Standard Sliding Mode Control Research Articles

Trajectory tracking for non-holonomic mobile robots: A comparison of sliding mode control approaches

This paper implements and compares the performance of three controllers based on Sliding Mode Control (SMC) applied to the motion control of mobile robots. The controllers include a standard SMC controller and two variations, namely Dynamic Sliding Mode Control (D-SMC) and Dual Sliding Mode Control (DM-SMC). The three controllers differ from conventional SMC approaches since they are designed based on a generic reduced-order empirical model that can represent any system that exhibits behavior akin to a First-Order Plus Delay Time (FOPDT) system. In this study, the comparison of controllers focuses on the Trajectory Tracking Problem (TTP) of a Nonholonomic Mobile Robot (NMR). Performance indices are employed to quantify the controllers' results across three trajectory types. Simulation results evidence that if a smooth curvature trajectory is tracked, the best performance (in terms of minimizing trajectory tracking error and controller effort) can be obtained by using a DM-SMC. On the other hand, if there are discontinuities in the curvature, the results suggest that a better alternative is the D-SMC since it compensates for abrupt changes as in the case of tracking a square trajectory. Overall, the findings from this work demonstrated that the use of simplified empirical models to design SMC-based motion controllers can be successfully applied to solve the TTP of NMR.

Improved super-twisting sliding mode control strategy in permanent magnet synchronous motors for hydrogen fuel cell centrifugal compressor

This paper rigorously addresses the intricate control demands of high-speed, high-pressure, wide adjustable speed range, and high energy utilization efficiency required in hydrogen fuel cell centrifugal compressor, with a focus on the speed control of 40,000 RPM permanent magnet synchronous motors (PMSMs). An improved second-order super twisting sliding mode control (STSMC) strategy is proposed to enhance system stability and robustness by integrating the beetle antennae search (BAS) algorithm and grey wolf optimization (GWO) algorithm. The global search capability of BAS is used to improve the local optima issues of GWO, and then the improved GWO algorithm is utilized to address the issues related to parameter selection and convergence speed inherent in the STSMC. Theoretical validity of the proposed strategy is asserted through Quadratic Lyapunov Function, and its practicality is affirmed by thorough simulation. Comparative analyses are conducted with PI controller, traditional Sliding Mode Controller (SMC), and standard Super-Twisting Sliding Mode Controller (ST) under several case studies to show the superiority of the propose STSMC.

Variable-gain sliding mode control for quadrotor vehicles: Lyapunov-based analysis and finite-time stability

This work presents a methodology for controlling a quadrotor vehicle in both regulation and trajectory tracking tasks when the system is affected by endogenous and exogenous disturbances. In the proposed approach, the quadrotor is driven by a second-order variable-gain sliding mode controller (VG-SMC), which includes a state-dependent variable-gain that allows enhancing the controller performance against disturbances. Besides, the proposed controller achieves finite-time convergence of the position and orientation error signals and their time derivatives. The performance of the closed-loop system is assessed by comparing it with a standard sliding mode controller whose control objective is to track two optimal smooth reference signals. The comparison between both controllers considers the undisturbed and the perturbed cases. Numerical simulations and experimental results demonstrate that the proposed VG-SMC controller provides better overall closed-loop results than those obtained by a fixed-gain sliding mode controller, despite the presence of disturbances.

A Novel Approach for Adaptive Partial Sliding Mode Controller Design and Tuning in Non-Minimum Phase Switch-Mode Power Supplies

In this article, a novel systematic approach is proposed for a partial sliding mode controller (SMC) design and tuning in non-minimum phase switch-mode power supplies (SMPS). To achieve a more simplified controller in comparison with the conventional SMCs, the partial SMC (PSMC) is introduced in this article, which just requires a part of the sliding surface for controller formulation. The accuracy of the developed PSMC is proved mathematically within the entire range of operation. Since the control parameters of the PSMC are not selected by trial and error, it can maintain the stability and robustness of the closed-loop system in a broad operational range. In this regard, and to develop a systematic approach for robust control of SMPS, a constant frequency equivalent SMC is designed using the converter nominal parameters. Then, the extracted controller is combined with an adaptive component to ensure asymptotical stability against load and line changes. Considering the Lyapunov stability criteria for nonlinear systems, it is proved that the presented SPMC can be used for output voltage regulation in both discontinuous and continuous operating modes with zero steady state error. To avoid the trial and error method during the controller tuning and parameters selection, the system characteristic equation is extracted using the Jacobian approach. Considering the roots of the characteristic equation and the stable range of the closed-loop system, the controller parameters are tuned. Furthermore, in addition to simulation, the developed approach is evaluated practically using the TMS3220F2810 digital signal processor. It is shown that the dynamic response of the proposed approach is faster than the standard double-loop SMC during load and line changes. Additionally, it is seen that the developed controller is robust against model changes in both continuous and discontinuous operations.

