Chapter 2 : Sensor characteristics Prof. Dehan Luo 第二章 传感器特性 第二章 传感器特性 Section One Transducers, sensors and measurements 变换器、传感器（敏感元件）、测量 Section Two Calibration, interfering and modifying inputs 标定、干扰、校正输入 Section Three Static sensor characteristics 传感器静态特性 Section Four Dynamic sensor characteristics 传感器动态特性 Intelligent Sensors System 2-1 School of Information Engineering

Chapter 2 : Sensor characteristics Prof. Dehan Luo Section One Transducers: sensors and actuators Transducer（变换器） A device that converts a signal from one physical form to a corresponding signal having a different physical form 将一种物理/物质信号转变为相应的另一种物理/物质信号的装置（器件） Physical form: mechanical, thermal, magnetic, electric, optical, chemical… （物理/物质量形式：机械、热、磁、电、光、化学…） Transducers are ENERGY CONVERTERS or MODIFIERS （变换器是一种能量转换器） Intelligent Sensors System 2-2 School of Information Engineering

Chapter 2 : Sensor characteristics Prof. Dehan Luo Transducers: sensors and actuators Sensor A device that receives and responds to a signal or stimulus 接收和响应信号或激励的装置（器件） This is a broader concept that includes the extension of our perception capabilities to acquire information about physical quantities Sensor: an input transducer (i.e., a microphone)（变换器输入） Actuator: an output transducer (i.e., a loudspeaker)（变换器输出） Intelligent Sensors System 2-3 School of Information Engineering

Chapter 2 : Sensor characteristics Prof. Dehan Luo Measurements A simple instrument model A observable variable X is obtained from the measurand（被测对象） X is related to the measurand in some KNOWN way （已知方法） (i.e., Measuring mass) The sensor generates a signal variable that can be manipulated（操纵）: Processed（处理）, transmitted（传输） or displayed（显示） In the example above the signal is passed to a display, where a measurement can be taken Intelligent Sensors System 2-4 School of Information Engineering

Chapter 2 : Sensor characteristics Prof. Dehan Luo Measurements Measurement The process of comparing an unknown quantity with a standard of the same quantity (measuring length) or standards of two or more related quantities (measuring velocity) 测量---一个未知量与其相同的标准量（长度测量）比较过程，或是与多个相关的标准量（速度测量）进行比较的过程 Intelligent Sensors System 2-5 School of Information Engineering

Section Two Calibration Chapter 2 : Sensor characteristics Prof. Dehan Luo Section Two Calibration The relationship between the physical measurement variable (X) and the signal variable ( Y) A sensor or instrument is calibrated by applying a number of KNOWN physical inputs and recording the response of the system Intelligent Sensors System 2-6 School of Information Engineering 传感器或仪器是通过实际输入和系统响应数据进行标定

Chapter 2 : Sensor characteristics Prof. Dehan Luo Additional inputs（附加输入） Interfering inputs (Y) Those that the sensor to respond as the linear superposition（线线叠加） with the measurand variable X Linear superposition assumption: S(aX+bY)=aS(X)+bS(Y) Modifying inputs (Z)（校正输入） Those that change the behavior of the sensor and, hence, the calibration curve Temperature is a typical modifying input Intelligent Sensors System 2-7 School of Information Engineering

Chapter 2 : Sensor characteristics Prof. Dehan Luo Section Three Static characteristics（静态特性） The properties of the system after all transient effects have settled to their final or steady state（瞬态响应结束后，系统特性处于最终和稳定状态） Accuracy（精确性、正确度） Discrimination（分辨率） Precision（精密度，精度） Errors、 Drift、 Sensitivity（误差、漂移、灵敏度） Linearity、 Hysteresis (backslash)（线性、滞后/回差） Dynamic characteristics（动态特性） The properties of the system transient response to an input 系统瞬时响应特性 Zero order systems（零阶系统） First order systems（一阶系统） Second order systems （二阶系统） Intelligent Sensors System 2-8 School of Information Engineering

