Sliding-Mode Control of a High-Speed Linear Axis Driven by Pneumatic Muscle Actuators

This paper presents a cascaded sliding-mode (SM) control scheme for a new pneumatic linear axis which could be seen as alternative to an electric direct linear drive. Its guided carriage is driven by a nonlinear mechanism consisting of a rocker with an antagonistic pair of pneumatic muscle actuators arranged at both sides. This innovative drive concept allows for both an increased workspace of approximately 1 m as well as higher carriage velocities of approximately 1.3 m/s as compared to a direct actuation. Modeling of the muscle-driven positioning system leads to a system of four nonlinear differential equations including polynomial approximations of the volume characteristic as well as the force characteristic of the pneumatic muscles. The differential flatness of the system is exploited in combination with SM techniques to stabilize the error dynamics in view of unmodeled dynamics. The internal pressure of each pneumatic muscle is controlled by a fast underlying control loop. Hence, the control design for the outer control loop can be simplified by considering these controlled muscle pressures as ideal control inputs. The control design of the outer control loop involves a decoupling of rocker angle as well as mean internal pressure of both pneumatic muscles as flat outputs. Additionally, model uncertainties in the equation of motion like nonlinear friction are directly counteracted by an observer-based disturbance compensation which reduces the chattering problem. Experimental results show an excellent control performance that outperforms alternative control approaches in a comparison.      

Phase-Locked Loops with Limiter Phase Detectors in the Presence of Noise

A nonlinear mathematical model of phase-locked loops with limiter phase detectors in the presence of noise is presented. The model, which is an extension of the well-known baseband model of loops with sinusoidal phase detectors without limiters, incorporates a modified nonlinear phase detector characteristic, the form of which is changed if the input carrier-to-noise ratio alters, as well as a modified phase noise as an input to the model. Both the modified phase detector characteristic and the spectral density of the modified noise term are calculated specifically for sinusoidal, triangular, and sawtooth types of limiter phase detectors, allowing the application of various methods to determine the loop noise performance. As an example, the phase error variance of a first-order phase-locked loop is calculated, thereby showing a strong dependence on the specific phase detector realization.     

Transient Mean and Variance of Phase Error of the First-Order Phase-Locked Loop

Based on the Fokker-Planck techniques, the time-dependent mean and variance of phase error of the first-order phase-locked loop in the presence of white Gaussian noise have been obtained via stochastic differential equations. The steady-state variance reduced from the transient case is simple in its form and agrees closely with the previous results obtained by different approaches.     

Transient analysis of the second-order phase-locked loop in the presence of noise (Corresp.)

The time-dependent probability-density function (pdf) of the state vector for the second-order phase-locked loop (PLL) is shown to be determined by an orthogonal function expansion. The expansion coefficients are the solutions to infinite dimensional ordinary differential equations, which are derived by Ito's stochastic calculus. Numerical solutions can be obtained by truncating them. It is also shown that certain parameters which characterize the distribution of a random variable on a circle, such as phase error, can be expressed by only one coefficient of the Fourier series of its pdf.     

Control of the cryosurgical process in nonideal materials

A study of a controlled cryosurgical process is presented. This study is based on the energy equations describing the probe response and the phase change occurring in the medium. First-order nonlinear differential equations (state equations) are obtained by applying the integral-solution method. In order to obtain maximal cell destruction, it is desired to control a specific cooling rate at the solid-liquid interface. This cooling rate defines the desired trajectories of the state variables through the state equations. In order to satisfy the cooling rate condition on the freezing front, a closed-loop is designed to control the probe temperature program. A simple analysis of the system stability employed linearization at several points along the desired trajectories. Ranges of stability were obtained for a system containing a proportional-integral controller. It was demonstrated that these stability ranges depend mainly on the selected sampling time of the discrete control loop and that the phase-change process does not significantly affect the stability results. A complete study of the nonlinear equations was performed by a computer simulation program which enables the selection of the final values of the controller parameters, in order to minimize the error and to ensure stability. In addition, the simulation program gives information about the effects of the A/D and D/A converters accuracy on the performance of the control loop. An A/D converter accuracy of 12 bits was found necessary in order to reduce the oscillations in probe temperature to acceptable values. The simulation also yields a complete calculated temperature field in the tissue during the controlled process. From these simulated results it can be seen that oscillations of +/- 0.5 degrees C in the desired probe temperature do not significantly affect the desired cooling rate at the freezing front. An initial overshoot of 1.5 degrees C in the desired probe temperature was obtained both experimentally and theoretically from the simulation. When this initial overshoot occurs at the beginning of the freezing process, it causes an error in freezing front velocity and consequently in ice-front position. From the numerical simulation, it can be deduced that the cooling rate obtained at the front deviates from the desired value by approximately 1%. The probe-temperature error increases at two instants: a) during the super-cooling effect and the subsequent sudden crystallization, and b) when the probe temperature is below -80 degrees C and unstable boiling of the cooling medium causes oscillations.     

