This paper considers the design of electron beam stabilisation control systems for synchrotrons that simultaneously determine the inputs to multiple arrays of actuators for regulating variations in the electron beam position. An approach based on determining the interaction of the controllable subspaces is used. This enables the control problem to be decomposed into a series of single-input, single-output; multiple-input, single output and multiple-input, multiple-output problems. An Internal Model Control structure is used to design the controllers for each case and mid-ranging control is proposed for the case where the control directions align. Results from a simulation study using machine data from the Booster synchrotron of the UK's national synchrotron facility, Diamond Light Source are presented.