Centralized PI controllers for interacting multivariable processes by synthesis method

Disturbance observer-based control with partially coupled inverse model for stable TITO processes with time delays

This paper presents a modified multivariable disturbance observer-based (MDOB) control method for stable two-input-two-output (TITO) processes with multiple time delays. Different from the existing MDOB control strategies with diagonal or full elements inverse model, a partially coupled inverse model is used here to provide better disturbance rejection performance. First, an interaction measure, relative input disturbance gain (RIDG), is defined to quantify the disturbance rejection capabilities of the two common types of MDOB techniques. Based on RIDG, the partially coupled inverse model is derived. Then, to deal with the cross terms of the filter elements in the outputs, a single iteration strategy is presented to derive them one by one. Meanwhile, analytical forms of the filter elements are obtained by minimizing the 2-norm of the outputs. Finally, filter parameters are tuned taking into account criteria of performance and robustness. And application of the proposed strategy on simulation examples verifies its effectiveness and superiority.

Centralized PI controller design method for MIMO processes based on frequency response approximation

A simple method of controller design for multi-input multi-output (MIMO) processes have been proposed in frequency domain. The intensive calculation for the inverse of the process transfer function matrix is simplified to a great extent by evaluating the process transfer function matrix at a low frequency point. The desired closed loop transfer functions are derived for the process using a single tuning parameter for each diagonal element of the process transfer function matrix which represents the desired closed loop time constant. Centralized PI controllers are then designed using a model matching technique by evaluating the transfer functions at a low frequency point. The PI controllers provide acceptable performances for lag dominated as well as time-delay dominated processes and is also applicable to high-dimensional processes. The proposed method is extended for the non-square MIMO processes using two approaches one of which squares up the process transfer function matrix to apply the proposed technique while the other is based on pseudo-inverse evaluation of the process transfer function matrix at a low frequency point.

An Analytical Design of Simplified Decoupling Smith Predictors for Multivariable Processes

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.

Design of multiloop PI controllers based on quadratic optimal approach

The LQR methodology is extended to produce multiloop PI controllers in this study. With this method, a multivariable P controller is first obtained and then diagonalized using an iterative procedure. The resulting controller is further complemented with the integral action in a similar process. The proposed tuning process explores different values of the control weight matrix to balance the output error and control signal in both stages, and is refined through additional indices related with the error to reference tracking, disturbance rejection and the associated control use. In addition, the diagonalization procedure is generalized to obtain multiloop versions of existing multivariable PI controllers. The developed theory was applied to the design of multiloop controllers for a distillation column as well as the diagonalization of existing controllers for a nonlinear CSTR. The tuning procedure allowed the synthesis of multiloop PI controllers with performance indices comparable to those reported by other authors. Furthermore, diagonalized controllers exhibited a similar operation as the original multivariable ones.

Decentralized PID controller for TITO systems using characteristic ratio assignment with an experimental application

This paper presents a decentralized PID controller design method for two input two output (TITO) systems with time delay using characteristic ratio assignment (CRA) method. The ability of CRA method to design controller for desired transient response has been explored for TITO systems. The design methodology uses an ideal decoupler to reduce the interaction. Each decoupled subsystem is reduced to first order plus dead time (FOPDT) model to design independent diagonal controllers. Based on specified overshoot and settling time, the controller parameters are computed using CRA method. To verify performance of the proposed controller, two benchmark simulation examples are presented. To demonstrate applicability of the proposed controller, experimentation is performed on real life interacting coupled tank level system.

Simple method of designing centralized PI controllers for multivariable systems based on SSGM

A method is given to design multivariable PI/PID controllers for stable and unstable multivariable systems. The method needs only the steady state gain matrix (SSGM). The method is based on the static decoupler design followed by SISO PI/PID controllers design and combining the resulted decoupler and the diagonal PI(D) controllers as the centralized controllers. The result of the present method is shown to be equivalent to the empirical method proposed by Davison EJ. Multivariable tuning regulators: the feed-forward and robust control of general servo-mechanism problem. IEEE Trans Autom Control 1976;21:35-41. Three simulation examples are given. The performance of the controllers is compared with that of the reported centralized controller based on the multivariable transfer function matrix.

Centralized PI control for high dimensional multivariable systems based on equivalent transfer function

This article presents a new scheme to design full matrix controller for high dimensional multivariable processes based on equivalent transfer function (ETF). Differing from existing ETF method, the proposed ETF is derived directly by exploiting the relationship between the equivalent closed-loop transfer function and the inverse of open-loop transfer function. Based on the obtained ETF, the full matrix controller is designed utilizing the existing PI tuning rules. The new proposed ETF model can more accurately represent the original processes. Furthermore, the full matrix centralized controller design method proposed in this paper is applicable to high dimensional multivariable systems with satisfactory performance. Comparison with other multivariable controllers shows that the designed ETF based controller is superior with respect to design-complexity and obtained performance.

Synthesis of Controllers for MIMO Systems with Time Response Specifications

This paper proposes the design of fixed low order controllers for Multi Input Multi Output (MIMO) decoupled systems. The simplified decoupling is used as a decoupling system technique due to its advantages compared to other decoupling methods. The main objective of the proposed controllers is to satisfy some desired closed loop step response performances such as the settling time and the overshoot. The controller design is formulated as an optimization problem which is non convex and it takes in account the desired closed loop performances. Therefore, classical methods used to solve the non convex optimization problem can generate a local solution and the resulting control law is not optimal. Thus, the thought is to use a global optimization method in order to obtain an optimal solution which will guarantee the desired time response specifications. In this work the Generalized Geometric Programming (GGP) is exploited as a global optimization method. The key idea of this method consists in transforming an optimization problem, initially, non convex to a convex one by some mathematical transformations. Simulation results and a comparison study between the presented approach and a Proportional Integral (PI) controller are given in order to shed light the efficiency of the proposed controllers.

RBFNDOB-based neural network inverse control for non-minimum phase MIMO system with disturbances

An adaptive control strategy combining neural network inverse controller (NNIC) with RBFN disturbance observer (RBFNDOB) is developed for a multi-input-multi-output (MIMO) system with non-minimum phase, internal and external disturbances in this paper. Since the inverse model of system is unstable due to the non-minimum phase, a pseudo-plant is constructed, then the RBFN is used to identify the inverse model of pseudo-plant, which can track the parameter variations of system. By copying the structure and parameters of the identifier, the NNIC is obtained. Cascading the NNIC with the original plant, the MIMO system can be decoupled and linearized into independent SISO systems. For the independent decoupled system, the RBFNDOB employs a RBFN to observe the external disturbances and this estimate value is used as a feed-forward compensation term in controller. The case study on ball mill grinding circuit is presented. The effectiveness of the proposed method is demonstrated by simulation results and comparisons.