Costas circuit under the action of additive harmonic interferences and wideband noise

The Markovian mathematical model of the Kostas phase-locked loop subjected to the simultaneous actions of additive harmonic interferences and a white Gaussian noise, which are described by stochastic differential equations involving the influence of the low-pass filters of the control loop on the useful pulsed signal shape, is discussed. The statistical characteristics of the error signal are analyzed in the linear approximation.     

可自适应调节带宽的新型非线性二阶锁相环

大捕获带宽的同步给传统二阶锁相环带来了巨大挑战。文中针对传统锁相环捕获带宽与抑制噪声能力两者之间的矛盾,提出一种耦合非线性环节的新型二阶锁相环,利用非线性模块自适应调整环路噪声带宽。输入输出相位误差较大时利用较大的带宽迅速减小频偏;当相位误差由于环路控制作用而减小时,利用较小的带宽抑制噪声以提高跟踪精度。仿真结果表明,非线性二阶锁相环跟踪速度显著提高,且相比传统二阶锁相环,捕获带宽从4 kHz最大提高到18.8 kHz。     

Phase-lock-loop statistics without recourse to Fokker-Planck techniques

To obtain the steady-state probability distribution of the phase error for a phase-lock loop driven by the sum of modulated carrier and narrowband stationary noise, a familiarity with Fokker-Planck techniques is usually a prerequisite to formulate a differential equation that has the required distribution as its solution. Here a simpler treatment is offered, which uses the more standard tools of probability theory. The distribution of the frequency error is also considered.     

Signal integrity analysis on a microstrip ultra-wideband coupled-line coupler

In this paper, a compact, single-section, Ultra-wideband (UWB) coupled-line coupler designed using concentric loop in the signal plane and defect in the ground plane is presented. Bandwidth enhancement is achieved with low coupling at the X-band satellite downlink range to improve the signal strength for defence applications. Return loss greater than 15 dB and isolation greater than 20 dB is achieved over the entire UWB band. The prototype is fabricated and tested to validate the simulation results. Further to detect the quality of the output signal, signal integrity analysis is performed and metrics such as error vector magnitude (EVM), magnitude and phase error, eye pattern, constellation plots and signal to noise ratio are presented for the proposed UWB coupled-line coupler.     

Compensation improvement of DPSK signal with nonlinear phase noise

When nonlinear phase noise is compensated by the received intensity, simple formulas are derived for the error probability of differential phase-shift keying signals. Simulation is conducted to verify the error probability. The tolerance of nonlinear phase noise is doubled by the compensator, allowing doubling of the transmission distance if nonlinear phase noise is the dominant impairment.     

Performance degradation of phase-modulated systems due to nonlinear phase noise

The error probability is calculated for phase-modulated systems with nonlinear phase noise. Using the assumption that the phase of amplifier noise and nonlinear phase noise are independent of each other, the error probability and penalty are calculated for both phase-shift keying (PSK) and differential phase-shift keying (DPSK) systems. The mean nonlinear phase shift must be less than about 1.00 and 0.63 rad for a penalty less than 1 dB for PSK and DPSK systems, respectively.     

Chaotic electronic oscillator from single amplifier biquad

The present letter reports a simple chaotic electronic oscillator. A single amplifier biquad (SAB) based active high-Q Band Pass Filter (BPF) is converted into a chaotic oscillator by introducing a single passive nonlinear element in the form of a general purpose pn junction diode, and a storage element in the form of an inductor. The chaotic circuit is mathematically modeled, which is a set of four coupled first-order autonomous nonlinear differential equations. The behavior of the proposed circuit is investigated through numerical simulations and electronic hardware experiments. It is found that the circuit shows complex behaviors, like, bifurcations and chaos, for a certain range of circuit parameters. The chaotic behavior of the circuit is ensured qualitatively by bifurcation diagram, phase plane plot and experimentally obtained power spectrum, and quantitatively by Lyapunov exponents and Kaplan–York dimensions.     

