Multiple-input Multiple-output Process Research Articles

Self-Tuning Two Degree-of-Freedom Proportional–Integral Control System Based on Reinforcement Learning for a Multiple-Input Multiple-Output Industrial Process That Suffers from Spatial Input Coupling

Proportional–integral–derivative (PID) control remains the primary choice for industrial process control problems. However, owing to the increased complexity and precision requirement of current industrial processes, a conventional PID controller may provide only unsatisfactory performance, or the determination of PID gains may become quite difficult. To address these issues, studies have suggested the use of reinforcement learning in combination with PID control laws. The present study aims to extend this idea to the control of a multiple-input multiple-output (MIMO) process that suffers from both physical coupling between inputs and a long input/output lag. We specifically target a thin film production process as an example of such a MIMO process and propose a self-tuning two-degree-of-freedom PI controller for the film thickness control problem. Theoretically, the self-tuning functionality of the proposed control system is based on the actor-critic reinforcement learning algorithm. We also propose a method to compensate for the input coupling. Numerical simulations are conducted under several likely scenarios to demonstrate the enhanced control performance relative to that of a conventional static gain PI controller.

Temperature and water level control system in water thermal mixing process using adaptive fuzzy PID controller

Thermal Mixing Process, which is important in various industries, is a multiple-input multiple-output process (MIMO). It works by regulating hot-water and cold-water flows to control the temperature and level of the mixture. The Adaptive Fuzzy PID Control (AFPIDC) algorithm is a combination of two types of controller, has a simple PID basis with added Fuzzy aspects to speed up control. The AFPIDC algorithm is applied to the simulation of water thermal mixing process and is done with MATLAB/SIMULINK program. The fuzzy algorithm uses two inputs (errors & changes of errors) and has three outputs (changes of PID constants). The system is tested by simulating setpoint changes and adding disturbance. The testing result shows that AFPIDC controllers performs better than PID in controlling temperature and level. In temperature control, the PID settling time is 830 seconds, AFPIDC is 328 seconds and the PID overshoot is 6,3% and AFPIDC is 0%. In level control, the settling time of PID is 3221 seconds, while AFPIDC is 235 seconds, with PID overshoot is 10,5%, while AFPIDC 0%. From testing the system with leakage disturbance, the temperature controller needs time to regain stability at PID 780 seconds, AFPIDC 250 seconds. Meanwhile the level controlling stabilizes at PID 4510 seconds, and AFPIDC at 225 seconds.

A Zoning-Based Secure Control Approach Against Actuator Attacks in Industrial Cyber-Physical Systems

The integration of cyber and physical domains improves the flexibility and efficiency of industrial systems. However, it also introduces security threats into the physical processes of the systems. More seriously, most of field devices, such as sensors and actuators, in industrial systems are vulnerable to security threats because they are usually not deployed with security countermeasures. Therefore, how to secure the physical processes of these industrial cyber-physical systems becomes an emerging problem. To address this problem, a zoning-based approach is presented in this article for identification and mitigation of actuator attacks in multiple-input multiple-output processes governed by linear time-invariant systems. It partitions the set of actuators into multiple zones that ensures the controllability of the surviving zones when a zone is compromised. When a zone is intruded, the system states of the compromised zone and other zones cooperate to confirm that the detected attack is against actuators. Then, to mitigate the impact of the actuator attack on the system functions, the attacked actuators are isolated. After that, the residual actuators in the surviving zones are used to reconfigure the control loops of the systems. Case studies are conducted to illustrate the effectiveness of the presented approach.

Tree physiology optimization on SISO and MIMO PID control tuning

The tuning of proportional–integral–derivative (PID) controller is essential for any control application in order to ensure the best performance by step change or disturbance. This paper presents the tuning of PID controller for single-input single-output (SISO) and multiple-input multiple-output (MIMO) control systems using tree physiology optimization (TPO). TPO is a metaheuristic algorithm inspired from a plant growth system derived based on the idea of plant architecture and Thornley model (TM). The basic principle of TM simplifies the plant growth into shoots and roots part. The plant shoots grow towards sunlight with the help of nutrients supplied by the root system in order to undergo photosynthesis process, a process of converting light photon into carbon. The carbon gain from the shoots extension will be supplied to the root system in order for the root to grow and search for water plus nutrients. As a result, the nutrients are supplied upwards towards shoot system for further extension. This concept runs iteratively in order to ensure optimum plant growth. The iterative search of shoot towards better light supported by the root counterparts leads to an optimization idea of TPO algorithm. TPO also has a unique exploration strategy due to its multiple branches and shoots that can be defined by user. This concept may improve the search mechanism with a better trade-off between diversification and intensification search. A simulation of SISO control system and an industrial application of MIMO control are applied to demonstrate the effectiveness of the proposed algorithm and compared with other optimization methods such as particle swarm optimization, Ziegler–Nichols, Tyreus–Luyben and Chien–Hrones–Reswick methods. The results clearly exhibit the capability of TPO algorithm towards finding the optimum PID parameters for SISO and MIMO process with faster settling time and better performance with respect to other methods.