Smart hybrid active/semi-active distributed structural acoustic control of thin- and thick-walled piezo-sandwich bimorph spherical shell cloaks

A novel three dimensional underwater smart piezo-sandwich spherical shell cloak is designed and analyzed based on the hybrid active/semi-active distributed structural acoustic control strategy. The sandwich configuration consists of series- or parallel-connected piezoelectric (PZT) bimorph actuator skin layers collocated with a semi-active electro-rheological fluid (ERF) core layer. Two separate coupled elasto-acoustic formulations are systematically developed. The first model is based on the variational principle of structural mechanics and the approximate Kirchhoff-Love thin shell theory while the standard sliding mode control (SMC) scheme is utilized to activate the acoustic scattering extinction capability of the hybrid structure. The second model is built on the exact linear theory of 3D piezoelasticity and the classical state-space transfer matrix approach along with the active damping control (ADC) strategy. Extensive numerical simulations reveal that the best broadband backscattering cancellation performance can effectively be achieved with the smart hybrid active/semi-active bimorph piezo-sandwich spherical shell cloak operating in parallel connection. To quantify the overall cloaking performance of the proposed design, the percentage error (%Err) of the external cloaked field relative to the background incident pressure field is calculated at selected dominant structural resonance frequencies within eight designated frequency bands (regions I to VIII). The remarkable (near-perfect) cloaking performance of the parallel-connected thick-walled hybrid bimorph piezo-sandwich shell (25%shellcloak) is demonstrated in the intermediate to high frequency regions (i.e., below 1.5% error in regions I, and III to VIII). This excellent invisibility performance is somewhat degraded in a narrow low frequency band (i.e., up to 8% error in region II) which is primarily linked to the elasto-acoustic resonances due to the coherent coupling of various types of highly interacting fluid- and shell-borne peripheral waves. On the other hand, the superior cloaking performance of the parallel-connected thin-walled hybrid bimorph piezo-sandwich shell (7%shellcloak) is observed predominantly in the low frequency range (i.e., below 1.5% error in regions I and II), while this exceptional performance is gradually degraded as the incident wave frequency is increased (i.e., up to 6.5% error in regions III to VIII), where partial or directional cancellation of the scattered field mostly occurs. Also, some important practical issues and limitations regarding the experimental implementation of proposed hybrid active/semi-active acoustic cloaking device are briefly discussed.

Adaptive Fuzzy-Based SMC for Controlling Torque Ripples in Brushless DC Motor Drive Applications

The use of Brushless-DC (BLDC) motor drives in many industrial settings has grown in recent years. In an ideal situation, the torque generated via BLDC motors with a trapezoidal back electromotive force (BEMF) remains unchanged. But, in actuality, the generated torque is distorted by torque ripples (TRs). These TRs make it essential that variable-speed drives operate smoothly. Power electronic switches are used by BLDC motors during commutation, which causes harmonics within the armature current. Sliding-mode control (SMC) is parameter-resistant and dynamic. SMC design involves reaching and sliding. SMC flaws include chattering. A reduced discontinuous gain control policy may strengthen this problem. The controller’s dynamic responsiveness will degrade. The standard SMC strategy’s indefinite converging rate for error to zero lowers dynamic reaction time. For the SMC to converge indefinitely, an adaptive strategy in fuzzy-based SMC (hybrid control technique) is developed to control the TRs in BLDC motor drives. In a BLDC motor, the recommended controller is used to regulate the harmonics as well as the speed. Based on modeling with MATLAB and observations on an operational 3 kW BLDC motor, the suggested approach is beneficial in the lowering of torque waves and current harmonics. The findings reported here support the efficiency of the suggested approach.

