feedback linearization

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.

In recent years, due to the widespread use of nonlinear under-actuated systems, many efforts have been made to design a controller compatible with these systems. In fact, the defect in stimulation is done in order to reduce the number of system acctuators, in order to lighten the mechanism and reduce the cost of production. Such applications require a high degree of precision and innovation in control and sustainability.This paper proposes an optimal adaptive control method for the stabilization of under-actuated fourth-order balls and beam system, which is a classical example of inherently unstable systems. The basic structure for this controller is the feedback linearization (FBL) technique, while a sliding surface is applied using the sliding mod along with an adaptive method to calculate the interest coefficients. In addition, the control coefficients are optimized using the hummingbird algorithm by considering two opposing objective functions. Finally, the effectiveness of the proposed method for controlling the nonlinear ball and beam system is investigated. The results of the simulations show the high efficiency of the proposed method compared to similar works.

This paper proposes a guidance law design for trajectory tracking of a leader UAV and formation flight of pursuer UAVs. According to nonlinear kinematics for both problems, the feedback linearization theory has ben used. Therefore, using this theory, the nonlinear problem has been transferred to a linear one and using the linear control theory the control parameters has been determined to achieve the desired performance. In the trajectory tracking problem, assuming a constant velocity leader, a change of the independent variable from the time to the downrange has been performed and the problem is transferred to a single-input single-output control problem, consequently, the controller is designed. In the formation flight problem, assuming pursuers with the bounded controllable velocity, we have a two-input two-output nonlinear system. Supposing no communications between pursuers and the leader, a second order sliding mode observer is utilized to estimate the required states in formation flight controller. Results show that the settling time of trajectory tracking error of the proposed nonlinear guidance law is almost 30% better than the nonlinear trajectory tracking controller based on the proportional navigation guidance law. Also, the designed formation flight has a good performance in controlling the formation flight. Also, the sliding mode observer is able to estimate the leader states even in the presence of noise.

Using pressure reducing valves to reduce the pressure in water distribution systems to the minimum of required value is one of the most effective ways for leakage reduction. Valve opening/closing, switching a pump on/off and water consumption fluctuation by a large consumer cause transient flows. Interference between transient flow and a PRV with constant needle-valve setting may intensify pressure waves in WDS. Applying smart PRVs can limitpressure fluctuation. In this research, Input-output feedback linearization method has been used for smart PRV control. The results of this method have been compared with PRV with CNVS and proportional-integral-derivative controller. A theoretical network taken from references was used to evaluate the proposed methods. Network demands include normal consumers and an industrial large consumer. Water hammer caused by consumption variations, PRV with CNVS operation, IOFL method and PID controllers were modeled in Simulink. PRV outlet head fluctuation in PRV with CNVS is 18 to 28 m in PID controller and in IOFL method are 26 to 28 m. Also, the results showed that the IOFL method has smoother and less fluctuation than PID. Root-mean-square error for PRV outlet head in CNVS, PID controller and IOFL is 1.6, 0.32 and 0.28, respectively. Therefore, IOFL method has less error and better performance than PID. Also, this method has simpler computational operations by converting nonlinear system equations to linear equations.

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.

 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).

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%.

In this paper, Blood Glucose control in type 1 diabetic patients in the presence of structured and unstructured uncertainties is studied. In order to increase the effectiveness of the proposed control approach, assumed that all the dynamics describing the regulation of Blood Glucose in type 1 diabetic patients are completely unknown. Based on the fuzzy approximation function, which is equipped with the adaptive algorithm and employing the approach of reducing the number of adaptive fuzzy parameters, the unknown dynamics of the Bergman model approximated. Then, based on the feedback linearization control approach and robust adaptive compensator, the design of feedback linearization robust fuzzy controller to regulate Blood Glucose in type 1 diabetic patients in the presence of meal is studied for the first time. Using Lyapunov theory, it is shown that all signals of the closed-loop system are uniformly ultimately bounded and the Blood Glucose of diabetic patients converges to the neighborhood of the desired value. Finally, the simulation results show a good controller performance in reducing effect of the meal disturbance, and robustness against uncertain dynamics and meal estimation errors. Moreover, in comparison with some existing results, a good performance of the introduced controller in controlling Blood Glucose of diabetic patients (i.e., keeping Blood Glucose in allowed range 70-120 mg/dl) validated.