Nonlinear predictive control of a boiler-turbine unit: A state-space approach with successive on-line model linearisation and quadratic optimisation

This paper details development of a Model Predictive Control (MPC) algorithm for a boiler-turbine unit, which is a nonlinear multiple-input multiple-output process. The control objective is to follow set-point changes imposed on two state (output) variables and to satisfy constraints imposed on three inputs and one output. In order to obtain a computationally efficient control scheme, the state-space model is successively linearised on-line for the current operating point and used for prediction. In consequence, the future control policy is easily calculated from a quadratic optimisation problem. For state estimation the extended Kalman filter is used. It is demonstrated that the MPC strategy based on constant linear models does not work satisfactorily for the boiler-turbine unit whereas the discussed algorithm with on-line successive model linearisation gives practically the same trajectories as the truly nonlinear MPC controller with nonlinear optimisation repeated at each sampling instant.

Single and Multiple variables control using Tree Physiology Optimization

This paper presents the tuning of single-input single-output (SISO), and multiple-input multiple-output (MIMO) control system using Tree Physiology Optimization (TPO). TPO is a metaheuristic optimization algorithm that has a clustered diversification search strategy inspired from plant shoots growth. The clustered diversification is referred as tree branch and leaves. The exploration is amplified from roots growth counterparts. In the proposed method, each shoot from each branch search for possible solution in parallel and the fitness is evaluated based on all best values found by branch search. The proposed algorithm is also compared with deterministic gradient-free algorithm: Nelder-Mead simplex (NMS) and another metaheuristic algorithm: Particle Swarm Optimization (PSO). Results shown that TPO is able to find good PID parameters with lesser settling time for SISO and MIMO process. NMS is also able to find good PID parameters for SISO with lesser performance index, however not able to find better solution in MIMO control. PSO converged prematurely in SISO control and has high overshoot for MIMO control optimization.

Unbiased MIMO VRFT with application to process control

Continuous process industries usually have hundreds to thousands of control loops, most of which are coupled, i.e. one control loop affects the behavior of another control loop. In order to properly design the controllers and reduce the interactions between loops it is necessary to consider the multivariable structure of the process. Usually MIMO (multiple-input, multiple-output) controllers are designed using MIMO models of the process, but obtaining these models is a task very demanding and time consuming. Virtual Reference Feedback Tuning (VRFT) is a data-driven technique to design controllers which do not use a model of the process; all the needed information is collected from input/output data from an experiment. The method is well established for SISO (single-input, single-output) systems and there are some extensions to MIMO process which assume that all the outputs should have the same closed-loop performance. In this paper we develop a complete framework to MIMO VRFT which provides unbiased estimates to the optimal MIMO controller (when it is possible) even when the closed-loop performances are distinct to each loop. When it is not possible to obtain the optimal controller because the controller class is too restrictive (for example PID controllers) then we propose the use of a filter to reduce the bias on the estimates. Also, when the data is corrupted by noise, the use of instrumental variables to eliminate the bias on the estimate should be considered. The article presents simulation examples and a practical experiment on a tree tank system where the goal is to control the level of two tanks.

Estimation of Parameter for Disturbance Model of 3-by-3 MIMO Process Using Relay Feedback Test

Ideal and biased relays are used to obtain input/output responses from unknown process systems of 3-by-3 Multiple-Input Multiple-Output (MIMO) nature with component transfer functions of first-order-plus-deadtime (FOPDT) (D/ <1) type. To characterize these responses through modeling, a systematic approach is followed to derive analytical expressions for these relay feedback responses. Unknown system parameters are identified using limit cycle data of undesirable relay response curves obtained from single relay feedback test on a linear 3-by-3 MIMO process. Time domain analytical expressions of these monotonic response curves are used to accurately derive boundary conditions and an estimation algorithm for 3-by-3 MIMO process (distillation).

