Sliding Mode Control: An Approach To Regulate Nonlinear Chemical Processes Oscar Camacho, Ph.D. Universidad de Los Andes, Venezuela Investigador Prometeo Escuela Politécnica Nacional Quito, Ecuador

Outline Introduction. Sliding Mode control(Basic concepts). Phase portrait of SMC. Reaching condition and the reaching mode Sliding condition and the sliding mode The VCS controller equation Design summary Considerations to design a SMC

Outline Chemical process Comparison between approaches Empirical models Considerations SMC approach SMC scheme SP-SMC Some results Conclusions References

Introduction

Introduction Most of the controllers synthesis come from models Models can be imprecise From a control point of view, modeling inaccuracies can be classified into: Structured or parametric: Inaccuracies on the terms included in the model Unstructured or unmodeled dynamics: Inaccuracies on system order

Introduction Modeling innacuracies can have strong adverse effects on nonlinear control systems. In the formulation of any control system, there will tipically be discrepancies between the actual plant and the mathematical model developed for control design. The engineer must ensure that resulting controller has the ability to produce the required performance levels in practice in spite plant/model mismatches

Introduction Robust control methods seek to solve the previous problem One particular approach to robust control design is: Sliding Mode Control Methodology

Sliding Mode Control (SMC) It is a particular type of Variable Structure control (VSC) (Emelianov,Utkin) VSCs are characterized by a suite of feedback control laws and a decision rule The decision rule, called the switching function. The switching function has as its input some measured of the current system behavior, and produces as an output the particular feedback controller

Sliding Mode Control (SMC) Let us define a time varying switching surface S(t) by: Where: The error is defined as ℷ › 0 and n is the order of the system The problem of tracking is equivalent to S(t)=0 S(t)=0 represents a motion called sliding motion

Phase Portrait of the System The first part is the reaching mode, also called nonsliding mode, in which the trajectory starting from anywhere on the phase plane moves toward a switching line and reaches the line in finite time. The second part is the sliding mode in which the trajectory asymptotically tends to the origin of the phase plane The line that describes S(t)=0, define the transient response of the system during the sliding mode During the sliding mode , trajectory dynamics are of lower order than the original model

Reaching condition and the reaching mode The following approach is used to prove the reaching condition: Direct switching function approach Or equivalent

Sliding condition or sliding mode Equivalent control procedure Which means that the trajectory is moving tangent to the sliding surface until reach the desired final value. Using the model process and the sliding condition, the equivalent control is obtained

Design summary The controller has two parts: Which is responsible for keeping the process variable on the surface, by solving: It is obtained an expression called the equivalent control, which can be interpreted as the continuous part of the controller

Design summary And It is responsible for guiding the process variable to the sliding surface . It consists in a gain switching around S(x,t). It can be represented by:

Design summary The discontinuous part is nonlinear and represents the switching element of the control law causing chattering around of the sliding surface.

Considerations to design a SMC Sliding surface or switching surface is defined or chosen by the user. S(t)=0 represents the desired system dynamics, which is of lower order than the given plant. High speed switching control is used to drive the state to the sliding surface. Once on the sliding surface, the state slides on the surface until reaches the equilibrium point, or desired final value.

Chemical processes Even though Sliding Mode Control has been widely investigated for a variety of systems, none of the previous works had presented a general approach for processes industry. Industrial chemical processes modeled using first principles tend to be of higher order and with complexity, the traditional SMC procedures present disadvantages in their application.

Comparison between approaches Characteristic Design depends on process model Inherent problem Chemical Processes models are difficult to obtain Solution The controller structure changes for each process Fixed structure Conventional Proposed

Proposal The robustness of the SMCr will compensate for modeling errors arising from the linearization of the non- linear model of the process Reduced order models present uncertainties arising from imperfect knowledge of the model. The process nonlinear effects contribute to performance degradation of controllers,

Empirical models Reaction Curve Method Empirical methods use low order linear models; most of the time First-Order-Plus Deadtime (FOPDT) models. This kind of model is able to adequately represent the dynamics of many industrial processes, especially chemical processes, over a range of frequencies, and is easily obtained from the reaction curve method

Chattering reduction

Dead time approximations

Taylor series and Pade aproximation

SMC Approach Reaching Mode Sliding Surface S(t)=0 Chattering!! de(t)/dt Sliding Mode e(t) If a general reduced order model of the process can be obtained and chattering can be reduced, This control strategy can become one of the most important discoveries in the process control field Substituting system dynamic equations

Controller synthesis (*) And since this is a second-order differential equation n = 2

Controller and tunings

SMC Scheme

Processes with difficult dynamics

Inverse response

Integrating systems

MIMO processes

Summary of tunings for SMCrs Self-regulating Inverse Response Integrating Deadtime compensator Multivariable λ1 λ0 KD δ

SP-SMC

Simulation Results

PID vs SMC (Variable deadtime)

DTSMC vs DTC

Robustness plot .

SMC Implementation

SMC Implementation

SMC Implementation

SMC Implementation In DCS Control room Operation 4 – 20 mA Field

Operation PID

Conclusions The proposed approach overcome traditional control schemes. The proposed controller can be used for SISO and MIMO systems. It can be used for process with elevated dead time, inverse response and integrating systems. The experimental results indicate the fact that the SMC is applicable to practical control systems.

References Murat Furat, Ve İlyas Eker “Experimental Evaluation of Sliding-Mode Control Techniques.” Çukurova University Journal of the Faculty of Engineering and Architecture, 27(1), pp. 23-37, (2012) B. B. Musmade , R. K. Munje, B. M. Patre . “Design of Sliding Mode Controller to Chemical Processes For Improved Performance”. International Journal of Control and Automation. (2011) Rong Hui –gui, Zhen Hui, Li zheng . “Tuning of Fuzzy PID controller for Smith Predictor.” J. Cent South Univ. Technol (2010). Camacho Oscar, R. Rojas and W. García-Gabin. “Some Long Time Delay Sliding Mode Control Approaches”. ISA Transactions, (2007) Chyi-Tsong Chen and Shih-Tien Peng. Design of a sliding mode control system for chemical processes. Journal of Process Control. (2005) Camacho Oscar and C. Smith, “Sliding Mode Control An Approach To Regulate Nonlinear Chemical Processes”. ISA Transactions. (2000).

Sliding Mode Control: An Approach To Regulate Nonlinear Chemical Processes Oscar Camacho, Ph.D. Universidad de Los Andes, Venezuela Investigador Prometeo Escuela Politécnica Nacional Quito, Ecuador