1. 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

2. 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

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

4. Introduction

5. 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

6. 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

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

8. 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

9. 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

10. 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

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

12. 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

13. 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

14. 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:

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

16. 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.

17. 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.

18. 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

19. 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,

20. 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

21. Chattering reduction

22. Dead time approximations

23. Taylor series and Pade aproximation

24. 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

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

26. Controller and tunings

27. SMC Scheme

28. Processes with difficult dynamics

29. Inverse response

30. Integrating systems

31. MIMO processes

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

33. SP-SMC

34. Simulation Results

35. PID vs SMC (Variable deadtime)

36. DTSMC vs DTC

37. Robustness plot .

38. SMC Implementation

39. SMC Implementation

40. SMC Implementation

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

42. Operation
PID

43. 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.

44. 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 , (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).

45. 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