PID control of MIMO process based on rank niching genetic algorithm

Non-linear multiple-input multiple-output (MIMO) processes which are common in industrial plants are characterized by significant interactions and non- linearities among their variables. Thus, tuning several controllers in complex industrial plants is a challenge for process engineers and operators. An approach for adjusting the parameters of n proportional---integral---derivative (PID) controllers based on multiobjective optimization and genetic algorithms (GA) is presented in this paper. A modified genetic algorithm with elitist model and niching method is developed to guarantee a set of solutions (set of PID parameters) with different tradeoffs regarding the multiple requirements of the control performance. Experiments considering a fluid catalytic cracking (FCC) unit, under PI and dynamic matrix control (DMC) are carried out in order to evaluate the proposed method. The results show that the proposed approach is an alternative to classical techniques as Ziegler---Nichols rules and others.

A framework for determining MIMO process parameters by a neuro-DM&ACO approach

A framework combining artificial neural network (ANN) modelling technique, data mining and ant colony optimisation (ACO) algorithm is proposed for determining multiple-input multiple-output (MIMO) process parameters from the initial chemical-mechanical planarisation (CMP) processes used in semiconductor manufacturing. Owing to the invisibility of the ANN in the solution procedures, the decision tree approach of data mining is adopted to provide the necessary information for a real-valued ACO. The simulation result demonstrates that the proposed method can be an efficient tool for selecting properly defined parameter combination with the CMP process.

Backstepping-enhanced decentralised PID control for MIMO processes with an experimental study

A novel decentralised PID controller design procedure based on backstepping principles is presented to operate multiple-input multiple-output (MIMO) dynamic processes. First, a control Lyapunov function (CLF) and virtual control variable based on the backstepping method are derived recursively for each loop and a multivariable controller is obtained. Appropriate selection of auxiliary control variables can then eliminate coupling effects between subprocesses, and a decentralised controller can be derived. By analysing the regulation dynamics, external disturbances are rejected via appropriate tuning of the backstepping design parameters. Sufficient stability conditions are then derived using the small-gain theorem for two-input two-output and MIMO closed-loop systems, respectively. Simulation results for the control of the Shell benchmark problem and experimental results with a real-time water-level control system are provided to demonstrate the effectiveness and practicality of the proposed design procedure.

Development of decoupling scheme for high order MIMO process based on PSO technique

Multiple-input multiple-output (MIMO) with N Input/ N Output processes are characterized by significant interactions between their inputs and outputs. The control of MIMO processes is usually implemented using sets of single-input single-output (SISO) loop controllers, which requires proper input---output pairing and development of decoupling compensator unit. In this paper, a generalized decoupling technique is proposed. The proposed technique uses relative gain array (RGA) to select proper pairing and particle swarm optimization (PSO) technique to estimate the optimal elements' values of steady state decoupling compensation matrix constituting the decoupling compensator unit. The proposed technique is applied on 4 Input/ 4 Output two coupled distillation columns process, it proves remarkable success in minimizing the interaction between every input and all outputs except that output has been proper paired with.

Analytical decoupling control strategy using a unity feedback control structure for MIMO processes with time delays

An analytical decoupling control method is proposed for multiple-input–multiple-output (MIMO) processes with multiple time delays. The desired diagonal system transfer matrix is proposed first in terms of the H 2 optimal performance specification, resulting in the ideal desired decoupling controller matrix derived within the framework of a unity feedback control structure. It is demonstrated that dead-time compensators must be enclosed in the decoupling controller matrix to realize absolute decoupling for MIMO processes with multiple time delays. To alleviate the difficulties associated with the implementation, the ideal desired decoupling controller matrix is transformed into a practical form using an analytical approximation approach. Correspondingly, the stability of the resultant control system is assessed, together with its robust stability in the presence of process uncertainties. An on-line tuning rule for the single adjustable parameter of each column controllers in the decoupling controller matrix is given to cope with the process unmodeled dynamics. Finally, illustrative examples are given to show the superiority of the proposed method over the recently improved decoupling control methods.

Construct MIMO process control system by using soft computing methods

The main objective of this study aims at multiple-input multiple-output (MIMO) process mode. Based on the integrated concepts of statistical process control (SPC) and engineering process control (EPC), soft computing (SC) technique and statistical analysis technique are combined to modularize the relationship between process output and process input, so optimal yield can be derived and process quality can be improved. This study intended to construct a MIMO process control system with soft computing methods for prediction and parameter control and detailed the internal operation for each sub-system and relationship among one another. Besides correct prediction and diagnosis for the noise due to system deviation, it effectively controls process input and output as well as achieves process optimization.

