Showing 13 results for Feedback Linearization
Volume 5, Issue 4 (4-2021)
Abstract
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%.
Golnaz Jafari Chogan, Mohammad Hasan Ghasemi, Morteza Dardel,
Volume 15, Issue 4 (6-2015)
Abstract
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.
Mohammad Ali Tofigh, Mohammad Mahjoob, Moosa Ayati,
Volume 15, Issue 8 (10-2015)
Abstract
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.
Mohammad Ali Tofigh, Mohammad Mahjoob, Seyed Mousa Ayati,
Volume 15, Issue 9 (11-2015)
Abstract
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.
Mohammad Ali Tofigh, Mohammad Mahjoob, Moosa Ayati,
Volume 15, Issue 9 (11-2015)
Abstract
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.
Habib Ahmadi, Mahdi Bamdad, Seyed Mohammad Mahdi Bahri,
Volume 15, Issue 9 (11-2015)
Abstract
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.
Vahid Marefat,
Volume 16, Issue 10 (1-2017)
Abstract
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.
Vahid Hassany, Mostafa Taghizadeh, Mahmood Mazare,
Volume 17, Issue 6 (8-2017)
Abstract
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.
Ali Hadi, Mahmood Mazare, Mohammad Rasool Najafi,
Volume 18, Issue 1 (3-2018)
Abstract
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.
M. Navabi, M.r. Hosseini,
Volume 18, Issue 1 (3-2018)
Abstract
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.
Fahimeh S. Tabataba’i-Nasab, , Ali Keymasi Khalaji,
Volume 18, Issue 3 (5-2018)
Abstract
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.
Z. Naseriasl , R. Fesharakifard, H. Ghafarirad ,
Volume 19, Issue 4 (4-2019)
Abstract
Nowadays, the need of welding industry's to improve weld quality has led to the consideration of robotic welding. The use of articulated industrial robots for welding has many challenges. Because some robots do not have the capability of online error compensating of the seam track. Therefore, in order to remove the welding seam tracking error, the use of an auxiliary mechanism is proposed in this article. This mechanism is a table with 1-degree of freedom (dof), which produces a continuous motion in workpiece under the welding torch. The rotational motion of the motor is transformed into a translational motion of the workpiece by a ball-screw system, where this linear motion compensates the tracking error. Since in the welding process, relative motion accuracy of the workpiece and the welding torch is crucial, proper control of the interface table ensures the weld quality. In this paper, two different methods for controlling the table with 1-dof are studied. In the first method, due to the complexity of friction model of the ball-screw mechanism and the presence of nonlinear terms, this part of the model is considered as an external disturbance, and, then, a PID controller for the linear part is designed. In the second method, known as feedback linearization, a control law is designed for that the tracking error tends to zero by passing time. Throught a comparison between the simulation results, the second control method demonstrates better precision relating the first controller. While the error of PID controller equals to 3 mm and the second controller’s error does not go beyond 0.5 mm. At last, the experimental cell used for the robotic welding is introduced to evaluate the mentioned results.
Hadi Sazgar, Ali Keymasi-Khalaji,
Volume 24, Issue 10 (9-2024)
Abstract
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
