Multivariable controller applied to an active magnetic compensating system for fast-field-cycling NMR

GUILLERMO FORTE; LUIS CANALI; ESTEBAN ANOARDO

Torino

Congreso; 5th conference on field cycling nmr relaxometry, Torino - Italia; 2007

Universidad de Torino

Field cycling NMR applications may require the cancellation of time dependent magnetic fields within an exclusion volume usually containing the sample. This is the case where external magnetic field contributions must be compensated at the ULF (ultra low frequency) limit. We present a system designed to compensate time dependent magnetic field components and gradients, operating at a maximum frequency of about 100Hz. The device is based on a special probe containing 10 Hall sensors, providing 6 inputs to the control system: magnetic field components and the constant gradients along the three spatial directions. The control system itself was developed within PC environment. In a forthcoming step and after all relevant testing of the device will be closed, it will be transferred to an adequate hardware platform in order to pull-up the sped of the device. A set of 6 coils (four saddle-type and two Helmholtz-type) driven by 6 independent current sources are used to correct the field. Since the magnetic field generated by each compensating coil affects the lecture of Hall sensors in all directions, the control system should include a suitable treatment for a multivariable (multiple-input multiple-output, MIMO) problem. This effect is negligible when compensating homogeneous fields, where the interactions between the control variables are due to constructive shortcomings. However, it is not possible to generate magnetic field gradient in just one direction without affecting the gradients in the other directions. A two-step compensator design approach was applied to solve the multivariable control problem. First, a ?pre-compensator? to deal with the interactions in the plant, was designed. It counteracts the interactions in the plant and results in a new shaped plant which is more diagonal and easier to control than the original one. Then, we developed a diagonal controller using methods like single-input single-output (SISO) systems. We used simple proportional, integrative and derivative (PID) controllers for each circuit control, adjusted to have an optimum perturbation rejection performance. This method, called decoupling control, need a good knowledge of the plant model (including its dynamic) in order to make the shaped plant diagonal at all frequencies. An alternative to the above design method is to directly synthesize a multivariable controller based on minimizing some objective function (norm).  Optimization in controller design is widely used since 1960?s with ?optimal control theory?. In H-infinite optimal control, the objective function is the H∞ norm. There are a lot of examples where this technique is used to solve a multivariable control problem Presentado como poster.