SLIDING MODE CONTROL AND ITS APPLICATION

SLIDING MODE CONTROL AND ITS

APPLICATION

Mr.BINDUTESH V SANER

Guided by Prof. B.J PARVAT

Pravara Rural Engineering College, Loni

11/11/2015

Mr.BINDUTESH V SANER SLIDING MODE CONTROL AND ITS APPLICATION

CONTENTS

1. INTRODUCTION

2. SLIDING MODE CONTROL

3. CONCEPT OF SLIDING MODE CONTROL

4. CHATTERING MAIN DRAWBACK

5. CHATTERING REDUCTION METHOD

6. MERITS & DEMERITS

7. DRAWBACK OF SMC

8. SMC IN TRANSLATIONAL TRAJECTOY OF QUADROTOR

9. CONCLUSION

10. REFERENCE


INTRODUCTION

◮ An ideal sliding mode exists only when the system statesatisfies the dynamic equation that governs the sliding modefor all time. This requires an infinite switching, in general, toensure the sliding motion.

◮ The sliding mode control approach is recognized as one of theefficient tools to design robust controllers for complexhigh-order nonlinear dynamic plant operating underuncertainty conditions.

◮ sliding controller design provides a systematic approach to theproblem of maintaining stability and consistent performance.


CONCEPT OF SLIDING MODE CONTROLLER

Advantage of sliding mode controllers is their insensitivity toparameter variations and disturbances once in the sliding mode,there by eliminating the necessity of exact modeling.The SMC design is composed of two steps.

◮ In the first step, a custom-made surface should be designed.While on the sliding surface, the plants dynamics is restrictedto the equations of the surface and is robust to match plantuncertainties and external disturbances.

◮ In the second step, a feedback control law should be designedto provide convergence of a systems trajectory to the slidingsurface; thus, the sliding surface should be obtained in a finitetime. The systems motion on the sliding surface is called thesliding mode.


◮ First Step: The first step in SMC is to define the slidingsurface, S(t),which represents a desired global behavior, such as stabilityand tracking performance.

s(t) = (d

dt+ λ)

nt∫

0

e(t)dt

◮ Second step: once the sliding surface has been selected,attention must be turned to designing the control law thatdrives the controlled variable to its reference value andsatisfies equation

U(t) = Uc(t) + Ud(t)

whereUd = b−1[−a1x1 − (c + a2)x2 − n sin(σ)]

◮ The continuous part is given by

Uc(t) = f (x(t), r(t))


Cont...

◮ The continuous part of the controller is obtained bycombining the process model and sliding condition.The discontinuous part is nonlinear and represents theswitching element of the control law.

◮ The aggressiveness to reach the sliding surface depends on thecontrol gain but if the controller is too aggressive it cancollaborate with the chattering.

UD(t) = KD

s(t)

| s(t) | +δ


Cont...

sliding mode can be clearly understood by the below figure


◮ Reaching phase:In this phase a trajectory, starting from anonzero initial condition and reach to sliding surface.

◮ Sliding surface:In which the trajectory on reaching the slidingsurface, remains there for all further times and thus evolvesaccording to the dynamics specified by the sliding surface.


CHATTERING main drawback of SMC

◮ In theory, the trajectories slide along the switching function.

◮ In practice, there is high frequency switching.

◮ A high-frequency motion called chattering (the states arerepeatedly crossing the surface rather than remaining on it),so that no ideal sliding mode can occur in practice.

◮ Yet, solutions have been developed to reduce the chatteringand so that the trajectories remain in a small neighborhood(boundary) of the surface.

Called as chattering because of the sound made by oldmechanical switches.


CHATTERING- REDUCTION

Chattering could be reduced or suppressed using differenttechnique such as,

◮ Non-linear gains

◮ Dynamic extension

◮ Higher order sliding mode control


MERITS & DEMERITS

MERIT

◮ Controller design provides a systematic approach to theproblem of maintaining stability & consistent performance inthe face of modeling imprecision.

◮ Possibility of stabilizing some nonlinear systems which are notstabilizable by continuous state feedback laws.

◮ Robustness property that is once the system is on slidingsurface then it produced bounded parameter variation andbounded disturbances.

DEMERITS

◮ The main obstacle to the success of these techniques in theindustrial community is the implementation had an importantdrawback that is the actuators had to cope with the high

frequency control actions that could produce prematurewear or even breaking.


What SMC does in quadrotor vehicles?

◮ Sliding mode control was chosen for its ability to stabilize theplatform in the face of unknown modeling errors.

◮ The control scheme operates by forcing an error vector towarda sliding surface in the state space .

◮ Once on the sliding surface, the vehicles dynamics are definedby the dynamics of the surface. These dynamicsconverge(move towards one point ie. towards sliding surface)the error vector towards zero.

◮ Sliding modes to control the quadrotor, but computed desiredroll and pitch angles as the controller output instead ofcalculating motor speeds.


Depicting the Euler angles of roll (φ), pitch(θ), and yaw(ψ) andthe cartesian co-ordinate frame.

◮ The motors operate in pairs with motors 1 and 3 operatingtogether and motors 2 and 4 operating together. By varyingthe speed of a motor, it is possible to manipulate the

generalized lift force.

◮ Changing the relative speeds of motors 1 and 3 controls thepitch angle, and consequently creates motion in the x-axis.

◮ Varying the speeds of motors 2 and 4 creates a roll anglewhich creates translational motion in the y-axis.

◮ Altitude is controlled by the sum of the forces of all themotors.

◮ Yaw moment is created from the difference in thecounter-torques between each pair of motors.


Figure: Quadrotor vehicle(non-linear system)


Model assumption for Quadrotor

For translational motion, the inputs become a desired roll, pitchand yaw value to create an attitude that translates the quadrotorto the desired position.To verify the validity of those assumptions, an estimated modelwas computed from groundtruth data to determine the accuracyand bounds of the parameters in the estimated model.The estimated model is shown in equation with the calculatedparameters.

x = 10.84(CφSθCψ + SφSψ)− 0.37x + 0.16 (1)

y = −10.49(CφSθCψ − SφCψ)− 0.18y − 0.28 (2)


Chattering effect

When the system is operating near the manifold(s ≈ 0), noise inthe observed quantities causes chatter to result from the functionsign(s). The function is smoothed using the approximation sign(s).control chatter is evident as shown in Figure.

Figure: Control Response with Chattering


Simulation result

Figure shows where the red line is the desired position/attitudeand the blue line is the simulated position/attitude.


Conclusion

◮ SMC has been an important theoretical research field. Today,it is becoming a good source of solutions to real-worldproblems. Its potential is limited only by the imagination ofthe people working in process control. Therefore, theprospects for the application for SMC in the processingindustries are immense.

◮ Main benefits of sliding mode control are the invariance andquality properties and the ability to minimize the problemsinto sub-tasks of lower in balance.

◮ However, it has been shown that imperfections in switchingdevices and delays were inducing.


REFERENCES

◮ H. Bouadi, M. Bouchoucha, and M. Tadjine, Sliding mode

control based on backstepping approach for an uav

typequadrotor, International Journal of Applied Mathematicsand Computer Sciences, vol. 4, no. 1, pp. 1217, 2008.

◮ William selby paper on sliding mode control for translational

trajectory following for a quadrotor vehicle 2012

◮ Slotine, J. J., and Li, W., Applied Nonlinear Control,Englewood Cliffs, NJ: Prentice Hall, 1991.


Thank you...!
