טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentAlbersheim Nir
SubjectRobust Identification for Auto Tuning of Decentralized
Dead Time Compensators for Multi Variables Systems
DepartmentDepartment of Mechanical Engineering
Supervisor Professor Emeritus Zalman Palmor


Abstract


 
This research represents the second phase of an R&D project whose goal was to develop an auto-tuner (AT) for decentralized Dead Time Compensator (DTC) for Multiple Inputs Multiple Outputs (MIMO) open loop stable systems.

II

 
An automatic identification algorithm for a transfer matrix each element of which can be modeled as a first or second order transfer function with dead times (DTs) has been developed. Such models are suitable for describing the majority of the systems in the process industries. The proposed algorithm consists of three stages. In the first stage the system is stimulated around the operating-point. The novel method, developed here, contains two feedback loops. The inner loop consists of the process and a known existing conventional controller and is kept close throughout the identification procedure. The outer loop contains a decentralized relay controller that forces sequentially a single cycle in each loop at its most significant frequency for identification. The outputs and the inputs of the inner loop are sampled during the excitation procedure. In the second stage these signals are converted using a Fast Fourier Transform (FFT) and the close loop frequency response matrix of the inner loop is obtained. As the transfer matrix of the inner loop controller is known the frequency response matrix of the process is calculated. The algorithm is equipped with means to avoid computational singularities. In the third and final stage of the identification process the algorithm fits four parameters of a second order model with a DT to each element of the frequency response matrix (a total of 4n2 parameters where n represents the number of inputs/outputs of the system). A nonlinear Least Squares (LS) problem is solved in order to determine the parameters. Since this latter problem is not a convex one a direct search method was combined with the least squares method. This combination enhances dramatically the convergence to the global minimum. The combination of LS and the search method reduces complexity by reducing the number of parameters to two only. Another advantage of the method is that a feasible range for each parameter can be prespecified.

III

 
The identification algorithm was realized and tested both in simulations (using the Matlab software) and on a laboratory setup. These tests demonstrated that the algorithm performs in a satisfactory manner and is robust.