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Showing papers presented at "Mediterranean Conference on Control and Automation in 2010"


Proceedings ArticleDOI
23 Jun 2010
TL;DR: In this paper, a new method for the estimation of the maximum tire/road friction coefficient is proposed to automatically detect possible state of loss of friction which result in an abrupt change on the road state.
Abstract: Recent statistics show that a large number of traffic accidents occur due to a loss of control on vehicle by the driver. This is mainly due to a loss of friction between tire and road. Many of these accidents could be avoided by introducing ADAS (Advanced Driver Assistance Systems) based on the detection of loss of tire/road friction. Friction (more specifically the maximum coefficient of friction) which is a parameter of tire/road interaction, mainly depends on the state of the road (dry, wet, snow, ice) and is closely related to the efforts at the tire level. In this paper, we propose, a new method for the estimation of the maximum tire/road friction coefficient, to automatically detect possible state of loss of friction which result in an abrupt change on the road state. This method is based on an iterative quadratic minimization of the error between the developed lateral force and the model of tire/road interaction. Results validate the application of the method.

80 citations


Proceedings ArticleDOI
23 Jun 2010
TL;DR: In this paper, a Model Predictive Control scheme based on Piecewise Affine (PWA) modeling of an Unmanned Quadrotor Helicopter (UqH) in attitude maneuvers is proposed.
Abstract: Accurate navigation and control of unmanned quadrotor helicopters in harsh environmental conditions due to wind disturbances is an open challenge. The aim of the work presented in this article is the design of a Model Predictive Control scheme based on Piecewise Affine (PWA) modeling of an Unmanned quadrotor Helicopter (UqH) in attitude maneuvers. The suggested algorithm is verified in experimental studies in the execution of sudden maneuvers subject to forcible wind disturbances. The UqH manages to reject the induced wind-disturbances while performing accurate attitude tracking.

52 citations


Proceedings ArticleDOI
23 Jun 2010
TL;DR: In this article, the authors present an intelligent control method for the maximum power point tracking (MPPT) of a photovoltaic system under variable temperature and insulation conditions using a fuzzy logic controller.
Abstract: This paper presents the analysis, modelling and control model of the electric part of a grid connected photovoltaic generation system. The model contains a detailed representation of the main components of the system that are the solar array, and the grid side multilevel neutral point clamped (NPC) voltage source inverter (VSI). In order to extract the maximum amount of from the photovoltaic generator, we propose an intelligent control method for the maximum power point tracking (MPPT) of a photovoltaic system under variable temperature and insulation conditions. This method uses a fuzzy logic controller. As part of our work, we will focus on voltage inverter at three levels to NPC structure. The latter can increase the voltage supplied to the load (network) through their topology. Thus, they can generate more voltage sinusoidal possible and improve the total harmonic distortion through the high voltage levels provided by the structure of this new converter. The grid interface inverter transfers the energy drawn from the PV module into the grid by keeping common dc voltage constant. The PQ control approach (Direct Power Control) has been presented for the multilevel inverter. The simulation results under Matlab/Simulink show the control performance and dynamic behaviour of grid connected photovoltaic system.

52 citations


Proceedings ArticleDOI
23 Jun 2010
TL;DR: A mathematical explanation of the ubiquity of PID controllers in the industry is provided by comparing their sampling with the one of “intelligent” PID controllers, which were recently introduced.
Abstract: The ubiquity of PID controllers in the industry has remained mysterious until now. We provide here a mathematical explanation of this strange phenomenon by comparing their sampling with the the one of “intelligent” PID controllers, which were recently introduced. Some computer simulations nevertheless confirm the superiority of the new intelligent feedback design.

