Issues in multirate process control

Multirate systems are encountered when some signals of interest are sampled at a different rate than others. For example, in the process industry, composition measurements in distillation columns are typically sampled at a slower rate than temperatures and flow rates. In the context of closed-loop control, such multirate systems pose a challenging problem due to several reasons such as increased complexity in the design with tighter performance specifications. Lifting techniques provide a suitable framework for posing a multirate univariate/multivariate problem as a multivariable single-rate problem. We discuss the application of lifting techniques with respect to asymptotic setpoint tracking. Theoretical results are provided to show that there are constraints on the controller gains for step-type reference signals to ensure there are no intersample oscillations in the closed-loop system. Discrete lifting usually introduces non-uniform steady-state gains for the open-loop lifted model which could result in oscillatory continuous output signals for the closed-loop system. These results are supported by simulation results of a slow sampled and fast control system. Further, we provide a continuous-time interpretation to the design of multirate controllers while providing benchmarks for comparing the closed-loop performance of multi-rate and single rate systems in the LQR framework