Controller Design for MIMO Processes Based on Simple Decoupled Equivalent Transfer Functions and Simplified Decoupler

Control of TITO processes using sliding mode controller tuned by ITAE minimizing criterion based Nelder-Mead algorithm

Control of multi input and multi output (MIMO) process with interaction is often encountered in process industry. Such MIMO processes are controlled using conventional sliding mode controller (SMC) and tuned by integral square error (ISE) minimizing criterion based Nelder-Mead algorithm. SMC tuned by integral time absolute error (ITAE) minimization criterion based Nelder-Mead algorithm is proposed in this work. Three categories of two inputs and two outputs (TITO) process models are represented in the matrix form, with each of the matrix element representing a first order plus dead time (FOPDT) process. These TITO models are categorized based on the ratio ε, between dead time and time constant of the FOPDT model which forms the matrix element of the TITO model. The performance of conventional SMC is evaluated for these three categories of TITO models, in which the TITO process models with the ratio ε greater than the one, exhibited by poor closed loop performance, whereas the proposed SMC when applied to the these process models delivered superior closed loop performance.

Experimental Investigation and Control of a Hot-Air Tunnel with Improved Performance and Energy Saving

The paper is focused on the identification, control design, and experimental verification of a two-input two-output hot-air laboratory apparatus representing a small-scale version of appliances widely used in the industry. A decentralized multivariable controller design is proposed, satisfying control-loop decoupling and measurable disturbance rejection. The proposed inverted or equivalent noninverted decoupling controllers serve for the rejection of cross-interactions in controlled loops, whereas open-loop antidisturbance members satisfy the absolute invariance to the disturbances. Explicit controller-structure design formulae are derived, and their equivalence to other decoupling schemes is proven. Three tuning rules are used to set primary controller parameters, which are further discretized. All the control responses are simulated in the Matlab/Simulink environment. In the experimental part, two data-acquisition, communication, and control interfaces are set up. Namely, a programmable logic controller and a computer equipped with the peripheral component interconnect card commonly used in industrial practice are implemented. A simple supervisory control and data acquisition human-machine interface via the Control Web environment is developed. The laboratory experiments prove better temperature control performance measured by integral criteria by 35.3%, less energy consumption by up to 6%, and control effort of mechanical actuator parts by up to 17.1% for our method compared to the coupled or disturbance-ignoring design in practice. It was also observed that the use of a programmable logic controller gives better performance measures for both temperature and air-flow control.

Robust optimal centralized PI controller for a fluid catalytic cracking unit

Fluidized Catalytic Cracking (FCC) is a complex process that arises due to feed composition, non-linearities, and dynamic mass and heat interactions in its components. FCC is difficult to model and monitor in industries, and one of the key reasons is that they are multivariable processes. Such processes are highly interacting and that makes the process of controlling even more difficult. The interaction between loops can be quantified easily by dRGA. An easy and effective way of controlling multivariable processes is to implement a centralized control system, considering the interactions between measured and manipulated variables. In this study, a centralized control system is designed for the riser section of the FCC unit. The dRGA method is modified to enhance the closed-loop response by formulating an optimization problem and obtaining an optimal controller settings. A rigorous simulation studies show an 826% reduction in ISE values, a 309% reduction in IAE values, and a 262% reduction in ITAE value of T r i s ${T}_{ris}$ from the dRGA method to the modified dRGA method. Further, IAE values for Y l p g ${Y}_{lpg}$ are reduced by 29% from dRGA to modified dRGA method and 34% from synthesis to modified dRGA method.

Enhanced Dynamic Set-point Weighting Design for Two-Input-Two-Output (TITO) Unstable Processes

Control of unstable systems with time delays usually result in overshoots in the closed loop responses. The intricacy involved in multivariable unstable processes further makes the problem more challenging. In industry, set-point weighting is one of the recommended methods to minimize the overshoot. However, design of the set-point weighting parameters determines the percentage of minimization of the overshoot. In this paper, a method is proposed to design the set-point weighting parameters for unstable multivariable processes which is relatively simple and also reduces the overshoot. Weighting is considered for both proportional (β) and derivative (γ) terms in the PID control law. In the closed loop relation for set-point tracking, the coefficients of ‘s’ and ‘s3’ both in the numerator and denominator are made equal in order to find dynamically β and γ. The obtained expressions for β and γ are simple and dynamically depends on the controller parameters and are applied to TITO systems in present work. Decouplers are used in TITO systems mainly to reduce the interaction between the loops so that they can be viewed as independent loops. Decoupler design suggested by (Hazarika and Chidambaram [1] has been used in this work and two TITO unstable processes with time delays are illustrated here. Comparison with the reported methods available in literature verifies that the proposed method gives improved closed loop performance.