Graph Approximating SM Discretization

Modern practical sliding mode (SM) control (SMC) involves discrete noisy sampling. Standard SMC discretizations feature the chattering effect, while implicit Euler methods need significant model knowledge, constant sampling steps and are difficult in application for higher relative degrees and multiple discontinuities. The proposed universal discretization method is based on the graph approximation of Filippov inclusions. It guaranties convergence to the continuous-time solutions and is computationally-simple. For the first time we demonstrate low-chattering discretization in the presence of large noises and multiple discontinuities.

A Singular Perturbation Approach-Based Non-Cascade Sliding Mode Control for Surface-Mounted PMSMs

Motivated by the fact that electrical transients are rather fast compared with mechanical response, the traditional cascade control structure constituted by the inner current and outer speed loops is usually employed in the permanent magnet synchronous motors (PMSMs) servo control community. According to the above-mentioned time-scale characteristic of the PMSMs drive systems, this technique addresses the problems of the non-cascade sliding mode control (SMC) strategy for the surface-mounted PMSMs. Firstly, by appropriately introducing the singular perturbation theory, the corresponding mathematical equations are modeled as a singular perturbation system. Meanwhile, a composite sliding mode surface is constructed based on the Lyapunov equation, such that the system stability can be also guaranteed. Then, according to the exponential reaching law, a standard non-cascade SMC law is designed. Furthermore, an optimal nonlinear function-based tracking differentiator (TD) is presented to smooth the reference velocity value, while providing differential signals. As a result, a novel TD-based SMC strategy is synthesized by incorporating a nonlinear function, thus improving the inherent chattering phenomenon. Finally, a surface-mounted PMSM servo system is performed to illustrate the advantages and effectiveness of the proposed approaches. The main contribution of this paper is to present an alternative non-cascade SMC framework based on the singular perturbation approach, which provides a novel control structure for a PMSM speed regulation system.

Optimized Fuzzy Enhanced Robust Control Design for a Stewart Parallel Robot

The remarkable properties of sliding mode control (SMC)—such as robustness, accuracy, and ease of implementation—have contributed to its wide adoption by the control community. To accurately compensate for parametric uncertainties, the switching part of the SMC controller should have gains that are sufficiently large to deal with uncertainties, but sufficiently small to minimize the chattering phenomena. Hence, proper adjustment of the SMC gains is crucial to ensure accurate and robust performance whist minimizing chattering. This paper proposes the design and implementation of an optimal fuzzy enhanced sliding mode control approach for a Stewart parallel robot platform. A systematic approach of designing the table of rules of the fuzzy system so as to provide the required coefficients of the sliding mode controller is proposed. The aim is to attain optimum performance and minimum control effort, thus eliminating the need for computationally expensive expert systems and yielding control outputs below the actuator saturation ranges. The proposed approach was validated using a six degrees-of-freedom Stewart platform subject to external disturbances. Its performance was compared to that of a standard SMC approach. The obtained results and comparative study showed that the proposed control algorithm not only reduces chattering, but also responds effectively to the realistic demands of control energy, while preventing actuator saturation.

Vertical thrust-based effective flat-spin recovery of aircraft restricting altitude loss

Among the various modes of aircraft spin, flat-spin being the most ruthless form, the severity and the flight parameters govern the recovery success rate. This paper presents a novel approach for utilizing vertical thrust to reduce the fatality of the flat-spin in terms of excessive altitude loss regulating the survivability post aircraft recovery. F-18 High Alpha Research Vehicle is considered for the present study to demonstrate effectiveness of the proposed method. The dynamics of vertical thrust add-on is conceptualized and incorporated to the standard aircraft. Subsequently, to validate the effectiveness of this mode of recovery as compared to the conventional primary control based method, standard sliding-mode control technique is adopted. Closed-loop simulation shows that vertical thrust restricts altitude loss and minimizes spin recovery time compared to the conventional mode of recovery from flat-spin. The outcome of the present study ensures the use of vertical thrust as a potential solution for minimizing aircraft flat-spin-related fatal accidents.

