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Research subject: Bio-hydrogen is a renewable energy source with many economic and environmental benefits as a fuel. Controlling the concentration of the substrate in the reactor has a significant effect on the amount of hydrogen production. However, bio-hydrogen production is a nonlinear process that requires the implementation of nonlinear control methods. In this paper, substrate concentration in an anaerobic bio-reactor is controlled using the feedback linearization method.
Research approach: The model employed for the simulation is a well-known model consisting of three state variables. The proposed controller is a globally linearized controller (GLC) designed based on the feedback linearization technique. In this method, the nonlinear system is precisely linearized by a transformation of the coordinate system. As a result, the linearized system can be controlled using a linear controller. In order to linearize the system, a nonlinear compensator is designed using the design model and applying the concepts of differential geometry. Proportional-integral (PI) controller is adopted as a linear controller. GLC controller performance has been compared with a nonlinear controller (NC) and a PI controller. The performance of these controllers has been studied by numerical simulation based on the integral of time-square error (ITSE).
Main results: The simulation results show that substrate concentration control can contribute to the hydrogen production. The control method applied has better set-point tracking than the other two control approaches. The ITSE performance index for the feedback linearization method is lower than the other two methods. The nonlinear feedback controller fails if the kinetic parameters are changed by 25%, but the PI method and the feedback linearization are robust against model uncertainty. An efficient controller guarantees stable bio-hydrogen production. Comparing open-loop and closed-loop simulation results shows that controlling the substrate concentration increases hydrogen production by 90%.

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The development in financial and banking sectors is an integral part of economic growth and development. The experiences of many developing countries show that reform driven policy in finance and banking system enhances economic prosperity and removes the macro investment impediment. This Paper evaluates the impact of Linearization policies (or financial restriction) and also changes in real interest rate on deposit and credit of financial sector development in Iran, over the period 1969-2003. The results show that there is a significant and negative relationship between restriction (and reserves control) and financial development. Also, there is significant relationship between changes in banking real interest rate (credit and deposit) and financial development. While the increase in real interest rate on informal markets leads to demand transfer from informal market to formal market and consequently towards the expansion of financial market in Iran. Therefore, low real interest rate, with regard to other policy considerations, would cause increase in potential investment and will improve the proper use of resources in the economy.

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Specifying of the dynamic behavior and impedance characteristics determination of the patients’ lower limb is a necessity for interactions with rehabilitation set-up. In simple proposed models of previous researches, the effects of joint angles on the impedance properties of the leg were not considered and the parameters were identified by nonparametric methods. Hence, the results of identification were not so much appropriate to analyze the rehabilitation process. So, in this paper, a 3 DOF nonlinear dynamic model is developed regarding to the angular stiffness and damping of the lower limb joints and moment of inertia of its moving organs. Then, a linear model is presented to identify the parameters by PEM method. The linearization and identification precisions are evaluated individually. The leg’s parameters are identified for 3 subjects with different mass numbers at four distinctive configurations which are considered during the walking. The identification accuracy is evaluated by comparison between the identified and geometrically estimated mass moment of inertia. Ultimately, the interaction performance of the patients’ leg with rehabilitation pneumatic actuator is investigated considering to leg rigidity and the amount of overweight. The results demonstrate good accuracy and high performance of the linear model for parameters identification.

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Transmission network expansion planning is a challenging problem with the aim to determine the type, location, and time of the equipment to be added to the existing transmission network in order to desirably meet the increasing load demand. On the other hand, reactive power sources are the other important components of the power system, which are used improve voltage profile and maintain the system stability. This paper, presents a comprehensive AC load flow based framework for concurrent expansion planning of transmission networks and reactive power resources. Although major advances have been made in optimization techniques, finding an optimal solution to a problem of this nature is still challenging. Using some linearization techniques, a mixed-integer linear programming (MILP) model for transmission expansion and reactive power planning is proposed. In order to show the influence of the concurrent transmission network expansion and reactive power resources planning in reducing investment costs, simulation studies and analysis of the numerical results are carried out on the Garver 6-Bus and the standard IEEE 24-bus test system.
 