Fractional Order PID Controller Design for Multivariable Systems using TLBO

The multivariable systems have to control by using multiloop controllers and each closed loop controller has unique characteristics. The successful model structure for design of control system is extremely subject to the accurate choice of the tuning parameters ( K_p, K_i, K_d, \lambda, \mu ) of the controller. The choice of optimal tuning parameters of Fractional Order PID (FOPID) controller leads to accurate controlling of desired level in multivariable system. Here, for multivariable system, a FOPID controller design based on the advanced optimization technique called Teaching Learning based optimization (TLBO) algorithm is proposed. The goal of paper is (i) The elimination of interaction between the control loops and (ii) Reference tracking along the disturbance in each loop. These objectives are satisfied by using four cost function, namely, integral absolute error (IAE), integral square error (ISE), integral time absolute error (ITAE) and integral time square error (ITSE). Out of these cost functions, ITAE based FOPID controller design using TLBO algorithm provides better performance in terms of fast reference tracking and disturbance elimination in the loop. Moreover, the comparative analysis of convergence characteristics of each objective of the controller by using TLBO is presented. The simulation study confirms that the TLBO algorithm based FOPID controller for multivariable systems (2 × 2) are more robust and exhibits superior response with respect to other algorithm.

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 and experimental realization of a robust decentralized PI controller for a coupled tank system

This paper presents design and realization of a robust decentralized PI controller for regulating the level of a coupled tank system. The proposed controller is designed based on a predefined reference transfer function model in which we adopt a frequency matching of actual and reference models. Realization of control algorithms for a multivariable system is often complicated owing to uncertainties in the process dynamics. In this paper, initially a frequency response fitting model reduction technique is adopted to obtain a First Order Plus Dead Time (FOPDT) model of each higher order decoupled subsystem. Further, using the obtained reduced order model, the proposed robust decentralized PI controller is designed. The stability and performance of the proposed controller are verified by considering multiplicative input and output uncertainties. The performance of the proposed robust decentralized controller has been compared with that of a decentralized PI controller. To validate the performance of the proposed control approach, real-time experimentation is pursed on a Feedback Instrument manufactured coupled tank system.

Internal Model Control for Rank-Deficient System with Time Delays Based on Damped Pseudo-Inverse

It is a challenge to design a satisfactory controller for a complex multivariable industrial system with minimal offsetting and a slow response. An internal model control method is proposed for rank-deficient systems with a time delay based on a damped pseudo-inverse. An internal model control was designed to obtain the desired dynamic characteristics of the system by transforming the time-delay system into a system without a time delay, following the Pade approximation approach. By introducing a damping factor, the internal model controller was designed based on a damped pseudo-inverse, since the inverse matrix of the rank-deficient system does not exist. Furthermore, a singular value decomposition was used to analyze the steady-state performance of the system. The selection of the damping factor was also presented, and a μ analysis was made to evaluate the stability of the system. To demonstrate the effectiveness of the proposed method, a crude distillation process with five inputs and four outputs was considered as an example. The simulation results illustrate that not only can the proposed strategy guarantee the system’s stability, but it also has a relatively good dynamic performance.

A New Hybrid BFOA-PSO Optimization Technique for Decoupling and Robust Control of Two-Coupled Distillation Column Process

The two-coupled distillation column process is a physically complicated system in many aspects. Specifically, the nested interrelationship between system inputs and outputs constitutes one of the significant challenges in system control design. Mostly, such a process is to be decoupled into several input/output pairings (loops), so that a single controller can be assigned for each loop. In the frame of this research, the Brain Emotional Learning Based Intelligent Controller (BELBIC) forms the control structure for each decoupled loop. The paper's main objective is to develop a parameterization technique for decoupling and control schemes, which ensures robust control behavior. In this regard, the novel optimization technique Bacterial Swarm Optimization (BSO) is utilized for the minimization of summation of the integral time-weighted squared errors (ITSEs) for all control loops. This optimization technique constitutes a hybrid between two techniques, which are the Particle Swarm and Bacterial Foraging algorithms. According to the simulation results, this hybridized technique ensures low mathematical burdens and high decoupling and control accuracy. Moreover, the behavior analysis of the proposed BELBIC shows a remarkable improvement in the time domain behavior and robustness over the conventional PID controller.

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.