Adaptive super-twisting sliding mode control for maximum power point tracking of PMSG-based wind energy conversion systems

This paper proposes a super-twisting adaptive sliding mode control law for maximum power point tracking of wind energy conversion systems based on permanent magnet synchronous generators (PMSGs). The employed sliding mode control algorithm can be considered an effective solution, as it retains the robustness properties of classical sliding mode control methods in the presence of disturbances and parameter uncertainties; at the same time, it provides chattering reduction via gain adaptation and generation of second-order sliding modes. In our work, a nonlinear multi-input multi-output tracking control problem is solved to maximize the captured power. Simulation results are presented using real wind speed data, and discussed for the proposed controller and four other sliding mode control solutions for the same problem, in the presence of variations of stator resistance, stator inductance and magnetic flux linkage. The proposed controller achieves the best trade-off between tracking performance and chattering reduction among the five considered solutions: compared to a standard sliding mode control algorithm, it reduces the amount of chattering from two to five orders of magnitude, and the steady-state error on PMSG rotor velocity of one order of magnitude. Also, it reduces the above-mentioned steady-state error of four orders of magnitude with respect to a previously-proposed linear quadratic regulator based integral sliding mode control law for the same system.

Adaptive output-feedback robust active disturbance rejection control for uncertain quadrotor with unknown disturbances

PurposeIn this research paper, an adaptive output-feedback robust active disturbance rejection control (RADRC) is designed for the multiple input multiple output (MIMO) quadrotor attitude model subject to unwanted uncertainties and disturbances (UUDs).Design/methodology/approachIn order to achieve the desired control objectives in the presence of UUDs, the low pass filter (LPF) and extended high gain observer (EHGO) methods are used for the estimation of matched and mismatched UUDs, respectively. Furthermore, for solving the chattering incurred in the standard sliding mode control (SMC), a multilayer sliding mode surface is constructed. For formulating the adaptive output-feedback RADRC algorithm, the EHGO, LPF and SMC schemes are combined using the separation principle.FindingsThe findings of this research work include the design of an adaptive output-feedback RADRC with the ability to negate the UUDs as well as estimate the unknown states of the quadrotor attitude model. In addition, the chattering problem is addressed by designing a modified SMC scheme based on the multilayer sliding mode surface obtained by utilizing the estimated state variables. This sliding mode surface is also used to obtain the adaptive criteria for the switching design gain parameters involved in the SMC. Moreover, the requirement of high design gain parameters in the EHGO is solved by combining it with the LPF.Originality/valueDesigning the flight control techniques while assuming that the state variables are available is a common practice. In addition, to obtain robustness, the SMC technique is widely used. However, in practice, the state variables might not be available due to unknown parameters and uncertainties, as well as the chattering due to SMC reduces the performances of the actuators. Hence, in this paper, an adaptive output-feedback RADRC technique is designed to solve the problems of UUDs and chattering.

Disturbance observer-based robust adaptive control for uncertain actuated nonlinear systemwith disturbances

PurposeThe aim of this research paper is to design a disturbance observer (DO)-based robust adaptive tracking control of uncertain nonlinear system subject to unknown nonlinear disturbance.Design/methodology/approachTo achieve desired control objectives, i.e. nonlinear trajectory tracking and disturbance attenuation, firstly, a control scheme is designed based on the adaptive criteria integrated in sliding mode control (SMC). In the second step, the disturbance estimation criterion is designed followed by patching with the controller obtained in the first step. Following the control development, using the Lyapunov candidate function, the stability criterion is ensured by designing appropriate adaptive gains.FindingsIn this paper, a robust adaptive nonlinear tracking method is presented. The findings includes the design of adaptive gains for the control parameters involved in the robust SMC technique, i.e. adaptive criterion is designed for the switching gain as well as for the gain used in sliding mode surface. Furthermore, a disturbance estimation criterion is developed to attenuate nonlinear disturbances with variable frequency and magnitude. Finally, the disturbance estimation scheme is combined with the control technique to obtain DO-based control (DOBC) algorithm.Practical implicationsSliding mode control is a powerful robust control method. And, combining it with the DO achieves the control objectives of plants subject to disturbances and uncertainties. However, usually the uncertainties and disturbances are unknown and time varying. Thus, during practical implementation, designing the standard SMC is a challenging task due to the constant gains involved in the control design. Hence, it is important to have a criterion which adapts to the varying dynamics of plants due to the uncertainties and disturbances for achieving practical implementation of the control system.Originality/valueSliding mode control has been widely used for achieving the desired control objectives and robustness in the close-loop nonlinear systems. Besides, the SMC technique has been combined with the DOs as well. However, mostly the ideal conditions were considered during these developments, which required the control gains to be designed simply by manual tuning appropriately. However, by considering the real-time dynamics, uncertainties and disturbances, the constant control gain criteria can fail. Furthermore, due to external and internal disturbances, the model plant can vary with time. Thus, it is important to design the adaptive criteria for the control gains in DOBC schemes.