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This paper investigates the robust finite time stability and finite time stabilization for a class of uncertain switched systems which have time delay. The emphasis of the paper is on the cases where uncertainties are time varying and unknown but norm bounded. By using the average dwell time approach and multiple Lyapunov like functions, delay dependent sufficient conditions for finite time stability of uncertain switched systems with time delay in terms of a set of the linear matrix inequalities are presented. Then, the corresponding conditions are obtained for finite time stabilization of uncertain switched time delay systems via a state feedback controller. The controller is designed by virtue of the linear matrix inequalities and the cone complement linearization method. We solved the problem of uncertainty in uncertain switched time delay systems by resorting to Yakubovich lemma. Finally, numerical examples are provided to verify the effectiveness of the proposed theorem.
 

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In this paper, adaptive control method is presented for a parallel cable with six degrees of freedom and six cable. Adaptive control method is a way for controlling systems that there is uncertainty in the parameters. The main objective of this study is tracking trajectory of a parallel cable robot which there is uncertainty in the mass of end effector and moments of inertia. Before addressing the issue of control, Jacobian matrix of robot is obtained. Then the dynamic equations of motion are derived using Lagrange method and is written in standard form. The presented adaptive control method is combination of feedback linearization method and Lyapunov stability theorem. Using feedback linearization method, control law is designed and adaptation law is planned by use of Lyapunov stability theorem. Due to the unique feature of cable suspended robots that cables can only pull the end effector, the cable tension values must be positive. In this paper, a method is used that cable tension values obtained positive for each initial condition and any desired path. Adaptive controller is designed such that unknown parameters of system is correctly estimated and system stability is guaranteed. Through several numerical simulations accuracy of kinematic, dynamic model and applied controller is shown. In order to demonstrate the effectiveness of adaptive control, the comparison between the adaptive control method and the method of feedback linearization is performed.

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In this paper, modeling and design of a trajectory tracking control system for a novel multi-rotor UAV (Unmanned Aerial Vehicle) is developed. The UAV is similar to a quadrotor with an extra no feedback propeller which is added to center of vehicle. The additional rotor improves the ability of lifting heavier payloads, and anti-crosswind capability for quadrotor. For validation, the dynamic model is obtained via both Newton Euler and Lagrange approaches. The dynamical model is under actuated, nonlinear, and has strongly coupled terms. Therefore, an appropriate control system is necessary to achieve desired performance. The proposed nonlinear controller of this paper is an input-output feedback linearization companioned with an optimal LQR controller for the linearized system. The controller involves high-order derivative terms and turns out to be quite sensitive to un-modeled dynamics. Therefore, precise model of UAV is derived by considering actuator’s dynamics. To compensate the actuator’s dynamic and moreover, to avoid complexity in the controller, a second control loop is utilized. The obtained simulation results confirm that the proposed control system has a promising performance in terms of stabilization and position tracking even in presence of external disturbances.

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In this paper, modeling and tow type of nonlinear controller for trajectory tracking of a novel five-rotor UAV (Unmanned Aerial Vehicle) is developed. Because of the very simple structure and high maneuverability, quadrotors are one of the most preferred types of UAVs but the main problem of them is their small payload. In the proposed novel model, one propeller is added to the center of vehicle to improve the ability of lifting heavier payloads, and to excel anti-crosswind capability of quadrotor. The dynamic model is obtained via Newton Euler approach. The model is under actuated, nonlinear, and has strongly coupled terms. Also, two types of nonlinear controllers are presented. First one is a conventional input-output feedback linearization controller which involves high-order derivative terms and turns out to be quite sensitive to sensor noise as well as modeling uncertainty. Second controller is a BackStepping controller based on the hierarchical control strategy that yields easier controller. The obtained simulation results confirm that the performance of BackStepping controller is convenient in terms of stability, position tracking and it is robust in presence of disturbance.

