Decoupling internal model control for non-square processes based on equivalent transfer function

Abstract

A novel design method of decoupling internal model control is proposed for non-square processes with multiple time delays that are often encountered in complicated industrial processes. The method can obtain a realizable decoupling controller of non-square processes with more inputs than outputs by inserting some compensated terms, which are derived analytically. Meanwhile, based on the relative normalized gain array, an equivalent transfer function matrix is introduced to approximate the pseudo-inverse of the process transfer function matrix, which makes the design of decoupling internal model control simple and easy to calculate. Filters are added to the control structure to improve the robustness. Simulation results have proved the effectiveness and reliability of the proposed method.

A comparative study on existing and new methods to design internal model controllers for non-square systems

“…The equivalent transfer function (ETF) method has been developed to approximate the inverse of the process transfer matrix based on the measurement of dynamic interactions of non-square systems (Jin and Jiang, 2013; Jin et al, 2014).…”

“…where k N , ij N is the normalized gain describing the dynamic properties of a particular transfer function g ij (s). It is defined as follows (Jin et al, 2014; Luan et al, 2017; Shen et al, 2010)…”

“…Processes with equal number of inputs and outputs are called square systems. Non-square systems are then referred to unequal number of inputs and outputs processes (Ben Omrane et al, 2012; Jin et al, 2014; Qibing et al, 2009; Quan et al, 2012). The control of such systems is challenging due to the existence of interactions among input and output variables.…”

Compensator design based on inverted decoupling for non‐square processes

“…The IAE (all) and ITAE (all) in Table 1 denote the sums of IAE and ITAE for each loop, respectively. TV (all) means the sums of each row and u (all) calculates the sums of each column in Table 1. Simulation 2 To illustrate the advantage of the proposed non‐square control algorithm over others, such as centralised PI controller adopting static decoupling and Smith delay compensation structure (PI‐Static) [10] (where approximated first‐order plus time‐delay models are used), multivariable PI controller based on ETF (PI‐ETF) [15] or decoupling internal model controller (D‐IMC) [14], the closed‐loop system response is shown in Fig. 5.…”

“…Recently, the concept of equivalent transfer function (ETF) has been introduced to design centralised decoupling controllers for multivariable processes [11, 12] by approximating the inverse of the transfer function matrix. Based on the relative normalised gain array, an ETF matrix is introduced [13] to approximate the pseudo‐inverse of the process transfer function matrix, which makes the calculation simple and easy for the design of decoupling IMC [14] or centralised PI/proportion integration differentiation (PID) control [15]. It should be noticed that the simple approximation for the pseudo‐inverse of a non‐square transfer function matrix may result in poor performance of the decoupling controller for high‐dimensional processes.…”