In conjunction with UC Santa Barbara, Magnetic Moments has assembled a collection of sample laboratory experiments for the MBC500. These experiments are suitable for use in a classroom setting, in order to encourage the investigation of several concepts in control theory.
Lab #1: Analytical Modeling of a Magnetic Bearing System
Lab #1 introduces control system design as a multistage process involving much more than the design of the controller itself. Before a controller can be designed, the designer must have sufficient knowledge of the system to be controlled. The designer begins by collecting information about the system from all available sources and then representing this information in the form of a system model. One source of information is the physics governing the system. An analysis of these physical laws will yield differential or difference equations which describe the motion of the system in response to certain input signals.
Laboratory #1
Solution #1
Lab #2: Magnetic Bearing System Identifaction
Experimental determination of a system model is an important part of the modeling process. This phase of controller design is referred to as system identifaction. In Lab #2, we use a Hewlett Packard 3562A Dynamic Signal Analyzer to collect experimental data from the MBC 500 Magnetic Bearing system. Specifically, we use the signal analyzer's swept sine function to experimentally determine the transfer function of a single input / single output (SISO) path through the magnetic bearing system. In the following discussion we describe the dynamic signal analyzer, its swept sine function, and the collection of frequency response data from the magnetic bearing system. After transferring the data from the signal analyzer to MATLAB, we use some MATLAB routines to find a suitable system model.
Laboratory #2
Solution #2
Lab #3: Notch Filtering of Resonant Modes
In Lab #3 we begin to stabilize the magnetic bearing system. We review the Nyquist Criterion and its application to design and analysis of unstable systems such as the magnetic bearing. Using this criterion, we see how resonant modes can threaten the stability of the closed loop system. Consequently, we design and build a notch filter to cancel the effect of the first resonant flexible rotor mode. This notch filtering is the first phase of our controller design.
Laboratory #3
Solution #3
Lab #4: Lead Controller Design for a Magnetic Bearing System
In Lab #4, we consider the design of a lead controller to stabilize one loop of the MBC 500 Magnetic Bearing system. We first develop a general method for designing lead controllers for unstable systems. Then we show how such a controller can be implemented using operational amplifiers, resistors and capacitors. After designing and building our lead controller, we verify and fine tune its transfer function using the dynamic signal analyzer. Finally, we connect the controller with the previously designed notch filter and the bearing system, and tune it to achieve stability and performance.
Laboratory #4
Solution #4
Lab #5: Controller Design for a Magnetic Bearing System
In Lab #5, we determine a discrete-time approximation to the notch filter / lead controller combination we designed in previous experiments. A digital implementation of such a discrete-time controller will include an analog to digital converter (ADC) on the input of the controller, and a digital to analog converter (DAC) on the output of the controller. The controller itself will be implemented in software using a computer. The algorithm for implementing the controller will be expressed as a Z-transform representation of the notch and lead controller. We then discuss the choice of the sampling frequency for the digital system, and convert our analog notch filter and lead controller into equivalent digital representations. We then implement this digitally using the dSPACE DS1003 Processor Board, the dSPACE ADC and DAC boards, the DS 2001 and DS 2101 I/O boards, and supporting software. Finally, we include an optional discussion on the design and implementation of an anti-aliasing filter.
Laboratory #5
Solution #5