47 citations


Proceedings ArticleDOI
23 Jun 2010
TL;DR: In this article, the design of linear quadratic Gaussian (LQG) controllers for variable-speed horizontal axis wind turbine (WT) is studied. And the main control objectives are to reduce structural dynamic loads and to regulate the power of the WT.
Abstract: This paper focuses on the design of Linear Quadratic Gaussian (LQG) controllers for variable-speed horizontal axis Wind Turbines (WT). These turbines use blade pitch angle and electromagnetic torque control variables to meet specified objectives for Full Load (FL) zone. The main control objectives are to reduce structural dynamic loads and to regulate the power of the WT. The controllers are designed in order to optimize a trade-off between several control objectives. Four different LQG using Individual Pitch Control (IPC) are designed, with Wireless-Sensors (WS) placed at the end of the blades for the last one. Their control model is progressively more complex. The first one takes into account a rigid simple behavior, the second control model considers the first mode of the drive-train flexibility, the third model takes into account the drive-train and tower flexibilities and the fourth that of the blades. Likewise, their optimization criteria consider for each controller a new control objective to alleviate fatigue loads in the drive-train, then, also in the tower and finally also in the blades. The evaluation of the fatigue loads affecting the WT components are based on a Rainflow Counting Algorithm (RFC) and the Miner's rule. The results indicate a significant reduction of fatigue loads especially in the drive-train and the blades when its flexibility is taken into account in the control models.

44 citations


Proceedings ArticleDOI
23 Jun 2010
TL;DR: In this article, two different catching methods are proposed: first, catching of the ball during the initial contact, and then catching the ball after an initial rebounce during the subsequent contact.
Abstract: Most industrial robots nowadays still employ strategies that neglect or minimize the effects of task dynamics. Some tasks, however, are intrinsically dynamic and can only be accomplished by considering their dynamic aspects. We address ball catching as a prominent and widely studied example for such a task. The paper follows a special approach to accomplish the task: the nonprehensile catching, which means catching without a form- or force-closure grasp. Depending on the tracked ball velocity, two different catching methods are proposed: First, catching of the ball during the initial contact. Second, catching the ball after an initial rebounce during the subsequent contact. For both approaches, the ball trajectory is predicted with a recursive least squares algorithm. The dynamic manipulability measure is used for the contact point selection. Once a permanent contact between ball and end effector is established, a balancing control based on force/torque feedback is applied. Both methods are experimentally validated using a six DoF industrial robot.

39 citations


Proceedings ArticleDOI
23 Jun 2010
TL;DR: In this paper, a 2DOF exoskeleton robot (ExoRob) was developed to provide naturalistic range movements of elbow (flexion/extension) and forearm (pronation/supination) motions.
Abstract: To perform essential daily activities the movement of shoulder, elbow, and wrist play a vital role and therefore proper functioning of upper-limb is very much essential. We therefore have been developing an exoskeleton robot (ExoRob) to rehabilitate and to ease upper limb motion. Toward to make a complete (i.e., 7DOF) upper-arm motion assisted robotic exoskeleton this paper focused on the development of a 2DOF exoskeleton robot to rehabilitate the elbow and forearm movements. The proposed 2DOF ExoRob is supposed to be worn on the lateral side of forearm and provide naturalistic range movements of elbow (flexion/extension) and forearm (pronation/supination) motions. This paper also focuses on the modeling and control of the proposed ExoRob. A kinematic model of the ExoRob has been developed based on modified Denavit-Hartenberg notations. Nonlinear sliding mode control technique is employed in dynamic simulation of the proposed ExoRob, where trajectory tracking that corresponds to typical rehab (passive) exercises has been carried out to evaluate the effectiveness of the developed model and controller. Simulated results show that the controller is able to maneuver the ExoRob efficiently to track the desired trajectories, which in this case consisted in passive arm movements. These movements are widely used in rehab therapy and could be performed efficiently with the developed ExoRob and the controller.

35 citations


Proceedings ArticleDOI
23 Jun 2010
TL;DR: In this paper, a fault tolerant control strategy for nonlinear Takagi-Sugeno (T-S) systems is proposed, which aims to compensate the actuator faults and allow the system states to track a reference corresponding to a fault free situation.
Abstract: A new actuator fault tolerant control strategy is proposed for nonlinear Takagi-Sugeno (T-S) systems. The control law aims to compensate the actuator faults and allows the system states to track a reference corresponding to a fault free situation. The design of such a control law requires the knowledge of the faults, this task is achieved with a proportional integral observer (PIO). The robust stability of the system with the fault tolerant control law is analyzed with the Lyapunov theory and the ℒ 2 optimization. Sufficient stability conditions are obtained in terms of linear matrix inequalities (LMIs). The gains of the FTC are obtained by solving these LMIs. A simulation example is finally proposed.

