FAULT-TOLERANT CONTROL OF CHEMICAL PROCESS SYSTEMS USING COMMUNICATION NETWORKS. Nael H. El-Farra, Adiwinata Gani & Panagiotis D.

Transcription

1 FAULT-TOLERANT CONTROL OF CHEMICAL PROCESS SYSTEMS USING COMMUNICATION NETWORKS Nael H. El-Farra, Adiwinata Gani & Panagiotis D. Christofides Department of Chemical Engineering University of California, Los Angeles 2003 AIChE Annual Meeting San Francisco, CA. November 20, 2003

2 Process control system failure: Typical sources: INTRODUCTION Failure in control algorithm Faults in control actuators and/or measurement sensors Induce discrete transitions in continuous dynamics Motivation for fault-tolerant control: Preserve process integrity & dependability Minimize negative economic & environmental impact: Raw materials waste, production losses, personnel safety,, etc. Dynamics of chemical processes: Nonlinear behavior Complex reaction mechanisms Input constraints Finite capacity of control actuators Arrhenius reaction rates

3 ISSUES IN FAULT-TOLERANT CONTROL OF CHEMICAL PROCESSES Availability of multiple control configurations: Actuator/sensor redundancy Different manipulated variables Illustrative example F 0, T 0, C A0 CSTR 1 F 1, T 1, C A1 In Controller Q 1 Temperature Out In CSTR 2 F 2, T 2, C A2 Composition Analyzer Controller Q 2 Out = Automatic Control Valve Temperature Composition Analyzer

4 ISSUES IN FAULT-TOLERANT CONTROL OF CHEMICAL PROCESSES Distributed interconnected nature of process units: Propagation of failure effects Large numbers of distributed sensors & actuators involved Efficient means of communication required Types of control system architecture: Plant Process 1 Plant Process n Actuator 1 Actuator m Actuator Actuator Computer Computer Computer Point-to-point connections Monitor Distributed control system

5 INTEGRATING COMMUNICATION NETWORKS IN CONTROL Defining feature: Information exchanged using a network among control system components Networked control structure a 1 a 2 actuator input a M u 1 u 2... u M actuator delay Network Channel v M v 2 Plant x(t) sensor... delay s R... Controller y 1 y 2 y R w R w 2 v 1 w 1 reference input sensor output s 2 s 1 Economic & operational benefits: Reduced system wiring Ease of diagnosis & maintenance Enhanced fault-tolerance: Rerouting signals Activation of redundant components Implementation issues: Bandwidth limitations Network delays

6 INTEGRATING COMMUNICATION NETWORKS IN CONTROL Process 1 Process 2 Process n Actuator 1 Actuator m n Actuator 1 Actuator m n Actuator 1 Actuator m Local Network Local Network Local Network Computer Computer Computer Plant Network Plant Supervisor Practical implementation considerations: Size and complexity of the plant Number of sensors & actuators Bandwidth limitations in data transmission Network scheduling and communication delays

7 PRESENT WORK Scope: Nonlinear process systems Input constraints Control system failures Objectives: Integrated approach for fault-tolerant control system design Design of nonlinear feedback controllers Nonlinear dynamics Input constraints Design of supervisory switching laws Orchestrate transition between control configurations Use of communication networks Application to two chemical reactors in series Approach: Lyapunov-based nonlinear control Hybrid systems theory

8 A HYBRID SYSTEMS FRAMEWORK FOR FAULT-TOLERANT PROCESS CONTROL State-space description: m ẋ(t) = f i (x(t)) + gi(x(t))u l l i(t) l=1 i(t) I = {1, 2,, N < } mode 1 mode 2. x = f (x) + g (x)u Discrete Events. x = f (x) + g (x)u u l i,min ul i (t) ul i,max x(t) IR n : continuous process state variables u i (t) IR m : manipulated inputs for i-th mode i(t) I : discrete variable controlled by supervisor N : total number of control configurations f i (x), g (l) i (x) : sufficiently smooth nonlinear functions Discrete Events Discrete Events. x = f (x) + g (x)u Discrete Events Discrete Events. x = f (x) + g (x)u Faults induce discrete events superimposed on continuous dynamics mode 3 mode 4

9 FAULT-TOLERANT CONTROL PROBLEM FORMULATION Coordinating feedback & switching over networks: Synthesis of a family of stabilizing feedback controllers Model for each mode of the hybrid plant: ẋ = f i (x) + G i (x)u i Magnitude of input constraints: u i u i,max Family of Lyapunov functions: V i, i = 1,, N Design of supervisory switching laws that orchestrate mode transitions i(t) = φ(x(t), i(t ), t) Design of network communication logic Handling bandwidth limitations Handling transmission delays Objective: Maintain closed-loop stability under failure situations

10 FEEDBACK CONTROLLER DESIGN Lyapunov-based nonlinear control law: u i = k i (x, u i,max )(L gi V i ) T Example: bounded robust controller (El-Farra & Christofides, Chem. Eng. Sci., 2001; 2003) Controller design accounts for constraints. Explicit characterization of stability region: Ω i (u i,max ) = {x IR n : V i (x) c max i & V i (x) < 0} Explicit guidelines for mode switchings Larger estimates using a combination of several Lyapunov functions

