Internal Model Control for Rank-Deficient System with Time Delays Based on Damped Pseudo-Inverse

Abstract

It is a challenge to design a satisfactory controller for a complex multivariable industrial system with minimal offsetting and a slow response. An internal model control method is proposed for rank-deficient systems with a time delay based on a damped pseudo-inverse. An internal model control was designed to obtain the desired dynamic characteristics of the system by transforming the time-delay system into a system without a time delay, following the Pade approximation approach. By introducing a damping factor, the internal model controller was designed based on a damped pseudo-inverse, since the inverse matrix of the rank-deficient system does not exist. Furthermore, a singular value decomposition was used to analyze the steady-state performance of the system. The selection of the damping factor was also presented, and a μ analysis was made to evaluate the stability of the system. To demonstrate the effectiveness of the proposed method, a crude distillation process with five inputs and four outputs was considered as an example. The simulation results illustrate that not only can the proposed strategy guarantee the system’s stability, but it also has a relatively good dynamic performance.

Optimal System for Improved Internal Model Control of Argon-Oxygen Decarburization Process Based on the Piecewise Linear Model and Time Constant of Filter Optimization

“…Ali et al presented a general IMC structure with multiple degrees of freedom for the design of control systems with multiple objectives; the control structure is demonstrated on a simulated thin-film drying process in continuous pharmaceutical manufacturing for several multiloop control structures [8]. Jiang et al [9] proposed an IMC method based on a damped pseudoinverse, and an analysis was made to evaluate the stability of the system. Qiu et al [10] proposed a modified stability-constrained identification method with established boundedness and continuity properties and demonstrated the effectiveness of the proposed algorithm with an example.…”

Perfect Control for Continuous-Time LTI State-Space Systems: The Nonzero Reference Case Study

“…At the beginning, the most important chemical engineering industry has to be mentioned, where the nonsquare system issue has probably been firstly raised. The distillation column [23], [24], Shell control problem [25], crude distillation process [26], mixing tank process [27], continuous stirred tank reactor [28] and chemicalmechanical polishing process [29] can constitute the main goal of our investigation. The discussed new method can also be applied to the signal processing branch covering the environmental MIMO structures.…”

Bulletin of the Polish Academy of Sciences: Technical Sciences

“…Henceforth, the resulted unified approach can successfully predefine the robust properties of analyzed plant, this advantage is clearly demonstrated in the paper. Indeed, the application of the new combined method can offer the opportunities to improve the inverse model control-originated algorithm devoted to any physical nonsquare plants [17][18][19][20][21][22][23][24]. Replacing the Moore-Penrose inverse by the S and σ inverses will certainly impact on the performance indices, directly leading to design of efficient multivariable control schemes.…”