Fractional Order Control of Active Magnetic Bearing Systems

Active magnetic bearings (AMBs) employ electromagnets to support machine components without mechanical contact. The magnetic forces are adjusted by feedback controllers to suspend the machine components within the magnetic field and to control the system dynamics during machine operation. Magnetic bearings offer many advantages for various applications. High-speed machines can operate smoothly because there is no friction during rotation. The maintenance cost and mechanical wear are low due to non-contact operation. A real time control in the AMB system helps to keep the rotor close to the center and to reduce vibrations during operation.

However, controller design for AMB systems is a challenging task because of the nonlinear nature of the plant dynamics, the very small degree of natural damping in the process, the strict positioning specifications often required by the application, and the system dynamics are open loop unstable. In most cases, PID is the chosen controller due to its simplicity and intuitiveness in the tuning of the controller parameters. However, sometimes a conventional PID controller cannot full the industry performance standards for AMB systems as specified by the American Petroleum Institute (API) and the International Organization for Standardization (ISO). In these cases, more complex controllers, such as LQG, H∞ and mu-synthesis, are used to meet the desired specifications. The tradeoff between the simplicity of the controller structure and the achievement of good performance is a relationship that control engineers seek to balance and optimize.

Recently, fractional order calculus theory, which is the generalized version of integer order calculus, has been adopted for many applications due to its accuracy for modeling the dynamics of systems and its simplicity in model structure to represent high order processes. Fractional order control is one of the fields that many researchers and engineers are interested in because the response of a system with a fractional order controller is not restricted to a sum of exponential functions, and, as a result, a wide range of responses neglected by integer order calculus could be approached. One of the most popular fractional order controllers is the generalized PID controller, which is also called a fractional order PID (FOPID) controller. FOPID has two extra parameters, the non-integer order of integral and derivative terms, in comparison with the integer order PID controller. FOPID control can improve performance and robustness compared to conventional PID control in many applications while keeping the control structure simple. This suggests that an FOPID controller has good potential to reduce the gap between the simplicity of the controller structure and high closed-loop performance aspects as mentioned above.

In this dissertation, a fractional order PID control for AMB systems is proposed. The feasibility of FOPID for AMB systems is investigated in two aspects. The first aspect is the control of rotor suspension by magnetic bearings both in radial and axial directions. The second aspect is the surge control in a centrifugal compressor which uses thrust AMB to modulate impeller tip clearance for surge stabilization. Tuning methods are developed based on the evolutionary algorithms for searching the optimal values of the controller parameters. The resulting FOPID controllers are then tested and compared with an integer order PID controller, as well as with advanced controllers such as LQG and H∞ controllers. The comparison is based on various stability performance and robustness specifications, as well as the controller dimension as implemented. Lastly, to validate the proposed method, experimental testing is carried out on a single-stage centrifugal compressor test rig equipped with magnetic bearings.