Power quality improvement in distribution system using distribution static compensator with super twisting sliding mode control

Nowadays, power quality (PQ) issues are gaining considerable attention to both electrical utilities and end-users as they are causing significant financial losses to industrial customers. Among PQ issues, voltage sag and swell are the most important and frequently occurring problems for sensitive load. Voltage sag/swell can be mitigated using a distribution static compensator (DSTATCOM), which is fast, effective, and flexible custom power device. Its performance mostly depends upon the designed control scheme for the switching of voltage source converter (VSC). In this research work, a fused control scheme based on second-order super twisting algorithm (STA) and sliding mode control (SMC) for VSC of DSTATCOM is developed, that can effectively eliminate the effects of voltage sag/swell as well as compensate active and reactive power in distribution system. STA along with standard SMC is used to eliminate the chattering effect which is the drawback of SMC alone, while keeping its other properties such as robustness, faster response time, and insensitive to load variation. The proposed control scheme for DSTATCOM is simulated on SimPower system toolbox of MATLAB/Simulink. Both linear as well as nonlinear loads have been considered for the purpose of static and dynamic analysis. Simulation results show that the super twisting sliding mode control (STSMC) for DSTATCOM can effectively detect and correct voltage sag/swell and compensate active and reactive power within 2.5 milliseconds as per semiconductor processing equipment voltage sag immunity standard for sensitive load (SEMI F-47 Standard). Total harmonic distortions (THD) measured in all simulated cases is found to be less than 5%. The frequency response analysis shows good stability properties of developed system. A comparison analysis is also carried out between the classical SMC and the proposed STSMC, in which the proposed algorithm with SMC shows better performance than classical SMC.

A fractional order sliding mode control-based topology to improve the transient stability of wind energy systems

This paper proposes a control topology that integrates the robust performance of fractional order sliding mode control with the high charging/discharging rate and low maintenance requirements of super-capacitors to improve the transient stability of wind energy systems. The observer-based fractional-order sliding mode control (FOSMC) approach is designed to regulate the dc-link voltage and mitigate dynamic instabilities resulting from grid faults, matched and mismatched uncertainties and parameter variations. The super-capacitor, on the other hand, serves as an additional energy storage element that prevents dangerous current surges thereby stabilizing the power delivered to the grid. The proposed approach was validated using a DFIG-based wind energy system installed in a small-scale standalone power supply network. The obtained results confirmed the approach’s ability to effectively reduce current fault induced ripples and properly regulate the dc link voltage. They also revealed a remarkable reduction in the thermal stress of semiconductor junctions in the presence of grid faults and disturbances. A further comparison with a standard sliding mode control (SSMC) approach showed that the use of fractional calculus to formulate the FOSMC resulted in smoother control actions and reduced chattering effects compared to SSMC.

Robust active disturbance attenuation control of an uncertain quadrotor

PurposeThe aim of this research is to design a robust active disturbance attenuation control (RADAC) technique combined with an extended high gain observer (EHGO) and low pass filter (LPF).Design/methodology/approachFor designing a RADAC technique, the sliding mode control (SMC) method is used. Since the standard method of SMC exhibits a chattering phenomenon in the controller, a multilayer sliding mode surface is designed for avoiding the chattering. In addition, to attenuate the unwanted uncertainties and disturbances (UUDs), the techniques of EHGO and LPF are deployed. Besides acting as a patch for disturbance attenuation, the EHGO design estimates the state variables. To investigate the stability and effectiveness of the designed control algorithm, the stability analysis followed by the simulation study is presented.FindingsThe major findings include the design of a chattering-free RADAC controller based on the multilayer sliding mode surface. Furthermore, a criterion of integrating the LPF scheme within the EHGO scheme is also developed to attenuate matched and mismatched UUDs.Practical implicationsIn practice, the quadrotor flight is opposed by different kinds of the UUDs. And, the model of the quadrotor is a highly nonlinear underactuated model. Thus, the dynamics of the quadrotor model become more complex and uncertain due to the additional UUDs. Hence, it is necessary to design a robust disturbance attenuation technique with the ability to estimate the state variables and attenuate the UUDs and also achieve the desired control objectives.Originality/valueDesigning control methods to attenuate the disturbances while assuming that the state variables are known is a common practice. However, investigating the uncertain plants with unknown states along with the disturbances is rarely taken in consideration for the control design. Hence, this paper presents a control algorithm to address the issues of the UUDs as well as investigate a criterion to reduce the chattering incurred in the controller due to the standard SMC algorithm.