Chapter 2 : Sensor characteristics Prof. Dehan Luo Accuracy, discrimination Accuracy is the capacity of a measuring instrument to give RESULTS close to the TRUE VALUE of the measured quantity （精确度是仪器给出测量结果与测量真值接近程度的能力） Accuracy is related to the bias of a set of measurements。 Accuracy is measured by the absolute and relative errors（精确度由绝对误差和相对误差来计算） ABSOLUTE ERROR= RESULT—TRUE VALUE RELATIVE ERROR = ABSOLUTE ERROR / TRUE VALUE Discrimination is the minimal change of the input necessary to produce a detectable change at the output（能够产生输出变化的最小输入变化量) Discrimination is also known as RESOLUTION When the increment is from zero, it is called THRESHOLD(门坎/域值） Intelligent Sensors System 2-9 School of Information Engineering

Chapter 2 : Sensor characteristics Prof. Dehan Luo Precision The capacity of a measuring instrument to give the same reading when repetitive measuring the same quantity under the same prescribed conditions（精密度指测量仪器在相同条件下重复测量同一个量时给出相同读数的能力） Precision implies agreement between successive readings, NOT closeness to the true value（精密度指连续读数之间的一致性而不是指与真值的接近程度） Precision is related to the variance（不一致） of a set of measurements Precision is a necessary but not sufficient condition for accuracy（精密 度是准确度的必要条件但不是充分条件） Two terms closely related to precision（与精密度相关的两个术语） Repeatability (可重复性） The precision of a set of measurements taken over a short time interval （短时间间隔测量数据的精密度） Reproducibility（可复现性） The precision of a set of measurements BUT taken over a long time interval or performed by different operators or with different instruments or in different laboratories（长时间间隔测量数据或由不同操作者测量的数据或在不 同实验室测量的数据或用不同仪器测量的数据的精密度） Intelligent Sensors System 2-10 School of Information Engineering

Chapter 2 : Sensor characteristics Prof. Dehan Luo Example Shooting darts（投标枪） Discrimination The size of the hole produced by a dart Which shooter is more accurate?（哪个射手更准确？） Which shooter is more precise?（哪个射手更精密？） Intelligent Sensors System 2-11 School of Information Engineering 平均值

Chapter 2 : Sensor characteristics Prof. Dehan Luo Accuracy and errors Systematic errors（系统误差） Result from a variety of factors（产生的因素） 1 Interfering（干扰）or modifying variables (i.e., temperature) 2 Drift （漂移）(i.e., changes in chemical structure or mechanical stresses) 3 The measurement process changes the measurand (i.e., loading errors负载 误差) 4 The transmission process changes the signal (i.e., attenuation 衰减）) 5 Human observers (i.e., parallax（视差） errors) Systematic errors can be corrected with COMPENSATION methods (i.e., feedback, filtering)（系统误差可用补偿方法校正） Intelligent Sensors System 2-12 School of Information Engineering

Chapter 2 : Sensor characteristics Prof. Dehan Luo Accuracy and errors Random errors（随机误差） Also called NOISE（噪声）: a signal that carries no information（不载有信息的信号） True random errors (white noise白噪声) follow a Gaussian distribution（高斯分布） Sources of randomness（随机误差源） 1 Repeatability of the measurand itself (i.e., height of a rough surface) 2 Environmental noise（环境噪声） (i.e., background noise picked by a microphone) 3 Transmission noise （传输噪声）(i.e., 60Hz) 4 Signal to noise ratio (SNR) （信噪比）should be >>1 With knowledge of the signal characteristics it may be possible to interpret a signal with a low SNR (i.e., understanding speech in a loud environment) Intelligent Sensors System 2-13 School of Information Engineering

Chapter 2 : Sensor characteristics Prof. Dehan Luo Example: systematic and random errors Systematic error (Bias) Random error (Precision) Intelligent Sensors System 2-14 School of Information Engineering

