Deadlock and Blockage Control of Automated Manufacturing Systems with an Unreliable Resource

Abstract

This work studies the deadlock and blockage control problem of an automated manufacturing system (AMS) with a single unreliable resource. It aims to develop a robust control policy to ensure that AMS can produce all parts in the absence of resource failures, and when the unreliable resource fails, the system can continuously produce all parts that do not require the failed resource. To this end, we divide the system into two regions, continuous and non-continuous, based on whether all parts in them can be produced continuously or not. For the non-continuous region, dominating region constraints are established to ensure that all parts in it do not block the production of parts in the continuous region, and an optimal deadlock avoidance policy based on a Petri net model is introduced to guarantee its deadlock-free operation. For the continuous region, we configure a resource order policy to ensure the smooth productions of AMS. By integrating the dominating region constraints and deadlock avoidance policy with the configured resource order policy, we propose a novel robust control policy. It is proven to be of polynomial complexity and more permissive than the existing one with the same resource order policy. Also, it is tested to be more permissive than other existing policies. φ(r s )∩φ(r t ) = ∅, ∀r s , r t ∈R F such that s ≠ t.Proof. Suppose that p jk ∈φ(r s )∩φ(r t ) for s ≠ t. Since p jk ∈φ(r s ), for some c ≥ 0, ρ(p j(k+c) ) = r s and p jk ∈φ(p j(k+c) ). Also, for some d ≥ 0, ρ(p j(k+d) ) = r t and p jk ∈φ(p j(k+d) ). Since r s , r t ∈R F , for some e ≥ c, d, ρ(p j(k+e) ) = r u . Without loss of generality, suppose that 0 ≤ c < d ≤ e. p jk ∈φ(p j(k+d) ) implies that ∀v∈[k, k + d), ρ(p jv )∉R F . This is a contradiction, since (k + c)∈[k, k + d) and ρ(p j(k+c) ) = r s ∈R F . ■We can easily prove the following properties. Property 3. Movements of parts within a dominating set do not violate Δ 1 . Property 4. Movements of parts out of N f do not violate Δ 1 . Theorem 5. Let S be an AMS, (N, M 0 ) be its buffer net, and (N f , M f 0 ) = (P f ∪R F , T f , F f , M f 0 ) be its FBS. Given M∈R(N, M 0 , Δ 1 ), let M f = ϒ (M) and ς(M) = {t | t ∈T f , M f [t>M f1 ∈R(N f , M f 0 , ς)}. If λ = 1 and ∀p∉P F , M(p) = 0, then ς(M) ≠ ∅and ∀t∈ς(M), t ∈ D M ð Þ = {t | t ∈T f , M[t>M 1 ∈R(N, M 0 , D)}. Proof. By Theorems 2 and 4, ς is a DAP for (N f , M f 0 ), and thus ς(M) ≠ ∅. Suppose that ∃t∈ς(M) but t ∉D(M). We consider two cases a) t is not enabled at M in N and b) firing t at M violates D. Case a) t is not enabled at M in N. Since M f [t>M f1 , M f ( (a) t) > 0. Since M f =ϒ (M), M(p) = M f (p) holds for p ∈P f . Hence, M( (a) t) > 0. Thus, t is not resource-enabled at M in N, that is, M(r 1 ) = 0, where r 1 = (r) t in N. If r 1 ∈R F and (r 1 , t)∈N f , then M(r 1 ) > 0 since M f (r 1 ) > 0 (M f [t>)and by Lemma 1, M(r 1 ) ≥ M f (r 1 ). Thus r 1 ∈R F and (r 1 , t) ∉N f . In this situation, firing t means moving a part within a dominating set. According to Property 3, M f1 (φ(r 1 )) = M f (φ(r 1 )). Since M∈R(N, M 0 , Δ ...

Strong Controllable Siphon Basis-Based Robust Deadlock Control for Manufacturing Systems With Multiple Unreliable Resources

“…The size of the established controller grows polynomially with Petri net models. Compared with [36]- [41], the studied AMSs contain multiple types of unreliable resources while others contain only one unreliable resource type.…”

“…(2) By adding a control place with a proper depth control variable and suitable related arcs to each SMS in a strong controllable siphon basis, we develop a robust controller with small size. (3) Compared with existing works [34], [36]- [41], we believe that the robustness level of our proposed controller is improved largely because it allows that multi-type and multi-unit unreliable resources fail simultaneously. The rest of the paper is organized as follows.…”

“…Based on the concept of strong transition covers, Feng et al [39] developed a 1-robust deadlock controller for the same AMSs. Later, Wu et al extended these results to general cases with multi-unit resource failures [41].…”

“…Most of them deal with the manufacturing systems with a unique unreliable resource type. In these systems, only one unit of unreliable resources is assumed to fail at a time [36], [38]- [41]. For example, for a class of manufacturing systems with one unreliable resource type, Wang et al [38] concentrated on distributing parts requiring failed resource throughout the buffer space of shared resources that the disturbed parts do not block the production of part types not requiring failed resource.…”

Masked observation for majority‐based control of a democratic progress model in the framework of discrete event systems

“…Discrete event systems (DESs) are dynamical systems of which state transitions happen by irregularly occurring events. Analysis and control of DESs can be applied to various dynamical systems including manufacturing [1][2][3], gene regulatory networks [4], high-speed railway stations [5], and network security [6]. Recently, diagnosis techniques for DESs (e.g., [7,8]) have been extensively investigated in order to determine if, once a fault has occurred in a DES, its occurrence can be detected in a finite number of steps.…”