Controllability and stability of repetitive batch processes

Batch control has traditionally addressed the problems related to the absence of a steady-state and the finite batch duration. Recently, batch control has added the dimension that arises naturally from the possibility of applying run-to-run control, i.e. it exploits the fact that most batch process are repeated over time. Hence, batch control calls for tools that are tailored to these new challenges and specificities of batch operations. These include a mathematical representation that explicitly shows the two independent time variables (the run time t and the run index k), two types of inputs (both constant and time-varying within a run) as well as two types of outputs (the run-time and run-end outputs). This paper introduces a definition of batch-output controllability that considers the two types of inputs and outputs. Also, a quantitative notion of stability that takes into account the finite-time nature of batch processes and typical phenomena such as the batch kick is presented. The tools required for evaluating these properties are readily adapted from the literature. As illustration, a semi-batch reactor example is considered in simulation. Various approaches to batch control are demonstrated and the associated controllability and stability issues discussed.