基于脉冲响应的参数辨识.ppt

Chapter 8 Parameter Identification By Impulse and Pulse Response,Li Shaoyuan E-mail: ,IMPULSE RESPONSE,Basic Principles,The main strategy of impulse-response identification is to obtain process transfer function models directly from experimental impulse-response data.,There is a direct relationship between a systems transfer function and the moments of its theoretical impulse response.,One major disadvantage: the impulse function is difficult to implement in practice.,General Theory,By definition of the Laplace transform of a function, therefore:,Now, the power series expansion for e-st:,it becomes:,Identification of Simple Model Forms,The procedure, using the impulse-response approach, is now summarized.,1. Experimentally obtain the systems impulse response. 2. From the impulse-response data, calculate the normalized moments 3. Postulate an approximate transfer function model. 4. Estimate the unknown parameters in the postulated, transfer function model by relating the transfer function to the moments.,First-Order Model,Second-Order Model,Second-Order-Plus-Single-Zero Model,First -Order-Plus-Time-Delay Model,Obtaining Moments From Experimental Data,Experimental impulse-response data are usually obtained at discrete points in time, usually at equally spaced time intervals. The integral will have to be approximated by quadratures or other efficient numerical integration schemes.,Impulse-response Data From Other Responses,In practice, it may not always be possible to implement an input function that is close enough to an ideal impulse;,From Experimental Step-Response Data,From Arbitrary Input/Output Data,For each observed experimental data point we may now write, using this expression:,which may be written together as:,Frequency Identification From Pulse Response,single output process is:,and since the frequency response can be obtained by setting s = j we have:,where U(j); and Y(j), are, respectively, the Fourier transformations of the input and output pulse test data, i.e.:,Frequency Response,where, for the output:,and, for the input,Frequency Spectra,analyze the input and output data for their “frequency content,” by inspecting the magnitudes of the functions U(j) and Y(j) at various frequencies.,for the input:,and for the output:,Frequency Spectra of a Pulse Signal,Identification for Self-Regulating Processes,Simulation Examples,the noise-to-signal ratio (NSR), defined as,Example 1. Consider a monotonic process given by,Nyquist plot and estimated under noise,Example 2. Consider a high order process,.,Nyquist plot and estimated under noise,Example 3. Consider a nonminimum-phase plus dead-time process,Nyquist plot and estimated under noise,Example 4. Consider an integrating process,.,Nyquist plot and estimated under noise,Transfer function modeling,second-order plus dead-time model is adopted, shown as,.,using the linear least-squares method and the solution is,The original model parameters a, b and c,Example 5: Lets take the high order process in Example 2 with no