器的设计.首先,利用T-S模糊模型来表达这个非线性、多时滞系统,并将建模误差,通过S-procedure,考虑到滤波器的设计中,建立基于T-S模糊模型的滤波器的存在条件,降低了滤波器设计的保守性.然后根据线性矩阵不等式(LMI)的性质将该模糊滤波器的设计转化为LMI的可行性问题,并采用凸优化技术的内点法求得LMI的可行解,设计出模糊滤波器.仿真结果表明,该方法是有效的.     

非线性反馈线性化方法在轮式移动机器人的应用

给出一种轮式移动机器人系统的受非完整约束的动态模型。基于此模型应用了非线性反馈精确线性化方法进行了机器人路径跟踪控制系统设计。经过输入输出反馈线性化后,系统实现了解耦和线性化,然后用配置极点的方法对变换后的线性系统进行了设计。仿真结果表明,用反馈线性化设计的机器人系统具有良好的性能。实验结果证明了上述方法的有效性。     

Partial decoupling in a class of nonlinear control systems

The letter treats a class of nonlinear control systems in state-space form. The problem considered is that of choosing two nonlinear feedback matrix functions F(x, t) and G(x, t) which decouple a candidate subset of the output set. The conditions under which this problem has a solution are derived and the procedure for computing the two nonlinear State feedback gain matrix functions required is given. An illustrative example is fully worked out.     

Robust H ∞ Control for a Class of 2-D Nonlinear Discrete Stochastic Systems

This paper is concerned with the problem of stability and robust H _∞ control for 2-D stochastic systems with parameter uncertainties and sector nonlinearities. The class of systems under investigation is described by the 2-D state-space Roesser model. Our attention is focused on the design of a state feedback controller for 2-D stochastic system with sector nonlinearity, such that the closed-loop 2-D stochastic system is asymptotically stable and has a prescribed H _∞ disturbance attenuation performance. First, a sufficient condition is established for the 2-D nonlinear stochastic systems to be asymptotically stable. Then, we extend the bounded real lemma for 2-D systems to 2-D stochastic systems with sector nonlinearities. Based on this lemma, solvability conditions for the H _∞ control of 2-D nonlinear stochastic systems in the form of LMIs (linear matrix inequalities) are derived. A numerical example illustrates the effectiveness of the proposed results.     

Joint Estimation of States and Parameters for an Input Nonlinear State-Space System with Colored Noise Using the Filtering Technique

This paper concerns the state and parameter estimation problem for an input nonlinear state-space system with colored noise. By using the data filtering and the over-parameterization technique, we transform the original nonlinear state-space system into two identification models with filtered states: one containing the system parameters and the other containing the noise model’s parameters. A combined state and parameter estimation algorithm is developed for identifying the state-space system. The key is that the estimation of system parameters uses the estimated states, and the estimation of states uses the preceding parameter estimates. A simulation example is provided to show that the proposed algorithm can work well.     

Nonlinear Feedback Control of a Bearingless Brushless DC Motor

The demands on bearingless drive configurations concerning performance as well as costs are high. The proposed bearingless brushless dc motor consists of five concentrated coils in a symmetrical arrangement, which generate radial forces and motor torque simultaneously in interaction with a permanent-magnet-excited disk-shaped rotor. Additionally, tilting deflection and the axial position of the rotor are stabilized passively by means of magnetic reluctance forces. Thus, system costs can be reduced significantly compared to a conventional bearingless motor setup, which actively stabilizes all 6 DOF. Due to the nonlinearity of the plant, the use of linear control design methods alone is not suitable for achieving a high operation performance. This paper introduces a novel radial position and motor torque control algorithm for a bearingless brushless dc motor based on the theory of feedback linearization. Thereby, the combined model of translatory and rotatory dynamics can be split into independent linear systems by means of a nonlinear change of system coordinates and a static-state feedback. Experimental results demonstrate the effectiveness of the proposed approach.      

Calculation of linear and nonlinear intersubband optical absorptions in a quantum well model with an applied electric field

Analytic forms of the linear and the third-order nonlinear optical intersubband absorption coefficients are obtained for general asymmetric quantum well systems using the density matrix formalism, taking into account the intrasubband relaxation. Based on this model, we calculate the electric field dependence of the linear and the third-order nonlinear intersubband optical absorption coefficients of a semiconductor quantum well. The energy of the peak optical intersubband absorption is around 100 meV (wavelength is 12.4 μm). Thus, electrooptical modulators and photodetectors in the infrared regime can be built based on the physical mechanisms discussed here. The contributors to the nonlinear absorption coefficient due to the electric field include 1) the matrix element variation and 2) the energy shifts. Numerical results are illustrated.     

An efficient dynamical model of reluctance actuators with flux fringing and magnetic hysteresis

This paper presents an efficient and accurate dynamical model of reluctance actuators, suitable for prediction and control applications. It is a hybrid lumped-parameter state-space model that takes into account the mechanical and electromagnetic dynamics, including eddy currents, flux fringing, magnetic hysteresis and saturation. Special emphasis is placed on the hysteresis model, which is based on the Jiles–Atherton theory. The novel parts of the model – the gap reluctance expression and the modified Jiles–Atherton hysteresis model – are identified, showing that the simulated results fit very well the experimental data. Furthermore, its potential application for control is exemplified with a feedback strategy, in which the design of the controller and observer are based on the proposed dynamical model.     

Contouring control of biaxial systems based on polar coordinates

A contouring controller for biaxial systems that integrates the effects of feedback, feedforward, and cross-coupled control is proposed in this study. Conventional approaches to contouring control suffer from the complicated contour-error model and from lack of a systematic way for controller design. The integrated controller is based on polar coordinates under which a relatively simple contour-error model can be obtained. Taking the simple contour error as a state variable, the contouring-control problem is transformed into a stabilization problem. The feedback-linearization technique incorporated with linear feedback or robust control (such as sliding-mode control) can then yield the integrated controller. The proposed method is verified both numerically and experimentally and is compared with the conventional approach. It is found that the proposed controller is better for high speed and/or noncircular contouring. In addition, it can be applied to either linear plants or nonlinear plants (like linear motors).     

Two's complement quantization in two-dimensional state-spacedigital filters

Two-dimensional (2-D) state-space digital filters are investigated for stability with and without quantization. A sufficient condition is obtained for the stability of the linear Fornasini-Marchesini (1976) state-space model. The same model is then studied for stability when implemented using two's complement truncation quantization, and a sufficient condition for asymptotic stability of the nonlinear filter is obtained. In the process, a theorem is proved which gives a sufficient condition for the stability of a one-dimensional (1-D) state-space digital filter under the same type of quantization