A simple tunable method for Profile Control - Least-squares configuration

For multiple-input and multiple-output (MIMO) process control, when inputs and outputs are equal in number, a widely adopted scheme in practice is to first decouple the process using a low-frequency square pre-compensator, and then 'tune' the decoupled loops as single control loops. Within the MIMO class, there are also problems having more process variables to be controlled than the available control inputs. This is referred to as the Profile Control (PC) problem. For PC problems, pre-compensation decoupling cannot apply. Applicable methods for PC include Receding-Horizon based real-time optimization and Singular Value Decomposition (SVD) based mode-decoupling configuration. We describe in this paper a simple alternative, the least-squares (LS) configuration, which employs an intuitive post-compensator, and retains the easy-to-tune decoupling control feature. Under mild conditions, we show convergence of this scheme to the steady-state LS solution. We also discuss its robustness against output disturbances, and its flexibility to accommodate actuator range limitations.