34 citations


Proceedings ArticleDOI
23 Jun 2010
TL;DR: In this article, a systematic tuning of the prediction horizon, the control horizon and the penalty weights is discussed such that desired closed-loop pole and zero locations result as long as the constraints are not active.
Abstract: Model Predictive Control (MPC) is widely used in the process industries. A successful implementation of MPC involves the setting of a considerable number of parameters which must be appropriately tuned. Despite a number of publications on MPC tuning, there is a lack of a systematic approach that relates MPC tuning to linear control theory. In this paper, a systematic tuning of the prediction horizon, the control horizon and the penalty weights is discussed such that desired closed-loop pole and zero locations result as long as the constraints are not active. We verify our approach on two challenging examples.

33 citations


Proceedings ArticleDOI
23 Jun 2010
TL;DR: In this article, the asymptotic stabilization problem of linear singular fractional-order systems is studied in terms of linear matrix inequalities, which are derived using the decomposition on the matrices of the original system.
Abstract: This paper presents the asymptotical stabilization problem of linear singular fractional-order systems. The results are obtained in terms of linear matrix inequalities, which are derived using the decomposition on the matrices of the original system. An illustrative example is provided to illustrate the proposed results.

31 citations


Proceedings ArticleDOI
23 Jun 2010
TL;DR: In this article, the authors consider the problem of distributed bearing-only formation control, where each agent measures the inter-agent bearings in a local coordinate system and is tasked at maintaining a specified angular separation relative to its neighbors.
Abstract: We consider the problem of distributed bearing-only formation control. Each agent measures the inter-agent bearings in a local coordinate system and is tasked at maintaining a specified angular separation relative to its neighbors. The problem we consider differs from other problems in the literature since no inter-agent distance measurements are employed. Each agent's control law is distributed and based only on its locally measured bearings. A strong convergence result is established which guarantees global convergence of the formation to the desired shape while at the same time ensures that collisions are avoided naturally. We show that the control scheme is robust to agent motion failures and the presence of additional group motion inputs. Finally, we extend our system to the case where the agent's motion is restricted to a sphere.

Proceedings ArticleDOI
23 Jun 2010
TL;DR: This paper deals with a fuzzy bilinear observer design for a class of nonlinear systems and the proposed Takagi-Sugeno Fuzzy Bilinear Observer (T-S FBO) is proposed.
Abstract: This paper deals with a fuzzy bilinear observer design for a class of nonlinear systems. The nonlinear system is modeled as a Takagi-Sugeno fuzzy bilinear model. The observer stability is assured irrespective of the inputs and stability conditions are expressed in terms of Linear Matrix Inequality (LMI). A numerical example is given to demonstrate the effectiveness of the proposed Takagi-Sugeno Fuzzy Bilinear Observer (T-S FBO).

Proceedings ArticleDOI
23 Jun 2010
TL;DR: In this paper, the authors analyze how recognized robust PI/PID tuning rules accomplish with respect to its robustness specification. And they conclude that even if the robustness issue has been incorporated in the new approaches for tuning and design of PI/PI controllers, this does not sufficient.
Abstract: This paper analyzes how recognized robust PI/PID tuning rules accomplish with respect to its robustness specification. A concrete analysis is conducted where the chosen PI/PID controller tuning rules are based on a precise quantitative robustness specification such as the Maximum Sensitivity; Ms; value. It is reported that the claimed robustness specification in most of the cases is not accomplished for some set of plants, on other cases it is accomplished with excessive margin, therefore providing a not satisfactory Robustness/Performance tradeoff. The conclusion drawn from this study is that even if the robustness issue has been incorporated in the new approaches for tuning and design of PI/PID controllers, this does not sufficient. In order to appropriately tackle the Robustness/Performance tradeoff, the achieved robustness level should not only be an integral specification, but its accomplishment should be checked.

Proceedings ArticleDOI
23 Jun 2010
TL;DR: In this paper, the authors discuss two methods to generate trajectories for a magnetic-levitation (Maglev) system in the presence of constraints and compare each method's performance, based on the notion of differential flatness and spline parametrisation of every signal.
Abstract: In this work, we discuss two methods to generate trajectories for a magnetic-levitation (Maglev) system in the presence of constraints and compare each method's performance. The methods are based on the notion of differential flatness and spline parametrisation of every signal. The first method uses the nonlinear model of the plant, which turns out to belong to the class of flat systems. The second method uses a linearised version of the plant model around an operating point. In every case, a continuous-time description is used. Experimental results on a real Maglev system, reported here, show that, in most scenarios, the nonlinear and linearised model produce almost similar, indistinguishable trajectories.