Adaptive Robust Fault-Tolerant Control Design for Wind Turbines Subject to Pitch Actuator Faults

This paper proposes an adaptive fault tolerant control (FTC) design for a variable speed wind turbine (WT) operating in the high wind speeds region. It aims at mitigating pitch actuator faults and regulating the generator power to its rated value, thereby reducing the mechanical stress in the high wind speeds region. The proposed FTC design implements a sliding mode control (SMC) approach with an adaptation law that estimates the upper bounds of the uncertainties. System stability and uniform boundedness of the outputs was proven using the Lyapunov stability theory. The proposed approach was validated on a 5 MW three-blade wind turbine modeled using the National Renewable Energy Laboratory’s (NREL) Fatigue, Aerodynamics, Structures and Turbulence (FAST) wind turbine simulator. The controller’s performance was assessed in the presence of several pitch actuator faults and turbulent wind conditions. Its performance was also compared to that of a standard SMC approach. Mitigation of blade pitch actuator faults, generation of uniform power, smoother pitching actions and reduced chattering compared to standard SMC approach are among the main features of the proposed design.

A robust controller for a variable-speed wind turbine using a single mass model

In this paper, a robust nonlinear controller based on integral sliding mode control (ISMC) strategy was proposed to maximize the captured energy for a variable speed wind turbine (VSWT). In order to reduce the reaching phase, an integral action is introduced in the switching surface of the sliding mode control (SMC) for a minimum steady state error. The controlled system stability is demonstrated using the Lyapunov theory and the trajectory tracking error converges in finite time to zero without any chattering problems. Various simulations, carried out via Matlab software, are discussed to highlight the proposed method performance, using a nonlinear single mass model. Finally, the simulation results show that the proposed Integral SMC strategy ensures better response speed and smaller steady-state error compared to the standard SMC.

Design of a chattering‐free integral terminal sliding mode approach for DFIG‐based wind energy systems

SummaryThis article proposes a Fuzzy Second Order Integral Terminal Sliding Mode (FSOITSM) control approach for DFIG‐based wind turbines subject to grid faults and parameter variations. Since traditional terminal sliding mode control (SMC) suffers from singularity, a novel integral terminal sliding manifold is proposed to eliminate chattering and improve the wind turbine's performance in the presence of faults and disturbances. A fuzzy system is proposed to auto‐tune the controllers' gains and ensures the invariance of the sliding surfaces even under heavy uncertainties, thus further improving the reliability and performance of the proposed controller. The performance of the proposed approach was assessed under various operating conditions. A comparison analysis with a standard SMC approach as well as the state of the art in voltage sag mitigation was also carried over. Reliability, robustness, and power availability under faulty grid conditions are among the main features of the proposed approach. In addition, the proposed approach exhibited chattering free dynamics and enabled the finite time convergence of the sliding manifold and overcame the singularity problem associated with standard TSMC.

Inter network synchronisation of complex dynamical networks by using smooth proportional integral SMC technique

This paper puts forward the inter network synchronisation of complex dynamical networks (CDNs) using drive-response philosophy. The inter networks consist of a drive network (each node represents a hyperchaotic system) and a response network (consists of chaotic system at each node). Synchronisation is achieved using a novel proportional integral (PI) based sliding mode control (SMC) scheme and inter network synchronisation criterion is derived. Unlike the conventional SMC technique, the proposed proportional integral-sliding mode control (PI-SMC) technique does not result decoupled error dynamics. A smooth switching surface is designed to eliminate the chattering effect. The different network configurations: small-world and scale-free networks, are simulated and the simulation results show that the proposed synchronisation scheme is effective for the inter network synchronisation between two or more CDNs. The effect of relevant parameters on the synchronisation process in the Watts-Strogatz (WS) small-world and Barabasi-Albert (BA) scale-free networks are analysed. Finally, the proposed PI-SMC technique is compared with standard SMC technique to justify the advantages over the standard SMC technique.