Design of IMC-PID Controller Cascaded Filter for Simplified Decoupling Control System

In this work, the IMC-PID controller cascaded filter based on Internal Model Control (IMC) scheme is systematically proposed for the simplified decoupling control system. The simplified decoupling is firstly introduced for multivariable processes by using coefficient matching to obtain a stable, proper, and causal simplified decoupler. Accordingly, transfer functions of decoupled apparent processes can be expressed as a set of n equivalent independent processes and then derived as a ratio of the original open-loop transfer function to the diagonal element of the dynamic relative gain array. The IMC-PID controller in series with filter is then directly employed to enhance the overall performance of the decoupling control system while avoiding difficulties arising from properties inherent to simplified decoupling. Some simulation studies are considered to demonstrate the simplicity and effectiveness of the proposed method. Simulations were conducted by tuning various controllers of the multivariate processes with multiple time delays. The results indicate that the proposed method consistently performs well with fast and well-balanced closed-loop time responses.

Fractional-Order PI Controller Tuning Rules for Cascade Control System

The fractional–order proportional integral (FOPI) controller tuning rules based on the fractional calculus for the cascade control system are systematically proposed in this paper. Accordingly, the ideal controller is obtained by using internal model control (IMC) approach for both the inner and outer loops, which gives the desired closed-loop responses. On the basis of the fractional calculus, the analytical tuning rules of FOPI controller for the inner loop can be established in the frequency domain. Besides, the outer loop is tuned by using any integer PI/PID controller tuning rules in the literature. The simulation study is considered for the stable process model and the results demonstrate the simplicity, flexibility, and effectiveness of the proposed method for the cascade control system in compared with the other methods.

Analytical Design of IMC-PID Controller for Ideal Decoupling Embedded in Multivariable Smith Predictor Control System

In this paper, the analytical tuning rules of IMC-PID controller are presented for the multivariable Smith predictor that involved the ideal decoupling. Accordingly, the decoupler is first introduced into the multivariable Smith predictor control system by a well-known approach of ideal decoupling, which is compactly extended for general nxn multivariable processes and the multivariable Smith predictor controller is then obtained in terms of the multiple single-loop Smith predictor controllers. The tuning rules of PID controller in series with filter are found by using Maclaurin approximation. Many multivariable industrial processes are employed to demonstrate the simplicity and effectiveness of the presented method. The simulation results show the superior performances of presented method in compared with the other methods.

Independent Design of Multi-loop PI/PID Controllers for Multi-delay Processes

The interactions between input/output variables are a very common phenomenon encountered in the design of multi-loop controllers for interacting multivariable processes, which can be a serious obstacle for achieving a good overall performance of multiloop control system. To overcome this impediment, the decomposed dynamic interaction analysis is proposed by decomposing the multiloop control system into a set of n independent SISO systems with the corresponding effective open-loop transfer function (EOTF) within the dynamic interactions embedded explicitly. For each EOTF, the reduced model is independently formulated by using the proposed reduction design strategy, and then the paired multi-loop proportional-integral-derivative (PID) controller is derived quite simply and straightforwardly by using internal model control (IMC) theory. This design method can easily be implemented for various industrial processes because of its effectiveness. Several case studies are considered to demonstrate the superior of the proposed method.