Proceedings ArticleDOI
23 Jun 2010
TL;DR: The design and implementation of a control system for autonomous navigation based on a Service Oriented Architecture (SOA) supporting a mobile robot suitable for industrial applications and shows good real-time performances.
Abstract: This paper presents the design and implementation of a control system for autonomous navigation based on a Service Oriented Architecture (SOA) supporting a mobile robot suitable for industrial applications The robot is required to perform generic high-level tasks in indoor structured environments The control architecture, developed within the Microsoft Robotics Developer Studio (MRDS), allows to encapsulate the controller functionalities as a set of services that interact and exchange data among them This approach allows to guarantee flexibility, scalability and reliability The accurate testing, carried out in simulated and real environments, shows good real-time performances

Proceedings ArticleDOI
23 Jun 2010
TL;DR: The approach presents the reachability and observability Gramians of the switched systems, which allows a balanced truncation model reduction procedure, which helps to keep the biggest singular values of the system.
Abstract: This paper describes the problem of model orderreduction for a class of hybrid discrete-time switched linear systems composed of linear discrete-time invariant subsystems with a switching rule. The paper investigates a novel method to model reduction. The approach presents the reachability and observability Gramians of the switched systems, which allows a balanced truncation model reduction procedure. The error limit depends on the truncated singular values and balanced truncation procedure helps to keep the biggest singular values of the system. A numerical example shows the effectiveness of the proposed approach.

Proceedings ArticleDOI
23 Jun 2010
TL;DR: In this paper, the control problem of the wind turbine driven doubly fed induction generator (DFIG) is faced, both in wind park operator and system operator perspective, both from an ancillary services to the system operator and the maximization of wind park operators profitability.
Abstract: In this paper the control problem of the wind turbine driven doubly fed induction generator (DFIG) is faced, both in wind park operator and system operator perspective. Two control schemes are proposed, based on feedback linearization theory for MIMO systems and PI controllers: the first one for simultaneous active and reactive power regulation, the second one for simultaneous propeller angular speed and reactive power regulation. They are shown to allow the deliver of ancillary services to the system operator and the maximization of wind park operator profitability respectively.

Proceedings ArticleDOI
23 Jun 2010
TL;DR: In this paper, the authors generalize and strengthen the method of Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC) for the stabilization of mechanical systems, and derive a new set of matching conditions where the new kinetic matching conditions are simpler than those in the literature.
Abstract: We generalize and strengthen the method of Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC) for the stabilization of mechanical systems. First, we replace the skew symmetry property of the interconnection matrix with the energy conservation property, and introduce a gyroscopic force replacing the interconnection sub-matrix that is usually denoted by J 2 . Second, we derive a new set of matching conditions where the new kinetic matching conditions are simpler than those in the literature. Third, we provide a necessary and sufficient condition for Lyapunov/exponential stabilizability by IDA-PBC for the class of all linear mechanical systems. Last, we give a necessary and sufficient condition for Lyapunov/exponential stabilizability by IDA-PBC for the class of all mechanical systems with one degree of underactuation. These conditions are easy to verify without solving any PDE's. Our results comprehend and extend most results on IDA-PBC in the literature.

Proceedings ArticleDOI
23 Jun 2010
TL;DR: In this paper, an adaptive proportional integral observer is designed to estimate both the system state and sensor and actuator faults which can affect the system, and the model of the system is first augmented in such a manner that the original sensor faults appear as actuator fault in this new model.
Abstract: This paper deals with the problem of fault estimation for linear and nonlinear systems. An adaptive proportional integral observer is designed to estimate both the system state and sensor and actuator faults which can affect the system. The model of the system is first augmented in such a manner that the original sensor faults appear as actuator faults in this new model. The faults are then considered as unknown inputs and are estimated using a classical proportional-integral observer. The proposed method is first developed for linear systems and is then extended to nonlinear ones that can be represented by a Takagi-Sugeno model. In the two cases, examples of low dimensions illustrate the effectiveness of the proposed method.

