lecture08过程控制讲义8.ppt

* Chapter 7 Development of Empirical Models From Process Data In some situations it is not feasible to develop a theoretical  (physically-based model) due to: 1. Lack of information 2. Model complexity 3. Engineering effort required. An attractive alternative: Develop an empirical dynamic model from input-output data. Advantage: less effort is required Disadvantage: the model is only valid (at best) for the range of data used in its development. i.e., empirical models usually don’t extrapolate very well. Chapter 7 Fitting First and Second-Order Models Using Step Tests Simple transfer function models can be obtained graphically from step response data. A plot of the output response of a process to a step change in input is sometimes referred to as a process reaction curve. If the process of interest can be approximated by a first- or second-order linear model, the model parameters can be obtained by inspection of the process reaction curve. The response of a first-order model, Y(s)/U(s)=K/(ts+1), to  a step change of magnitude M is: Chapter 7 The initial slope is given by: The gain can be calculated from the steady-state changes in u and y: Chapter 7 Figure 7.3 Step response of a first-order system and graphical constructions used to estimate the time constant, 2. The line drawn tangent to the response at maximum slope (t = ?) intersects the y/KM=1 line at (t = ? ? ? ). 3. The step response is essentially complete at t=5t.  In other words, the settling time is ts=5t. 1. The response attains 63.2% of its final response at time, t = ???. First-Order Plus Time Delay Model For this FOPTD model, we note the following charac-teristics of its step response: Chapter 7 Chapter 7 Figure 7.5 Graphical analysis of the process reaction curve to obtain parameters of a first-order plus time delay model. Chapter 7 There are two generally accepted graphical techniques for determining model parameters ?, ?, and K. Method 1: