scholarly journals Design of a Discrete Tracking Controller for a Magnetic Levitation System: A Nonlinear Rational Model Approach

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Fernando Gómez-Salas ◽  
Yongji Wang ◽  
Quanmin Zhu
Keyword(s):  
Discrete Time ◽  
Magnetic Levitation ◽  
Approximate Model ◽  
Space Representation ◽  
State Space Representation ◽  
Classical State ◽  
System A ◽  
Levitation System ◽  
Magnetic Levitation System ◽  
Model Approach

This work proposes a discrete-time nonlinear rational approximate model for the unstable magnetic levitation system. Based on this model and as an application of the input-output linearization technique, a discrete-time tracking control design will be derived using the corresponding classical state space representation of the model. A simulation example illustrates the efficiency of the proposed methodology.

scholarly journals Robust Sliding Mode Control of a Magnetic Levitation System: Continuous-Time and Discrete-Time Approaches

2021 ◽  
Author(s):  
Pratik Vernekar ◽  
Vitthal Bandal
Keyword(s):  
Discrete Time ◽  
Feedback Linearization ◽  
State Feedback ◽  
Magnetic Levitation ◽  
Sliding Mode ◽  
Lyapunov Stability Theory ◽  
Mismatched Uncertainties ◽  
Levitation System ◽  
Full State Feedback ◽  
Magnetic Levitation System

This paper presents three types of sliding mode controllers for a magnetic levitation system. First, a proportional-integral sliding mode controller (PI-SMC) is designed using a new switching surface and a proportional plus power rate reaching law. The PI-SMC is more robust than a feedback linearization controller in the presence of mismatched uncertainties and outperforms the SMC schemes reported recently in the literature in terms of the convergence rate and settling time. Next, to reduce the chattering phenomenon in the PI-SMC, a state feedback-based discrete-time SMC algorithm is developed. However, the disturbance rejection ability is compromised to some extent. Furthermore, to improve the robustness without compromising the chattering reduction benefits of the discrete-time SMC, mismatched uncertainties like sensor noise and track input disturbance are incorporated in a robust discrete-time SMC design using multirate output feedback (MROF). With this technique, it is possible to realize the effect of a full-state feedback controller without incurring the complexity of a dynamic controller or an additional discrete-time observer. Also, the MROF-based discrete-time SMC strategy can stabilize the magnetic levitation system with excellent dynamic and steady-state performance with superior robustness in the presence of mismatched uncertainties. The stability of the closed-loop system under the proposed controllers is proved by using the Lyapunov stability theory. The simulation results and analytical comparisons demonstrate the effectiveness and robustness of the proposed control schemes.

scholarly journals Comparison of Nonlinear and Linear Controllers for Magnetic Levitation System

2021 ◽  
Vol 11 (17) ◽  
pp. 7795
Author(s):  
Danica Rosinová ◽  
Mária Hypiusová
Keyword(s):  
Nonlinear Control ◽  
Discrete Time ◽  
Feedback Linearization ◽  
Magnetic Levitation ◽  
Control Design ◽  
Pole Placement ◽  
System Control ◽  
Levitation System ◽  
Magnetic Levitation System ◽  
Pole Placement Controller

Nonlinear system control belongs to advanced control problems important for real plants control design. Various techniques have been developed in this field. In this paper we compare two different approaches to a nonlinear unstable Magnetic levitation system control. The first control design approach further develops our recent results on robust discrete-time pole-placement, based on convex DR-regions. The second studied approach is based on feedback linearization and the simplified development of the corresponding nonlinear control law is provided. Both approaches are compared and evaluated. The efficiency of robust discrete-time pole-placement controller is shown as well as its competitiveness in comparison with nonlinear control for Magnetic levitation system.

scholarly journals Robust Sliding Mode Control of a Magnetic Levitation System: Continuous-Time and Discrete-Time Approaches

2021 ◽  
Author(s):  
Pratik Vernekar
Keyword(s):  
Discrete Time ◽  
Feedback Linearization ◽  
State Feedback ◽  
Magnetic Levitation ◽  
Sliding Mode ◽  
Lyapunov Stability Theory ◽  
Mismatched Uncertainties ◽  
Levitation System ◽  
Full State Feedback ◽  
Magnetic Levitation System

Abstract This paper presents three types of sliding mode controllers for a magnetic levitation system. First, a proportional-integral sliding mode controller (PI-SMC) is designed using a new switching surface and a proportional plus power rate reaching law. The PI-SMC is more robust than a feedback linearization controller in the presence of mismatched uncertainties and outperforms the SMC schemes reported recently in the literature in terms of the convergence rate and settling time. Next, to reduce the chattering phenomenon in the PI-SMC, a state feedback-based discrete-time SMC algorithm is developed. However, the disturbance rejection ability is compromised to some extent. Furthermore, to improve the robustness without compromising the chattering reduction benefits of the discrete-time SMC, mismatched uncertainties like sensor noise and track input disturbance are incorporated in a robust discrete-time SMC design using multirate output feedback (MROF). With this technique, it is possible to realize the effect of a full-state feedback controller without incurring the complexity of a dynamic controller or an additional discrete-time observer. Also, the MROF-based discrete-time SMC strategy can stabilize the magnetic levitation system with excellent dynamic and steady-state performance with superior robustness in the presence of mismatched uncertainties. The stability of the closed-loop system under the proposed controllers is proved by using the Lyapunov stability theory. The simulation results and analytical comparisons demonstrate the effectiveness and robustness of the proposed control schemes.

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