Chapter 2 : Sensor characteristics Prof. Dehan Luo More static characteristics Input range（输入范围） The maximum and minimum value of the physical variable that can be measured (i.e., -40F/100F in a thermometer)(F—degree of Fahrenheit) (C—celsius) (能被测量的实际变量最大与最小值） Output range（输出范围） can be defined similarly Sensitivity（灵敏度） The slope（ 斜率）of the calibration curve y=f(x) An ideal sensor will have a large and constant（不变的） sensitivity Sensitivity-related errors: saturation（饱和） and “dead-bands（死区）” Linearity（线性度） The closeness of the calibration curve to a specified straight line (i.e., theoretical behavior, least-squares fit)标定曲线与给定直线（例如：理 论直线、最小二乘方直线等） Intelligent Sensors System 2-15 School of Information Engineering

Chapter 2 : Sensor characteristics Prof. Dehan Luo More static characteristics Monotonicity（单调性） A monotonic curve is one in which the dependent variable always increases or decreases as the independent variable increases or decreases(单调曲线是指相关/输出变量随独立/输入变量增加而增加或减小而减小） Hysteresis（滞后、磁滞） The difference between two output values that correspond to the same input depending on the trajectory（轨迹） followed by the sensor (i.e., magnetization in ferromagnetic materials)（对应同一个相 同输入的两个输出值之差，如铁磁材料中的磁化） Hysteresis caused by looseness（松动） in a mechanical joint (滞后由机械联结松动而引起） Intelligent Sensors System 2-16 School of Information Engineering

Chapter 2 : Sensor characteristics Prof. Dehan Luo Section Four Dynamic characteristics（动态特性） The sensor response to a variable input is different from that exhibited when the input signals are constant (the latter is described by the static characteristics（传感器对变量输入的响应不同于对 常量输入的响应） The reason for dynamic characteristics is the presence of energy-storing elements（动态特性的机理是能量存储元件的作用） Inertial （惯性元件） : masses, inductances（质量、电感） Capacitances （容性/阻尼元件） : electrical, thermal（电的、热的） Dynamic characteristics are determined by analyzing the response of the sensor to a family of variable input waveforms:（动态特性是通过分析传 感器对一系列输入信号波形的响应来确定） Intelligent Sensors System 2-17 School of Information Engineering White noise 白噪声 Sinusoidal 正弦 Ramp斜坡 Impulse脉冲 Step阶跃

Chapter 2 : Sensor characteristics Prof. Dehan Luo Dynamic models The dynamic response of the sensor is (typically) assumed to be linear Therefore, it can be modeled by a constant-coefficient linear differential Equation（传感器动态响应假设是线性的，因此，它可用常系数线性差分方程模型描述） In practice, these models are confined to zero, first and second order. Higher order models are rarely applied模型限制为零阶、一阶和二阶，高阶很少应用 These dynamic models are typically analyzed with the Laplace transform（拉普拉斯变换）, which converts the differential equation（微分方程） into a polynomial expression（多项式表达） Think of the Laplace domain as an extension of the Fourier transform（富里叶变换） Fourier analysis is restricted to sinusoidal signals x(t) = sin(wt) = e-j wt Laplace analysis can also handle exponential behavior x(t) = e-ót sin(wt) = e-(ó +jw)t Intelligent Sensors System 2-18 School of Information Engineering

Chapter 2 : Sensor characteristics Prof. Dehan Luo The Laplace Transform (review) The Laplace transform of a time signal y(t) is denoted (表示）by L[y(t)] = Y(s) The s variable is a complex （复数）number s=ó+jw The real（实数） component ó defines the real exponential behavior The imaginary（虚数） component defines the frequency of oscillatory behavior（震荡特性频率） The fundamental relationship is the one that concerns （涉及）the transformation of differentiation Other useful relationships are Intelligent Sensors System 2-19 School of Information Engineering

Chapter 2 : Sensor characteristics Prof. Dehan Luo The Laplace Transform (review) Applying the Laplace transform to the sensor model yields G(s) is called the transfer function （传递函授数） of the sensor The position of the poles of G(s) -zeros of the denominator- in the s-plane determines the dynamic behavior of the sensor such as （在S平面内，分母零极点位置决定了传感器动态性能，如） Oscillating components （振荡参数） Exponential decays（指数衰减） Instability（不稳定性） Intelligent Sensors System 2-20 School of Information Engineering

