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.

In this paper, a new formulation of fractional order proportional integral (PI)/ proportional integral derivative (PID) controller is proposed. The proposed controller will be justified for some well-known two-input-two-output (TITO) processes. In order to deal with interactions between process variables in a multivariable system, as well as multiple delay times in process transfer functions, the simplified decoupling Smith predictor (SDSP) structure is also used. The issue of decoupling realizability is solved by the PSO algorithm and fractional order processes are also suggested for model reduction. The tuning rules of the controller are derived in analytical terms based on the internal model control (IMC) structure. The effectiveness and robust stability of the proposed approach are illustrated by comparing it with other methods. To have a fair comparison, the robustness criterion using the M-Δ structure with μ-synthesis is adopted and the μ value of the proposed method is always kept smaller than the value of the others.

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The fractional-order proportional-integral (FOPI) controller tuning rules based on the fractional calculus for the parallel cascade control systems are systematically proposed in this paper. The modified parallel cascade control structure (PCCS) with the Smith predictor is addressed for stable, unstable, and integrating process models with time delays. Normally, the PCCS consists of three controllers, including a stabilized controller, for a class of unstable and integrating models, a disturbance rejection controller in the secondary loop, and a primary servomechanism controller. Accordingly, the ideal controller is obtained by using the internal model control (IMC) approach for the inner loop. The proportional-derivative (PD) controller is suggested for the stabilized controller and is designed based on a stability criterion. Based on the fractional calculus, the analytical tuning rules of the FOPI controller for the outer loop can be established in the frequency domain. The simulation study is considered for three mentioned cases of process models and the results demonstrate the flexibility and effectiveness of the proposed method for the PCCS in comparison with the other methods. The robustness of the proposed method is also justified by perturbed process models with ±20% of process parameters including gain, time constant, and delay time.