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In this paper, modeling and feedback linearization controller for trajectory tracking of a novel six-rotor UAV (Unmanned Aerial Vehicle) is developed. Because of the very simple structure and high maneuverability, quadrotors are one of the most preferred types of UAVs but the main problem of them is their small payload. In the proposed novel model, two coaxial propellers are added to the center of vehicle to improve the ability of lifting heavier payloads, and to excel anti-crosswind capability of quadrotor, while the dynamic and steering principle is preserved. The dynamic model is obtained via Newton Euler approach. Model is under actuated, nonlinear, and has strongly coupled terms. Also, two types of nonlinear controllers are presented. First one is a conventional input-output feedback linearization controller which involves high-order derivative terms and turns out to be quite sensitive to sensor noise as well as modeling uncertainty. Second controller is a feedback linearization based on the hierarchical control strategy that yields easier controller. To compensate actuator’s dynamic and moreover, to avoid complexity of controller, a two-stage algorithm is utilized. The obtained simulation results confirm that the performance of hierarchical controller is more convenient in terms of position tracking and disturbance rejection than conventional controller.

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In this paper, dynamics and control of a Tendon-based continuum robot is investigated. The curvature is assumed that constant in each section of continuum robot. Kinematic equation is established on the basis of the Euler-Bernoulli beam. The dynamic model of the continuum robot is derived by using Lagrange method. In this paper, robot control is performed in two parts: firstly, Dynamic model is assumed to be known and position and velocity tracking control has been by using the feedback linearization method, But uncertainties in the dynamic model, are constantly challenged the control of continuum robots. For unknown parametric quantities such as mass coefficients, one way is simply substitutes a fixed estimate for the unknown parametric quantities. In this case tracking error is not equal to zero but it’s bounded. For many applications, we cannot assume that tracking error vector is not equal to zero. In such cases we use adaptive controller. In this paper the total mass of the primary backbone and secondary backbone are uncertain parameters, therefore, a new adaptive controller is presented to estimate those uncertainties while cause to asymptotically stable for tracking error. Simulation results show good performance in velocity and position tracking.

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In this paper a nonlinear controller is going to be designed for micro-beam’s deflections under mechanical shock effects. The micro-beam is supposed to undergo mechanical shocks. Mechanical shocks are one of the failure sources and the controller is to considerably suppress shock’s unfavorable effects. Half-Sine, rectangular and triangular pulses are chosen as reference shock signals to represent true complicated shock signals in nature which consist of different harmonics. Two layers of electrodes are placed in both sides of the micro-beam and they are used to actuate the micro-beam by different voltage levels. Upper layer is specifically meant for control purpose. Nonlinear equations governing micro-beam’s deflection dynamics are derived, discretized by Galerkin method to a set of nonlinear duffing type ODE and used to investigate micro-beams response to each shock input signal. Controller design is based on a simple nonlinear model formed by micro-beam’s first mode shape. Proper second order behavior is generated by feedback linearization method as controller logic. Finally controller performance and shock rejecting capability is evaluated by numerical simulations. Controller is shown to be very effective in diminishing shock unfavorable effects and postponing pull-in instability by numerical simulations.

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The purpose of this article is dynamic modeling of a quadrotor and control of its Roll and Pitch angles based on the experimentally measured sensors data. So, after driving nonlinear model of quadrotor equations, the control of the quadrotor’s angular situation was simulated using PID and feedback linearization algorithms. Due to the widespread application of MEMS sensors in measuring the status of various systems and to have a more realistic simulation, sensors data was measured and used in simulation of controllers. Due to errors of MEMS sensors, vibration of motors and airframe, being noise on outputs, Kalman filter was used for estimation of angular situation. As one of the purposes of this paper was the use of its results in actual control of a quadrotor, motor model was used to determine PWM control signals. The results obtained from simulation in Simulink showed good performance of both controllers in controlling roll and pitch angles.