Nonlinear feedback control of multivariable non-minimum-phase processes

A new method of controlling nonlinear processes with a non-minimum-phase delay-free part is presented. Two control laws are derived for stable, multiple-input multiple-output processes. They are obtained by requesting an approximately linear, input–output response and exploiting the connections between model-predictive control and input–output linearization. Conditions under which the closed-loop system is asymptotically stable are given. The application and performance of the control laws are illustrated using numerical simulation of two chemical reactor examples that exhibit non-minimum-phase behavior.

Global predictive control: A unified control structure for decoupling setpoint tracking, feedforward compensation and disturbance rejection dynamics

Predictive control has now reached a mature level. However, a unification of long-range predictive controllers, such as unified predictive control (UPC), generalised predictive control (GPC) and partial state model reference control (PSMRC) is still lacking. The paper presents global predictive control (GlobPC), which unifies, for stable processes, these controllers. GlobPC is based on an internal model framework where three independent control criteria are minimised: one for tracking, one for regulation and one for feedforward. Using three criteria allows for the desired tracking to be obtained, and for regulation and feedforward to behaviours in an optimal way, while keeping them perfectly separated. The GlobPC structure also exhibits a clean separation of the stochastic and deterministic parts of the control algorithm. The state–space model representation is used for a more uniform and easy programming of GlobPC for both single-input single-output and multiple-input multiple-output processes. An application to a pilot plant illustrates the benefits of the method.

Decoupling of Multivariable Rule-Based Fuzzy Systems

Decoupling of interactions among variables in multiple-input, multiple-output (MIMO) rule-based systems is addressed. It is well known that by proper decoupling the design of a controller for a MIMO process can be substantially simplified. Also the computational costs are reduced which facilitates the real-time implementation of the control system. However, decoupling methods are well developed for linear systems only. No general approach seems to be available for nonlinear MIMO systems. It is shown in this article that if a nonlinear MIMO system is represented by a set of linguistic if-then rules, the decoupling can be accomplished in a systematic way. An algorithm for the design of a decoupler (pre-compensator) is presented and illustrated by an example.

Automatic tuning of decentralized PID controllers for MIMO processes

Abstract An automatic tuning algorithm for decentralized PID control in multiple-input multiple-output (MIMO) plants is presented. This algorithm generalizes the authors' recent auto-tuner for two-input two-output systems to any number of inputs and outputs. The algorithm consists of two stages. In the first, the desired critical point, which consists of the critical gains of all the loops and a critical frequency, is identified. The auto-tuner identifies the desired critical point with almost no a priori information about the process. During the identification phase all controllers are replaced by relays, thus generating limit cycles with the same period in all loops. It is shown that each limit cycle corresponds to a single critical point of the process. By varying the relays parameters different points can be determined. The auto-tuner contains a procedure which converges rapidly to the desired critical point while maintaining the amplitudes of the process variables as well as of the manipulated variables within prespecified ranges. In the second stage, the data of the desired critical point is used to tune the PID controllers by the Ziegler-Nichols rules or their modifications. This paper focuses on the first stage. The steady-state process gains, which are required for the appropriate choice of the desired critical point, are determined by the auto-tuner in closed-loop fashion simultaneously with the identification of the critical point. The identification of the process gains is achieved at no extra plant time. Based upon a large number of simulated cases, the proposed auto-tuner seems to be efficient and robust. The paper discusses the underlying principles of the auto-tuner and its properties and capabilities are demonstrated via examples.

Closed loop identification of MPC models for MIMO processes using genetic algorithms and dithering one variable at a time: Application to an industrial distillation tower

Model Predictive Controllers (MPC) typically use step response models. The identification of these models is usually carried out under Open-Loop conditions, where large quantities of data are collected and/or large process perturbations are used. This makes the identification simpler, but is costly in terms of personnel requirements and degraded process performance during the test. This paper reports a methodology for identifying Multiple-Input Multiple-Output (MIMO) step response models while the process is operating under multivariable control. The identification of MIMO step response models can be achieved by adding an external test signal to one variable at a time. The method has been successfully applied to a distillation tower in a petroleum refinery. During the test the tower was controlled by an existing MPC with the constraint handling active.