Proceedings ArticleDOI
23 Jun 2010
TL;DR: This paper presents a simple continuous-time linear vaccination-based control strategy for a SEIR (susceptible plus infected plus infectious plus removed populations) propagation disease model that takes into account the total population amounts as a refrain for the illness transmission.
Abstract: This paper presents a simple continuous-time linear vaccination-based control strategy for a SEIR (susceptible plus infected plus infectious plus removed populations) propagation disease model. The model takes into account the total population amounts as a refrain for the illness transmission since its increase makes more difficult contacts among susceptible and infected. The control objective is the asymptotically tracking of the removed-by-immunity population to the total population while achieving simultaneously that the remaining populations tend asymptotically to zero.

Proceedings ArticleDOI
23 Jun 2010
TL;DR: In this paper, the authors proposed a reset adaptive observer (ReO), which is an adaptive observer consisting of an integrator and a reset law that resets the output of the integrator depending on a predefined condition.
Abstract: This paper proposes a novel kind of adaptive observer called reset adaptive observer (ReO). A ReO is an adaptive observer consisting of an integrator and a reset law that resets the output of the integrator depending on a predefined condition. The main contribution of this paper is the application of the reset element theory to the adaptive observer LTI framework. The introduction of the reset element in the adaptive laws can decrease the overshooting and settling time of the estimation process without sacrificing the rising time. The stability and convergence LMI-based analysis of the proposed ReO is also addressed. Additionally, an easily computable method to determine the ℒ 2 gain of the ReO dealing with noise-corrupted systems is presented. A simulation example shows the potential benefit of the proposed reset adaptive observer.

Proceedings ArticleDOI
23 Jun 2010
TL;DR: In this article, a self-motion vector is introduced at the level of the inverse kinematic solution in order to produce the obstacle avoidance (the secondary task), thus, robot avoids obstacles without influencing the main task (trajectory tracking).
Abstract: In this paper, we develop a control of a redundant robot manipulator. That has to carry out a trajectory tracking in operational space while avoiding an obstacle. For this purpose, extended Jacobian method is used. The Self-motion vector is introduced at the level of the inverse kinematic solution in order to produce the obstacle avoidance (the secondary task). Thus, robot avoids obstacles without influencing the main task (trajectory tracking). The self-motion is computed from the optimization of scalar function depending on an anti collision constraint. Finally, this control method has leaded to a trajectory tracking in Cartesian space while avoiding the obstacle.

Proceedings ArticleDOI
23 Jun 2010
TL;DR: The results suggest that PIDPLUS can well be used for wireless control, but better performance could be attained by further development of the controller tuning methodology.
Abstract: The PIDPLUS algorithm is one of the candidates to be used in wireless automation systems. The control performance of this algorithm under packet losses is investigated in the paper. First, the performance of PIDPLUS is evaluated with respect to packet loss rates for a general first-order plus time-delay process, a model widely used for controller tuning. This simulation study reveals how the performance is affected by packet losses in a wireless control system. Secondly, we will elaborate on the implementation of PIDPLUS and discuss its design, tuning and performance in wireless control systems in light of an unstable case process. The results suggest that PIDPLUS can well be used for wireless control, but better performance could be attained by further development of the controller tuning methodology.

Proceedings ArticleDOI
23 Jun 2010
TL;DR: In this article, the authors presented a procedure of fault detection and isolation of proton exchange membrane (PEM) fuel cell based on its mathematic model by analytical redundancy approach, which was linearized into eight state equations representation.
Abstract: This paper presents a procedure of fault detection and isolation of proton exchange membrane (PEM) fuel cell based on its mathematic model by analytical redundancy approach. The model is linearized into eight state equations representation. The transient phenomena captured in the model include the compressor dynamics, the flow characteristics, mass and energy conservation and manifold fluidic mechanics. Analytical redundancy relations (ARR) are generated and numerical simulation results are given. Major faults such as flooding, drying within fuel cells, and compressor over-voltage are detected and isolated. The diagnosability of fuel cell system is also obtained.

Proceedings ArticleDOI
23 Jun 2010
TL;DR: In this paper, a new methodology for Fault Detection and Isolation (FDI) to a Fuel Cell System is presented. But the work is devoted to finding an optimal set of sensors for model-based FDI.
Abstract: This paper presents the application of a new methodology for Fault Detection and Isolation (FDI) to a Fuel Cell System. The work is devoted to find an optimal set of sensors for model-based FDI. The novelty is that binary integer linear programming (BILP) is used in the optimization formulation, leading to a reformulation of the detectability and isolability specifications as linear inequality constraints. The approach has been successfully applied to a Fuel Cell System.