Quadrotor is an underactuated and nonlinear coupled system. in this paper for controlling the dynamic of the system, feedback linearization (FL) method is used to convert the nonlinear model to a simple linear one. Moreover, a combination of fractional order PID (FOPID) with FL is used to improve the tracking ability. Tuning the parameters of NFOPID, because of two more orders of integral and derivation is a complicated task; therefore neural networks (NNs) method is used to cope with this duty. Back propagation (BP) algorithm is used to train the weights of the NNs. Because of the flexibility and online learning of the NNs, the proposed controller can be robust against uncertainties and disturbances. The fractional order operator has infinite dimension and for practical implementation modified Oustaloup's method is used in this paper. and finally the results of the simulations also validate the effectiveness and robustness of the proposed scheme.

The conventional methods for designing autopilots deal conservatively with uncertainties such that the autopilot should be slowed down to the extent in which the system can maintain its desired performance in the presence of a certain uncertainty. However, there will be no guarantee of good performance in the presence of all uncertainties while the capabilities of the system will not be used properly. In the proposed method, using the extended state observer, the lumped uncertainties along with the system’s states will be estimated, and using feedback linearization approach, along with the nonlinear terms will be removed from the control loop. What remains is a simple linear system that is easier to control. In this method, uncertainties is treated without conservatism and consequently performance is improved in different conditions. Finally, for comparing the results of proposed method with linear autopilot a 1000 times Mont Carlo running with specific condition has been used and is shown that the proposed method is better than the conventional method in performance.

The reference trajectory tracking is one of the most important issues in the field of tractor-trailer wheeled mobile robots control. In this paper, thetrajectory tracking control issues of a tractor-trailer wheeled mob ile robot has been significantly solved in the presence of structural uncertainties,non-hol o n o mic constraints and external disturbance. The proposed scheme is based on a design that the tractor-trailer’s state space representation is extracted from its dynamic and ki n e matic models and presented ina companion format first. In the following,by considering the state space representation of system, the control algorithm is presented includingtwo external and internal control loops. Toward this end, the control law has been developed in the inner loop via input-output feedback linearization in a nonlinear feedback formwh i ch is continuously eliminating the nonlinear dynamics of the system. Then,by using a comb ination of the output that is pr o duced in linearization steps with a terminal sliding mode control algorithm and sketching a neural robust ad aptive finite time controller in the outer loop, the accurate and fast performance of the closed loop system has been guar a nteed in the presence of uncertainties. The proposed control algorithmfinally guarantees the boundedness of closed-loop signals and accurate finite time convergence of tracking errors. At the end, the effectiveness of the proposed sch eme has been demo nstrated and shown through the extended Lyapunov theorem and simulated by MATLAB application.

This paper concerned with the performance improvement of quad rotor using by variable pitch control system. The methodology was laid out based on dynamic modeling of six degree of freedom motion, trim calculations, linearization, and robust control system design for a candidate variable pitch quad-rotor at hover. Therefore, a comprehensive mathematical model of rotors was derived based on the blade element-momentum theory (BEMT) at low Reynolds number, and then, the engine and propulsion models were appended to form the real quad-rotor as a whole. Two control loops including of an inner loop for attitude control system and the outer loop for motion control applied with the robust control system, is the main structure of control system design. Linear controller and feedback linearization controller was also implemented to cover the stability of the quad rotor and compensation of fixed and variable pitch control mechanisms.. Variable pitch quad rotor helped the user to made bigger quad rotor with the less problem in control system which prepared from gyroscopic effect in fixed pitch quad rotor.

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.