An Analytical Design of Simplified Decoupling Smith Predictors for Multivariable Processes

Abstract

In this study, the issues of complicated interactions between process variables were solved by decoupling techniques; in particular, simplified decoupling was used due to its simplicity and robustness. A new approach to solving decoupling realizability was developed by using the modified particle swarm optimization (PSO) algorithm. However, time delays still existed in the diagonal elements of the decoupled matrix, and they resulted in a more sophisticated controller design and sluggish responses in the outputs. To overcome the adverse effects of time delays, a Smith predictor, also known as a dead time compensator, is normally used. In this work, a Smith predictor structure in combination with simplified decoupling for multivariable processes was proposed in order to enhance system performances in terms of the servomechanism problem. The proportional integral or proportional integral derivative (PI/PID) controller tuning rules for several common industrial processes, such as first-order, second-order, and second-order with negative zero systems, were obtained. Many multivariable industrial processes were adopted to simulate the effectiveness of the proposed method in terms of the servomechanism problem and robust response.

A Novel Design of Fractional PI/PID Controllers for Two-Input-Two-Output Processes

“…In this work, the controller structure called simplified decoupling Smith predictor (SDSP) [15] is used to deal with the main issues of multivariable processes including interactions between process variables and multiple delay times. The whole structure of the controller is shown in Figure 1.…”

“…In this paper, the IMC-based FOPI/FOPID design is adopted to find out analytical tuning rules of both FOPI and FOPID controllers for TITO processes. Moreover, as mentioned in the previous work [15], one of the advantages of the proposed structure (SDSP) is to remove dead time out of the diagonal elements of the decoupled transfer function matrix. Therefore, only the delay-free parts of it are addressed to design the controllers.…”

“…In this work, the simplified decoupling Smith predictor structure (SDSP) for multivariable processes proposed by Chuong et al [15] is adopted to deal with interactions between process variables as well as multiple time delays of the processes. The realizability problem plays a crucial role in implementing a decoupler because of the requirements of being stable and proper of all its internal transfer functions.…”

“…Therefore, the whole controller structure used in this work is called fractional simplified decoupling Smith predictor (F-SDSP). The particle swarm optimization (PSO) algorithm for approximation procedure proposed in [15] is employed to find out the parameters of approximated fractional functions. Bouyedda et al [14] performed a similar work by using the Genetic Algorithm (GA) to reduce a high integer-order transfer function of a SISO system to a lower fractional-order one.…”

“…Note that, in this work, the fractional order transfer function (FOTF) is used instead of the integer order one. In addition, to evaluate the robustness stability of the proposed method, the M-∆ structure normally used for integer order systems [15][16][17][18][19][20][21][22] is also applied for fractional order ones. Then, the µ-synthesis, known as structured singular value (SSV), is employed to measure the robustness of the fractional controllers for multivariable processes with multiplicative output uncertainty.…”