Multivariable PID control by decoupling

This paper presents a new methodology to design multivariable PID controllers based on decoupling control. The method is presented for general n×n processes. In the design procedure, an ideal decoupling control with integral action is designed to minimize interactions. It depends on the desired open loop processes that are specified according to realizability conditions and desired closed loop performance specifications. These realizability conditions are stated and three common cases to define the open loop processes are studied and proposed. Then, controller elements are approximated to PID structure. From a practical point of view, the windup problem is also considered and a new anti-windup scheme for multivariable PID controller is proposed. Comparisons with other works demonstrate the effectiveness of the methodology through the use of several simulation examples and an experimental lab process

Smith Predictor with Inverted Decoupling for Square Multivariable Time Delay Systems

Versión del autorThis paper presents a new methodology to design multivariable Smith predictor for n×n processes with multiple time delays based on the centralized inverted decoupling structure. The controller elements are calculated in order to achieve good reference tracking and decoupling response. Independently of the system size, very simple general expressions for the controller elements are obtained. The realizability conditions are provided and the particular case of processes with all of its elements as first order plus time delay systems is discussed in more detail. A diagonal filter is added to the proposed control structure in order to improve the disturbance rejection without modifying the nominal set-point response and to obtain a stable output prediction in unstable plants. The effectiveness of the method is illustrated through different simulation examples in comparison with other works

Iterative Method for Tuning Multiloop PID Controllers Based on Single Loop Robustness Specifications in the Frequency Domain

Multiloop proportional-integral-derivative (PID) controllers are widely used for controlling multivariable processes due to their understandability, simplicity and other practical advantages. The main difficulty of the methodologies using this approach is the fact that the controllers of different loops interact each other. Thus, the knowledge of the controllers in the other loops is necessary for the evaluation of one loop. This work proposes an iterative design methodology of multiloop PID controllers for stable multivariable systems. The controllers in each step are tuned using single-input single-output (SISO) methods for the corresponding effective open loop process (EOP), which considers the interaction of the other loops closed with the controllers of the previous step. The methodology uses a frequency response matrix representation of the system to avoid process approximations in the case of elements with time delays or complicated EOPs. Consequently, different robustness margins on the frequency domain are proposed as specifications: phase margin, gain margin, phase and gain margin combination, sensitivity margin and linear margin. For each case, a PID tuning method is described and detailed for the iterative methodology. The proposals are exemplified with two simulations systems where the obtained performance is similar or better than that achieved by other authors