Frequency Control Design For Multivariable Processes Based On Equivalent Transfer Function

Most of the processes and equipments in industrial fields have severe interactions, foreexample, chemical plants are essentially complicated MIMO (multi-input and multi-output)systems with dead time, interactions between each input and output; others like microbialfermentation process, referring to reproduction and growth in life, are multivariable systemscontaining time-variant, non-linear, uncertain, etc. Since characteristics of complication, giant,interactions between each loop, also time delay, variant parameters, non-linear, most ofexisting single-input single-output (SISO) methods fail to be applied to MIMO systems withsatisfied control performance, which cause difficulty on multivariable system design.According to the analysis of loop interactions, this paper proposes a novelfrequency-dependent design method for multivariable systems based on equivalent transferfunction (ETF). The specific research content is as follows:(1) General loop pairing criterion for multivariable systems is obtained. Consideringdifferent set-points, such as step inputs, ramp inputs and so on, relative normalized gain arrayis calculated on the basis of typical elements of multivariable systems, which are first-orderplus dead time and second-order plus dead time. To overcome the shortage of the RNGApairing criterion that is only applicable to pair the multivariable systems under step inputs,this paper derivate normalized gain array for model under various input forms, whichprovides a general pairing technique for multivariable systems.(2) To simplify the steps containing decoupling method and model reduction technique,this paper proposes a novel method to calculate the parameters of the ETF. According to therelationship between the ETF matrix and the open-loop transfer function, the procedureobtaining the ETF is improved, which comprehensively describes the dynamic imformation ofthe open loop model. When the interactions among different loops are modest, a simpledecentralized controller is normally adequate to satisfy the desired closed-loop performanceafter pairing the manipulated variables and controlled variables and choosing the dominantloops. The design method use internal mode control technique to calculate the parameters ofthe PID (proportional integral derivative) controller. However, if there has severe loopinteractions, the decentralized controller may fail to give the acceptable responses and acentralized or decoupling controller is preferred to decrease the interactions between eachloop that attains the desired performance.(3) Based on the quantitation of the loop interactions, this paper first discusses thestabilization problem of for multivariable system with time delays using multi-loop PIDcontroller. Due to ETFs described the decoupling relationships, multivariable systemdecomposes to a set of SISO loops to be developed the stabilizing region of the PIDparameters, hence, which provides a novel research idea of stabilizing PID control formultivariable systems.The purpose of this dissertation is to research methods of controller design formultivariable systems via the technique of ETF. The method of this paper is more easilyapplicable to industrial practice, also many control problems for complex multivariable systems have been solved to promote the development of multivariable process theory and toenrich the practical applications.