Proceedings ArticleDOI
23 Jun 2010
TL;DR: This paper proposes a tool for energy balance prediction based on ANFIS (Adaptive Neuro Fuzzy Inference System), modified in order to obtain an accurate forecasting for medium term.
Abstract: Nowadays, there are huge ranges of energy market participants. Commercial success of this area actor depends on the ability to submit competitive predictions relative to energy balance trends Thus, it seems convenient to “anticipate” this parameter evolution in time in order to act consequently and resort to protective actions. In this context, this paper proposes a tool for energy balance prediction based on ANFIS (Adaptive Neuro Fuzzy Inference System). This neuro- fuzzy predictor is modified in order to obtain an accurate forecasting for medium term. The solutions are illustrated on a real application and take into account the known “future”: the programmed actions.

Proceedings ArticleDOI
23 Jun 2010
TL;DR: In this paper, a distributed predictive control strategy for building temperature regulation is proposed, where each controller solves a local optimization problem using information about the expected behavior of the other local regulators.
Abstract: This paper proposes a distributed predictive control strategy for building temperature regulation. The originality of the approach consists of using a dynamic prediction horizon MPC, allowing a more effective disturbances rejection. Then this idea is extended, for multizone temperature control in buildings, in a distributed manner, where each controller solves a local optimization problem using information about the expected behavior of the other local regulators. The effectiveness of the proposed approach is showed through different simulations.

Proceedings ArticleDOI
23 Jun 2010
TL;DR: In this article, the design and implementation of a Fault Diagnosis system for a compression's process integrated in an IGCC (Integrated Gasification & Combined Cycle) section of a refinement plant is described.
Abstract: In the present paper the design and implementation of a Fault Diagnosis system for a compression's process integrated in an IGCC (Integrated Gasification & Combined Cycle) section of a refinement plant is described. Both single and multiple faults have been considered which may cause errors in the sensor readings and/or in the actuators used in the process. A multivariable data-driven approach, that is a principal component analysis (PCA) technique has been adopted for monitoring the chemical process performances. A new procedure for the determination of number of principal components based on the statistical test ANOVA is introduced which constitutes the original contribution of the paper. The proposed approach on detection and isolation of faults have been tested and validated on the plant and its goodness and effectiveness could be proven.

Proceedings ArticleDOI
23 Jun 2010
TL;DR: This paper proposes a Discrete Event System (DES) approach for detecting ARP spoofing attacks, which does not require any extra constraint like static IP-MAC or changing the AR.
Abstract: Local Area Network (LAN) based attacks are caused by compromised hosts in the LAN and mainly involve spoofing with falsified IP-MAC pairs. Since Address Resolution Protocol (ARP) is a stateless protocol such attacks are possible. Several schemes have been proposed in the literature to circumvent these attacks, however, these techniques either make IP-MAC pairing static, modify the existing ARP, patch operating systems of all the hosts etc. In this paper we propose a Discrete Event System (DES) approach for detecting ARP spoofing attacks. This approach does not require any extra constraint like static IP-MAC or changing the AR

Proceedings ArticleDOI
23 Jun 2010
TL;DR: In this paper, the stability of a three phase two-level rectifier with two operation modes, as rectifier or as inverter, is analyzed in two-time-scale based on the decomposition of the model into reduced and boundary-layer models.
Abstract: In this paper, the stability of a three phase two-level rectifier is studied. This type of power converter has two operation modes, as rectifier or as inverter. The dynamics of the rectifier consist of a set of equations highly nonlinear. Through the definitions of the instantaneous active and reactive powers, the model of the system is sometimes expressed in terms of power instead of current. Since this new model takes the form of a standard singular perturbation model, the system can be studied in separate time scales. This work propose an analysis of the system in two-time-scale based on the decomposition of the model into reduced (slow) and boundary-layer (fast) models where both should satisfy some conditions to prove the stability of the equilibrium point of the whole system. This analysis will show the stability of the equilibrium of the system via Lyapunov's method and, consequently, will eliminate stiffness difficulties for the implementation of a future controller.