Robust Control for Single Unit Resource Allocation Systems
Shengyong Wang, Song Foh, Mark Lawley · InTech eBooks · 2011
Motivating examples for properties of robust supervisory controlThis subsection motivates a set of desired properties for a robust controller based upon an example production system.Figure 1 presents an example manufacturing system with two unreliable resources.The stages, routes, and resource capacities are given, as is the complete discrete event model.This model enumerates the resources, capacities, events, and so forth.For now, we will constrain our discussion to the system states presented in Figures 234.We recall that, by definition, a resource allocation state is safe if, starting from that state, there exists a sequence of resource allocations/deallocations that completes all parts and takes the system to the empty and idle state, the state in which no resources are allocated and no servers are busy.Our underlying assumption is that if a resource allocation state is safe, then, under correct supervision and starting from that state, it is possible to produce all part types indefinitely.We have several control objectives for the system of Figure 1.First, we desire that the controller guarantee deadlock-free operation, i.e., that it keeps the system producing all part types.Second, in the event that r 2 fails, we want to continue producing part types not requiring r 2 , {P 3 ,P 4 }, without having to intervene by clearing the system of parts requiring r 2 .Similarly, in the event that r 9 fails, we want to continue producing part types not requiring r 9 , {P 1 ,P 2 ,P 4 }, again without having to intervene by clearing the system of parts requiring r 9 .Further, if both r 2 and r 9 are in the failed state, we want to continue producing part types not requiring r 2 or r 9 , {P 4 }, again without explicit intervention.Consider for example the state given in Figure 2.This state is safe; however, if r 2 fails while processing part p 27 in this state, the production of both P 3 and P 4 will be blocked by two p 23 s at r 4 .Note that if we advance a p 23 from r 4 to r 6 , then production of P 4 can proceed.However, production of P 3 will now be blocked.Thus, this state does not satisfy our condition that after the failure of r 2 , we should be able to continue producing both P 3 and P 4 .As another example, consider the state of Figure 3. Again, we see that this state is safe.However, if r 9 fails while processing part p 35 in this state, production of part types P 1 and P 2 will be blocked by p 34 at r 6 , although the production of P 4 is unaffected.