应用逆算子方法定量分析线性缓变p－n结

逆算子方法是一类新的求解强非线性问题的非数值方法．本文采用此类方法分析线性缓变ｐ－ｎ结．先把分析问题表述为一维非线性Ｐｏｉｓｓｏｎ方程，再应用逆算子方法求解该强非线性常微分方程，并采用Ｍａｔｈｅｍａｔｉｃａ软件推导其近似解析解，还对求得的近似解作了误差分析研究．模拟计算结果较为精确、可靠，基本上实现了线性缓变ｐ－ｎ结的定量分析，有助于更深入地定量研究ｐ－ｎ结的物理机理．此项研究表明，逆算子方法具有一定的优越性，它将为半导体器件的数值分析开辟一条新的途径．     

The vibration error of the fiber-optic gyroscope rotation rate and methods of its suppression

The error of the fiber-optic gyroscope (FOG) rotation rate measurement is considered. This error is induced by FOG vibrations (for open- and closed-loop FOGs). For a closed-loop FOG, a differential equation describing the loop dynamics is derived. The coefficients of this equation contain terms varying in time with the vibration frequency. For the first time, it is shown that, in addition to the traditional rotation rate measurement error due to the superimposition of vibration-induced optical power oscillations and the phase difference in the FOG coil, there is one more error, which is due to vibration modulation of the loop bandwidth. Alternative methods of information processing are investigated, and, on the basis of them, a new circuit is proposed for the suppression of vibration errors.     

用于锁相环快速锁定的鉴频鉴相器设计

针对鉴频鉴相器(PFD)的盲区现象对锁相环路的锁定速度的影响,设计了一种PFD结构,可以实现锁相环路的快速锁定。该结构在传统PFD的基础上,利用内部信号的逻辑关系进行逻辑控制,其输出特性呈现非线性;在输入相位差大于π时,抑制了复位脉冲的产生,避免了输入时钟边沿的丢失,有效消除了盲区,加快了锁相环的锁定速度。设计采用SMIC 0.18μm标准CMOS工艺,采用全定制设计方法对该PFD结构进行了设计、仿真分析和验证。结果表明,采用该PFD结构的锁相环,在400 MHz工作频率下锁定时间为2.95μs,锁定速度提高了34.27%。     

面向数控锁相环的一种非线性动态带宽调整算法

传统的锁相环常采用动态带宽调整算法,由于鉴相器输出的相位误差和反馈时钟频率为非线性关系,动态带宽调整算法常引入错误调节。因此本文面向数控锁相环,提出了一种非线性动态带宽调整方法,较小鉴相误差只有多次出现后才调整数控锁相环带宽,避免了不必要的带宽调整。为了验证提出的算法,本文开发了数控锁相环的Matlab行为级模型,其仿真结果表明其锁定时间下降到原方法的28.6% ~ 85.7%。论文证明了合适的非线性控制算法更有利于降低锁定时间。     

Experimental investigation of a modified NOLM for phase-encoded signal regeneration

We experimentally investigate the amplitude and phase transfer characteristics of a modified nonlinear optical loop mirror (NOLM) with a directional attenuator (DA-NOLM) optimized for differential phase-shift keying signal regeneration. The results show that the phase relation is preserved in the setup and thus the DA-NOLM is suitable for amplitude regeneration of phase-shift-keyed signals.     

差分环形振动器的相位噪声与时间抖动研究

基于差分环形振荡器的相位噪声理论,详细介绍了相位噪声、时间抖动的定义,提出了相位噪声的计算公式,并推导了由相位噪声到时间抖动的换算公式。实施了Matlab和Spectre联合仿真,结果验证了计算公式的准确性。相位噪声在环路带宽外的计算值与Spectre仿真值的绝对误差不超过2.35 dB;时间周期抖动计算值与Spectre仿真值的绝对误差为1.847 ps,可对低相位噪声的差分环形振荡器设计提供参考和指导。     

二阶锁相环非线性捕获和非线性跟踪性能研究

采用MATLAB软件,编制了求解描述二阶PLL非线性捕获的二阶非线性微分方程的程序,计算机自动绘制了相轨迹和时间响应图;求出了二阶PLL的捕获带随初始相差的变化关系曲线.     

光电跟踪转台伺服控制策略研究

针对高性能光电跟踪转台负载重、摩擦大、跟踪精度要求高等特点,提出了基于复合控制的伺服控制策略,速度环路设计了带有扰动观测器的线性二次最优反馈控制器,并在前向通道增加了零相位误差跟踪控制器(ZPETC),提高速度环的跟踪性能,位置环采用非线性PID反馈控制方式降低超调,提高稳态精度;将低速率的位置给定信息分别进行插值细分和滤波,通过高增益微分器和卡尔曼预测滤波,对转台速度和加速度进行预测和估计,进行前馈实现复合控制,实践证明,这种策略可以有效提高大加速度下的跟踪精度。