1. A multi-tier controller for directing operation of a system performing a process, having multiple process parameters (MPPs), at least one of the MPPs being a controllable process parameter (CTPP) and one of the MPPs being a targeted process parameter (TPP), and having a defined target value (DTV) representing a first limit on an actual average value (AAV) of the TPP over a defined time period of length TPL AAV2 , with the AAV computed based on actual values (AVs) of the TPP over the defined period, comprising: a first logical controller having logic to predict future average values (FAVs) of the TPP over a first future time period (FFTP) having a length of at least TPL AAV2 , and extending from a current time T 0 to an future time T AAV2 , at or prior to which the TPP will move to steady state, wherein the FAVs are predicted based on (i) the AAVs of the TPP at various times over a first prior time period (FPTP) having a length of at least TPL AAV2 and extending from a prior time of T -AAV2 to the current time T 0 , (ii) the current values of the MPPs, and (iii) the DTV; and a second logical controller having logic (a) to establish a further target value (FTV) representing a second limit on the AAV of the TPP for a second future time period (SFTP), the SFTP having a length equal to TPL AAV1 which is less than the length TPL AAV2 and extending from the current time T 0 to a future time T AAV1 , wherein the FTV is established based on one or more of the predicted FAVs of the TPP over the FFTP, (b) to determine a target set point for each CTPP based on (i) the AAVs of the TPP at various times over a second prior time period (SPTP) having the length TPL AAV1 and extending from a prior time T -AAV1 to the current time T 0 , (ii) the current values of the MPPs, and (iii) the FTV, and (c) to direct control of each CTPP in accordance with the determined target set point for that CTPP.