Katsuba O.A., Pahomov G.G.
Russia, Samara, SSTU,
ADAPTIVE CONTROL SYSTEM OF THE PROCESS OF GAS SEPARATION BASED ON
DYNAMIC MODELS WITH ERROR IN INPUT PREDICTORS.
The report presents the adaptive control system based on the identification approach with errors available not only in output signals, but in input ones as well. These errors belong to the class of changeable processes of martingale-differences type. For identification of the indicated model the original and generalized method of the least squares is applied as two quadratic forms ratio.
Кацюба O.A., Пахомов Ю.Ю.
Россия, Самара, СамГТУ,
АДАПТИВНАЯ СИСТЕМА УПРАВЛЕНИЯ ПРОЦЕССОМ ГАЗОРАЗДЕЛЕНИЯ НА
ОСНОВЕ ДИНАМИЧЕСКИХ МОДЕЛЕЙ С ПОМЕХОЙ ВО ВХОДНЫХ ПРЕДИКТОРАХ.
Предлагается адаптивная система управления на основе идентификационного подхода при наличии помех во входных и в выходных сигналах. Эти помехи принадлежат к классу изменчивых процессов типа мартингал-разностей. Для идентификации указанной модели применен оригинальный обобщенный метод наименьших квадратов в виде отношений двух квадратичных форм.
Gas separation process is intended for separating gases of pyrolysis in order to extract ethylene fraction, propane-propylene fraction, methane-hydrogen and ethane fractions at synthetic alcohol production.
The object of automation is a dynamic control system, the main peculiarity of which is availability of errors of input variables measurements having the same order that errors of output variable. Another feature of the above mentioned object is its variability due to the drift of some parameters such as: change of raw material, seasonal changes and etc., therefore the task of stabilization can be solved only in the class of the adaptive systems. Strictly adaptive systems on base of dual control needs a precise apriory information in the form of density of distribution of different values.
In this report the class of errors in input and output variables is consider, which represents variable dependent successions. The above mentioned peculiarity makes it impossible to apply all the well-known methods of identification effectually, such as, the method of the least squares (LSM) and others like that.
The process considered in the operational range may be represented quite precisely by the linear difference equation:
Let the next conditions be fulfilled:
1°. Occasional processes meet the following conditions:
Е - operator of the expected value,
- algebra induced by the family of the random values
2°. The set, to which the true values of the stable system parameters are belonged, is considered to be compact.
4°., does not depend on and does not depend on,
then a new criterion is allowed
-mean values of variances , .
The report shows that if the allowed critarion is applied ( which generalizes the method of the least squares and represents the ratio of two quadratic forms), the estimations will correspond to the facts and comply with reality, allowing for a certain portion of error.
The above mentioned method is applied in case , when there is the aggregate of the measured parameters or values available.
where - visible and invisible states of vectors ,
- visible and invisible input signals, .
The report presents also the results of the analysis of the evaluated parameters errors and shows the comparison with the classic methods of the least squares and instrumental variables.