Chapter 2: Sensor characteristics Prof. Dehan Luo Pole location and dynamic behavior（极点位置与动态特性） Intelligent Sensors System 2-21 School of Information Engineering

Chapter 2: Sensor characteristics Prof. Dehan Luo Zero-order sensors(零阶传感器） Input and output are related by an equation of the type （1） Zero-order is the desirable response of a sensor No delays（无延迟） Infinite bandwidth（无限带宽） The sensor only changes the amplitude of the input signal （2）Zero-order systems do not include energy-storing elements （3）Example of a zero-order sensor（零阶传感器举例） A potentiometer used to measure linear and rotary displacements（用于测量线性位移和旋转位移的点位器） This model would not work for fast-varying displacements （该模型不适宜测量快速变化的位移） Intelligent Sensors System 2-22 School of Information Engineering

Chapter 2: Sensor characteristics Prof. Dehan Luo First-order sensors (一阶传感器） Inputs and outputs related by a first-order differential equation（一阶微分方程的输入/输出关系） 1 First-order sensors have one element that stores energy （一个储能元件） 2 Step response（阶跃响应） A is the amplitude of the step k （=1/a0） is the static gain, which determines the static response τ (=a1/a0) is the time constant, which determines the dynamic response（ τ 是决定动态响应的时间常数） 3 Ramp response（斜坡响应） 4 Frequency response（频率响应） Better described by the amplitude and phase shift plots Intelligent Sensors System 2-23 School of Information Engineering

Chapter 2: Sensor characteristics Prof. Dehan Luo First-order sensor response Intelligent Sensors System 2-24 School of Information Engineering

Chapter 2: Sensor characteristics Prof. Dehan Luo Example of a first-order sensor（一阶传感器举例） Intelligent Sensors System 2-25 School of Information Engineering

Chapter 2: Sensor characteristics Prof. Dehan Luo Second-order sensors（二阶传感器） Inputs and outputs are related by a second-order differential equation（二阶微分方程输入/输出关系） We can express this second-order transfer function as Where k is the static gain ξ is known as the damping coefficient ωn is known as the natural frequency Intelligent Sensors System 2-26 School of Information Engineering

Chapter 2: Sensor characteristics Prof. Dehan Luo Second-order response(二阶系统响应） 1 Step response（ 阶跃响应） Response types（响应类型） Under damped (ξ <1 欠阻尼） Critically damped (ξ =1 临界阻尼） Over damped (ξ >1 过阻尼） Response parameters（响应参数） Rise time (tr 上升时间) Peak overshoot (Mp 超调量) Time to peak (tp 超调时间) Settling time (ts 稳定时间) Intelligent Sensors System 2-27 School of Information Engineering

Chapter 2: Sensor characteristics Prof. Dehan Luo Second-order response (cont.) 2 Ramp response（斜坡响应） 3 Frequency response（频率响应） Intelligent Sensors System 2-28 School of Information Engineering

Chapter 2: Sensor characteristics Prof. Dehan Luo Example of second-order sensors(二阶传感器举例） Spring-mass-dampen accelerometer（弹簧—-质量—阻尼加速度计） The armature（电枢） suffers an acceleration We will assume（假设） that this acceleration is orthogonal（直角） to the direction of gravity X0 is the displacement of the mass M with respect to the armature(相关于电枢） The equilibrium equation is（平衡方程是）: Intelligent Sensors System 2-29 School of Information Engineering

Chapter 2: Sensor characteristics Prof. Dehan Luo References [1] R. Pallas-Areny and J. G. Webster, 1991, Sensors and Signal Conditioning, Wiley, New York [2] J. G. Webster, 1999, The Measurement, Instrumentation and Sensors Handbook, CRC/IEEE Press , Boca Raton, FL. [3] H. R. Taylor, 1997, Data Acquisition for Sensor Systems, Chapman and Hall, London, UK. [4] J. Fraden, 1997, Handbook of Modern Sensors. Physics, Designs and Applications, AIP, Woodbury, NY [5] J. Brignell and N. White, 1996, Intelligent Sensor Systems, 2nd Ed., IOP, Bristol, UK   Intelligent Sensors System 2-30 School of Information Engineering