njit-etd2003-081 - New Jersey Institute of Technology
njit-etd2003-081 - New Jersey Institute of Technology njit-etd2003-081 - New Jersey Institute of Technology
95 3.13 System Identification Measuring the frequency response of a linear system is a typical first step in characterizing its dynamic behavior. To understand a system and its signal processing often demand information beyond the frequency response. Underlying differential and/or difference equations provide a concise mathematical description defining all other dynamic behavior. The task of estimating these equations from measurements of the input and output signals is referred to in the control literature as the process of System Identification (SID). In 1971 two Swedish researchers, Aström and Eykhoff, published a paper that started the field of System Identification (SID) [53]. Although many advances have been made in unifying the underlying theories, there continues to be a wide variety of approaches promoted in technical journals, textbooks, and conferences over three decades after the original paper. Figure 3.13 Examples of typical plant.
96 The bulk of the theory and applications of SID evolved from control systems research. In control language, the dynamic system being identified (or modeled) is called the plant. The plant can take on a wide variety of forms. In general, a plant is an object or collection of objects, producing an output by modifying an input. The input to the plant could be temperature, pressure, voltage, current, position, velocity, acceleration, and so on. The input can also contain more than one variable (e.g., several signals from transducers measuring various conditions of an engine). The output from the plant can be in the form of any of the inputs (temperature, pressure, position, etc.) and it also can contain several signals. Single-input, single-output (siso) plants are addressed here since they are the most prevalent. The siso models can be combined to create multi-input, multi-output models if necessary. Figure 3.13 depicts an example of an electrical plant. The plant can be accurately described mathematically by linear constant/coefficient, differential equations. A plant described by these equations is said to be Lumped-Linear-Time- Invariant (LLTI). Even plants that are mildly non-linear, slowly time varying, and possibly distributed in nature (e.g., those requiring partial differential equations for a full description) can often be adequately modeled using these LLTI assumptions. 3.13.1 Estimating Transfer Functions of Non -linear Systems Accurate transfer function estimation of linear, noise-free, dynamic systems is typically an easy task. Often, however, the system being analyzed is noisy or not perfectly linear. All real-world systems suffer from these deficiencies to a degree, but biological systems
- Page 73 and 74: 44 Two common types of time-frequen
- Page 75 and 76: 46 STFT: Short-Time Fourier Transfo
- Page 77 and 78: 48 3.3 The Analytic Signal and Inst
- Page 79 and 80: 50 The advantage of using equation
- Page 81 and 82: 52 3.5 Covariance and Invariance Th
- Page 83 and 84: where H(f), S(f) are Fourier transf
- Page 85 and 86: 56 Another shortcoming of the spect
- Page 87 and 88: 58 should take the kernel of the WD
- Page 89 and 90: 60 called the cross Wigner distribu
- Page 91 and 92: 62 3.6.3 The Choi-Williams (Exponen
- Page 93 and 94: 64 Figure 3.3 Performance of the Ch
- Page 95 and 96: 66 [-Ω,Ω ], then its STFT will be
- Page 97 and 98: 68 This condition forces that the w
- Page 99 and 100: 70 where c is a constant. Thus, the
- Page 101 and 102: Figure 3.5 The time-frequency plane
- Page 103 and 104: 74 The measure dadb used in the tra
- Page 105 and 106: 76 and the wavelet transform repres
- Page 107 and 108: 78 Figure 3.6 Figure depicting the
- Page 109 and 110: 80 The final step to obtain the pow
- Page 111 and 112: 82 It should be noted that if the w
- Page 113 and 114: 84 The normal respiration rate can
- Page 115 and 116: Figure 3.12 Power spectrum of BP II
- Page 117 and 118: RR similar manner to give: When com
- Page 119 and 120: 90 when there is significant correl
- Page 121 and 122: 92 3.12 Partial Coherence Analysis
- Page 123: 94 after removal of the effects of
- Page 127 and 128: 98 technique is measurement time. T
- Page 129 and 130: 100 usually attainable. The key poi
- Page 131 and 132: 102 variability exists in the propa
- Page 133 and 134: 104 eXogenous input (ARX) was used
- Page 135 and 136: 106 The baroreflex, an autonomic re
- Page 137 and 138: 108 the principal components are no
- Page 139 and 140: 110 The mathematical solution for t
- Page 141 and 142: 112 3.15 Cluster Analysis The term
- Page 143 and 144: 114 formed) one can read off the cr
- Page 145 and 146: 116 3.15.5 Squared Euclidian Distan
- Page 147 and 148: 118 Alternatively, one may use the
- Page 149 and 150: 120 Sneath and Sokal used the abbre
- Page 151 and 152: 122 may seem a bit confusing at fir
- Page 153 and 154: CHAPTER 4 METHODS The purpose of th
- Page 155 and 156: 126 4.1.2.1 Autonomic Testing. HR V
- Page 157 and 158: 128 of heart rate, blood pressure,
- Page 159 and 160: 130 The patients who underwent LVRS
- Page 161 and 162: 132 panel of the Correct.vi. It was
- Page 163 and 164: 134 4.2.3 Power Spectrum Analysis o
- Page 165 and 166: 136 weighted-average value of the c
- Page 167 and 168: 138 For each given scale a within t
- Page 169 and 170: 140 frequency F to the wavelet func
- Page 171 and 172: 142 4.2.8 System Identification Ana
- Page 173 and 174: 144 In this study a simpler approac
95<br />
3.13 System Identification<br />
Measuring the frequency response <strong>of</strong> a linear system is a typical first step in<br />
characterizing its dynamic behavior. To understand a system and its signal processing<br />
<strong>of</strong>ten demand information beyond the frequency response. Underlying differential<br />
and/or difference equations provide a concise mathematical description defining all<br />
other dynamic behavior. The task <strong>of</strong> estimating these equations from measurements <strong>of</strong><br />
the input and output signals is referred to in the control literature as the process <strong>of</strong><br />
System Identification (SID).<br />
In 1971 two Swedish researchers, Aström and Eykh<strong>of</strong>f, published a paper that<br />
started the field <strong>of</strong> System Identification (SID) [53]. Although many advances have<br />
been made in unifying the underlying theories, there continues to be a wide variety <strong>of</strong><br />
approaches promoted in technical journals, textbooks, and conferences over three<br />
decades after the original paper.<br />
Figure 3.13 Examples <strong>of</strong> typical plant.
Change language