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In this paper, dynamic modeling and position control of a nonlinear servo – hydraulic actuator system under variable loads is proposed. In dynamic model of the under studied system, governing equation of valve, leakage and friction is considered. To achieve to the desired performance of the system under variable loads with extend variation amplitude, a one control method is applied which is robust in the presence of the variation. Also, as a nonlinear servo hydraulic actuator system has a nonlinear dynamics and the extracted dynamic model is not accurate to proposed behavior of the system, one controller can be required which is robust against the nonlinearity and uncertainty effects. The controller should be having an appropriate response, more accuracy and stability. Regarding to position control of the nonlinear servo hydraulic actuator system in presence of variable loads, nonlinear controllers are designed using feedback linearization and sliding mode techniques. In addition, in order to show the robustness of proposed controllers, a time varying disturbance and noise are applied in the simulation and results of the simulation are compared with classical PID controller. Controller parameters is optimized using harmony search algorithm and simulation results show the outperforming of sliding mode control in spite of variable loads against feedback linearization technique and PID controllers.

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Abstract: In recent years nonlinear static analysis method has been widely used in the field of performance based earthquake engineering. Whereas the capabilities of this method is well recognized, it still has inherent shortcomings. Accordingly, by considering aspects such as nonlinear properties of members, higher modes effect, and the computational cost, the accuracy of the method should be investigated. Although an enormous study have been carried out to improve the pushover analysis, the proposed methods are almost deterministic and cannot directly consider the seismic records uncertainties. Toward this challenge, the present study aims to examine the requirements of inelastic static analysis method through a comparison with incremental dynamic analysis results. The general purpose of the pushover method is to yield the maximum story responses (shear and drift) expected during the earthquake. For this reason, the selection of the dynamic response absolute maxima is discussed and different criteria are investigated; maximum displacement versus corresponding base shear, maximum displacement versus maximum base shear and, finally, maximum base shear versus corresponding displacement. Therefore, using the information obtained from dynamic analysis, the characteristic of the proper lateral forces that can represent the average of the maximum effect of the ensemble of earthquake records and consider the inherent records uncertainties, can be obtained. So, to derive the characteristics of equivalent lateral forces based on the dynamic response of the system, four different lateral force profiles can be considered; (1) F1: lateral forces create the same average story forces as dynamic analysis, (2) F2: the profile and intensity of the lateral forces that produce the average of the maximum story shear induced by seismic record ensemble, (3) D1: the lateral force profile is chosen in a way that it can produce the same maximum story drifts as dynamic analysis, and (4) D2: the forces that their responses best represent the average of the story lateral displacement in dynamic analysis. The comparisons are performed for three levels of the typical small, medium and high-rise buildings denoted as four, twelve and twenty-story shear frames. The mathematical model of the frames are chosen as the smoothly varying differential Bouc–Wen model. Because of the versatility and mathematical tractability of the Bouc-Wen model, by altering different parameters of the model, it can simulate various structural behavior with any degree of nonlinearity. The estimated responses are compared to those resulted from the nonlinear dynamic analysis. The comparison procedure in the validation process is conducted in two levels; structural global level results (base shear and roof displacement) and story level results (the story drift and lateral force profiles). Furthermore, using the considered characteristics of the lateral load profile, the probabilistic capacity curve which has the potential to be used for assessing different parts of the structure for different performance levels is extracted. As we expect from static nonlinear analysis the demand of the stories should reach their maximum. In fact, in the low-rise structure when the roof displacement reach its maximum, all of the stories also lean towards their maximum demands. By increasing the structures height (followed with higher modes effect), the result of classic pushover analysis cannot correctly estimate the demands and it differs from the result of dynamic analysis.

