In figure Controller State at the kth Sampling Instant (b), M = 4 and P= 9, and the controller is optimizing the first M moves of the prediction horizon, after which the manipulated variable remains constant for the remaining P – M = 5 sampling instants.
The following figure shows an alternative blocked strategy—again with 4 planned moves—in which the first occurs at sampling instant k, the next at k+2, the next at k+4, and the final at k+6. A block is one or more successive sampling periods during which the manipulated variable is constant. The block durations are the number of sampling periods in each block. In figure Blocking Example with Four Moves the block durations are 2, 2, 2, and 3. (Their sum must equal P.)
As for the default (unblocked) mode, only the current move, uk, actually goes to the plant. Thus, as shown in the figure above, the controller has made a plant adjustment at each sampling instant.
So why use blocking? When P >> M (as is generally recommended), and all M moves are at the beginning of the horizon, the moves tend to be larger (because all but the final move last just one sampling period). Blocking often leads to smoother adjustments, all other things being equal.
See the subsequent case study examples and the literature for more discussion and MIMO design guidelines.