Distillation column control has been a challenging problem for numerous research activities. Review of past research reveals that among the advanced control methods applied to this system, little attention has been paid to feedback linearization, even in absolutely theoretical cases. This is due to the singularity of the system in steady-state, which invalidates the linearized control law. In this paper, to overcome this problem, a new idea has been suggested that is based on approximate feedback linearization. Based on this idea, an approximate non-linear model has been introduced for the distillation column which can exactly be linearized while reserving the structural properties of the basic system. The control law is derived from the approximate model and then applied to the basic system. The introduced error between the approximate and basic systems is then fed back by two single loop PID controllers to improve the performance of the system. Further, in these approach disturbances due to changes of feed flow and composition has been perfectly decoupled using the disturbance decoupling theory.

In this study, feedback linearization (FL) for 6R manipulator is designed, simulated and implemented. The presented input-output FL controller has achieved the desired performance for the complicated nonlinear terms in the arm‟s dynamic equations. Simulations were used to test the performance of the controller for point-to-point motion as well as continuous trajectory. The results of the point-to-point motion simulations and experiments were compared, where it indicates that the proposed approach preserved smooth motion in a very short process time with good accuracy. The dynamic load carrying capacity (DLCC), which is a criterion to determine FL controller performance on 6R robot, is also investigated, based on saturated torque of the motors and allowable error bounds. Moreover, it was shown that the control law is able to accurately represent closed-loop equations and simultaneously imposed desirable behavior on 6R robot.

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.

In cruise control systems, the performance of the controller is important. Hence, in order to have accurate results, the nonlinear behavior of a vehicle model should also be considered. In this article, a vehicle with a nonlinear model is controlled by using a nonlinear method. The nonlinear term of the model is the generated torque of engine, which is a polynomial equation. In addition, feedback linearization is used as a nonlinear method in order to design two parallel controllers to control the movement of the vehicle. These two parallel controllers are used to control braking and gas pedals which are in charge of the angular velocity of the wheels. To check the performances of controllers, first, each controller is used separately. Finally, two parallel controllers are used to track the reference signal. Comparison between results shows that the designed controller is able to reduce the convergence time of about 10 seconds. This improvement is near 35% in comparison with near studies. In addition, it can reduce the error between the velocity of the vehicle and the values of the reference signal that results in more safety for passengers.

Based on the wavelet transform and fuzzy set theory, we present a fuzzy' wavelet network (FWN) for approximating feedback linearization control input. Each fuzzy rule corresponds to a sub-wavelet neural network (sub-WNN) consisting of wavelets with a specified dilation value. The degree of contribution of each sub-WNN can be controlled flexibly. The constructed rules used to approximate the control signal in which the mathematical model of the system under control is unknown can be adjusted by learning the translation parameters of the selected wavelets and determining the shape of Gaussian membership functions of a fuzzy system. The proposed FWN shows good approximation accuracy and fast convergence. Finally a nonlinear inverted pendulum system is applied to verify the effectiveness and ability of the proposed network.