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Container crane is an under-actuated system, which is why it is much more difficult to control such systems. In this paper, partial feedback linearization and sliding mode controllers are employed to control a 2D container crane with varying cable length. Since, the dynamic model of the system cannot present the real one and the system contains some uncertainties, a controller is designed to reduce the effect of model uncertainties and external disturbances. Since the considered system is under-actuated, in order to design controller, first, dynamics of the system is divided into two parts, actuated and under-actuated. Then, stability of the controllers is discussed. An objective function is considered as the combination of integral of absolute error and rate of variation of control signal. The introduced objective function is minimized employing Harmony Search and particle swarm optimization algorithms and optimum values for parameters of the designed controllers are determined to make it possible to compare performance of the mentioned controllers in their optimum conditions. Simulation results show suitable performance of the designed controllers by harmony search algorithm for the 2D crane in the presence of mass uncertainty, actuator disturbances and sensor noises.

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The rotational Equations of motion of spacecraft are generally nonlinear, so use of nonlinear control techniques are helpful in real conditions. Feedback linearization theory is a nonlinear control technique which transforms nonlinear system dynamics into a new form that linear control techniques can be applied. Choosing output functions in input-output linearization which is a specific method of feedback linearization, has a significant effect on internal dynamics stability. In this study the kinematic equations of spacecraft motion are expressed by quaternion parameters, these parameters are selected as output functions. Linear quadratic regulator as a linear optimal control law is used to design a controller for linearized system in feedback linearization control and also to design attitude control of spacecraft separately. By considering the actuator constraints on different control methods that are used here, the EULERINT which is the integral of the Euler angles error about the Euler axis, is evaluated. Then, the power and control effort of the actuators are considered for comparison between controllers. The simulation results show that the amount of EULERINT for feedback linearization method is less among the others. Also study of the power and control effort shows that Feedback linearization method is not only quicker but also more efficient and displays better performance of the actuators.

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In this paper, a new controller is presented based on robust feedback linearization controller in combination with integral-exponential error dynamics and potential functions for tracking control of an underwater robot in an obstacle-rich environment. Underwater robots are considered as nonlinear, underactuated systems with indefinite, uncertain dynamics. In this research, by assuming a boundary for external disturbances and uncertainties a proposed robust control method has been put to use. Along with the robust feedback linearization algorithm which has been developed based on the dynamics of the nonlinear error defined for the underwater robot, and in order to avoid the obstacles, the control laws are combined with the virtual potential functions. The considered virtual potential functions make a repulsive force between the robot and the obstacles which intersect the desired path and then they bring about a safe move of the robot in obstacle-rich environments. Finally, the performance of the proposed new control algorithm is compared with the results of the implementation of classical sliding mode control laws. The results show the effectiveness of potentially directed proposed controller through obstacle-rich paths which operate far better facing obstacles.

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In many wheeled robot applications, in addition to accurate position control, dimensional and weight limitations are also important. The limitation of weight and dimensions means that it is not possible to use arbitrarily large actuators. On the other hand, accurate and fast tracking usually requires high control gains and, as a result, large control inputs. If the control input exceeds the saturation limit of the operator, in addition to increasing the tracking error, it may lead to robot instability in some cases. Therefore, it will be precious to provide a control method that can simultaneously provide high control accuracy and guarantee the robot's stability, taking into account the saturation limit of the actuators (speed and torque) in a predetermined manner. This issue has been addressed in the present study. The proposed control includes two parts: a kinematic controller and a dynamic controller. The kinematic control design is based on the Lyapunov approach, which can adjust the speed saturation limit of the actuators. For dynamic control, the robot velocity components are considered as control reference values ​​and the robot wheel torque is considered as control inputs. In the dynamic control design, the torque saturation limit of the actuators is included in a predetermined way. To evaluate the performance of the proposed nonlinear control, various analyses were performed on the wheeled robot. The results showed that the proposed control algorithm while guaranteeing stability and following the path with high accuracy, has also fully met the requirements of the actuators’ saturation limits