Design of an adaptive state feedback controller for a magnetic levitation system

Abstract

This paper presents designing an adaptive state feedback controller (ASFC) for a magnetic levitation system (MLS), which is an unstable system and has high nonlinearity and represents a challenging control problem. First, a nonadaptive state feedback controller (SFC) is designed by linearization about a selected equilibrium point and designing a SFC by pole-placement method to achieve maximum overshoot of 1.5% and settling time of 1s (5% criterion). When the operating point changes, the designed controller can no longer achieve the design specifications, since it is designed based on a linearization about a different operating point. This gives rise to utilizing the adaptive control scheme to parameterize the state feedback controller in terms of the operating point. The results of the simulation show that the operating point has significant effect on the performance of nonadaptive SFC, and this performance may degrade as the operating point deviates from the equilibrium point, while the ASFC achieves the required design specification for any operating point and outperforms the state feedback controller from this point of view.

Comparison of Nonlinear and Linear Controllers for Magnetic Levitation System

“…The aim is to find the corresponding control law u such that the linear system ( 25) is for state variables (24) equivalent to nonlinear system (23) with the appropriately determined control u. Note that z 3 in (24) corresponds to the right hand side of dx 2 dt in (23). Thus, u conforming to the dx 3 dt in ( 23) should be determined so that dz 3 dt in ( 25) is fulfilled.…”

“…Magnetic levitation plant, where a magnetic object is positioned in the air space, provides a challenging control task owing to strong nonlinearity and inherent instability. Various methods have been proposed to control the magnetic levitation, as for example feedback linearization approach in [21,22], adaptive state feedback [23], frequency domain method [24] or CDM (Coefficient Diagram Method) based design in [4]. Most of them consider continuous-time control.…”

Discrete-Time Pole-Region Robust Controller for Magnetic Levitation Plant

“…In [17,21], a linearized model of magnetic levitation is derived based on first principles, the former uses Jacobian linearization, while the latter applies a general linearization technique. Various continuous-time control schemes for magnetic levitation can be found, for example, feedback linearization approach in [18], CDM based design in [19], adaptive state feedback [20]; in all these papers, the results were verified by simulation. To the authors' best knowledge, there are no papers on discrete-time pole-placement for magnetic levitation, besides our recent results [16,23,24].…”

“…Magnetic levitation belongs to challenging plants to control, due to its nonlinearity, instability and fast dynamics, with broad application area. Many authors devoted their research to modeling and control of a magnetic levitation system, [17][18][19][20][21][22][23][24]. In [17,21], a linearized model of magnetic levitation is derived based on first principles, the former uses Jacobian linearization, while the latter applies a general linearization technique.…”

Stability and performance evaluation of the speed control of DC motor using state-feedback controller

“…Furthermore, single or multiple input output systems can also be analysed [17], [18]. The principle of feedback of all state variables feeding the input of the system was through a feedback matrix in the control strategy is preferable using full-state variable feedback control [19], [20]. State feedback is very useful for multi-input multi-output systems and for control systems with optimum constraints, such as those requiring a minimum time to final value or minimal control effort.…”