11 Control problem formulation MODEL PREDICTIVE CONTROL Finite-horizon optimal control: P (x, t) : min{j(x, t, u( )) u( ) U, V σ (x(t + )) < V σ (x(t))} Performance index: J(x, t, u( )) = F (x(t + T )) + t+t t [ x u (s; x, t) 2 Q + u(s) 2 ] R ds Q : weighted norm. T : horizon length. Q, R > 0 : penalty weights. F ( ) : terminal penalty. Same V σ as that for bounded controller design. Bounded controller may provide good initial guess. past future k k+1 x k+i k predicted state trajectory computed manipulated input trajectory... prediction horizon k+p

12 HYBRID PREDICTIVE CONTROL (El-Farra et. al., Automatica, 2004; IJRNC, 2004; AIChE J., 2004) Switching logic: Supervisory layer Contol level stability region Bounded controller "Constraints" Ω (u max) Switching logic i=2 i =? i=1 x(t) Perofrmance objectives MPC controller "Optimality" u i (x(t)) = M i (x(t)), b i (x(t)), 0 t < T t T T = inf{t 0 : L fi V i (x) + L gi V i (x)m i (x(t )) 0} Plant. x(t) = Ax(t) + Bu (t) i u < u max Initially implement MPC, x(0) Ω σ (u max ) x(0) Bounded controller s Stability region Ω( ) u max Monitor temporal evolution of V σ (x M (t)) Switch to bounded controller only if V σ (x M (t)) starts to increase V(x)=C 2 V(x)=C 1 Switching x(t * ) V(x)=C max Active MPC Active Bounded control

13 SUPERVISORY SWITCHING LOGIC FOR FAULT-RECOVERY (El-Farra & Christofides, AIChE J., 2003) Basic mechanism for preserving closed-loop stability: Switching between failed & well-functioning configurations Limitations imposed by input constraints Stability regions of control configurations Switching policy: mode switching ensures fault-tolerance provided that State within the stability region of fall-back configuration at time of failure x(t f ) Ω j (u j,max ) x(0) "safe" switching to mode 1 Stability region for mode 2 Ω 2 (u max) t 2-1 Stability region for mode 1 "safe" Ω (u ) 1 max switching to mode 2 Switching between stability regions t 1-2 Implications: Determines tolerable-failure times for a given reconfiguration strategy Determines selection of fall-back configuration for a given failure time

14 DESIGN & IMPLEMENTATION OF COMMUNICATION LOGIC Unit 1 Unit 2... Unit n Plant Process Model Process Model Fault-recovery Tasks Design robust controller u = p(x,u max, b ) Compute fault-recovery region := (x,u max, b, t fail ) Local Controller Failure Information Type of failure Time of failure Operating Conditions Size of disturbance Plant Supervisor Other communication traffic from other local controllers Local Controller Incorporate delays Select/activate fall-back config. Objective: Minimize effects of fault propagation Minimize unnecessary communication costs (tradeoff between network resources & control performance) Account for transmission delay

15 APPLICATION TO CHEMICAL REACTORS F 0, T 0, C A0 CSTR 1 F 1, T 1, C A1 F 3, T 03, C A03 In CSTR 2 F 2, T 2, C A2 Temperature Out In Out Composition Analyzer Local Network Local Network Temperature Composition Analyzer Computer Plant Network Computer Process dynamic model: dc A1 dt dt 1 dt dc A2 dt dt 2 dt Plant Supervisor = F ( ) 0 E (C A0 C A1 ) k 0 exp C A1 V 1 RT 1 = F 0 (T 0 T 1 ) + ( H ( ) r) E k 0 exp C A1 + Q 1(t) V 1 ρc p RT 1 ρc p V 1 = F ( ) 1 E (C A1 C A2 ) k 0 exp C A2 + F 3 (C A03 C A2 ) V 2 RT 2 V 2 = F 1 (T 1 T 2 ) + ( H r) k 0 exp V 2 ρc p ( E RT 2 ) C A2 + Q 2(t) ρc p V 2 + F 3 V 2 (T 03 T 2 )

16 FAULT-TOLERANT CONTROL PROBLEM FORMULATION F 0, T 0, C A0 CSTR 1 F 1, T 1, C A1 F 3, T 03, C A03 In CSTR 2 F 2, T 2, C A2 Temperature Out In Out Composition Analyzer Local Network Local Network Temperature Composition Analyzer Computer Plant Network Computer Control objective: Plant Supervisor Under normal operation: stabilize both reactors at unstable steady-states Under controller failure: preserve closed-loop stability of CSTR 2 Candidate control configurations: Under normal operation: (Q 1, Q 2 ): Q 1 Q max 1, Q 2 Q max 2 Under failure conditions: (Q 2, C A03 ): Q 2 Q max 2, C A03 C A03s C max A03

17 CLOSED-LOOP SIMULATION RESULTS Closed-loop state & input profiles under well-functioning & failed controllers (failure occurs at t = 5 min) Temperature, T 1 (K) Temperature, T 2 (K) Reactant concentration, C A1 (kmol/m 3 ) x 105 Reactant concentration, C A2 (kmol/m 3 ) x 105 Rate of heat input, Q 1 (KJ/hr) CSTR 1 Rate of heat input, Q 2 (KJ/hr) CSTR 2

18 CLOSED-LOOP SIMULATION RESULTS Closed-loop state & input profiles for CSTR 2 when (Q 1, Q 2 ) configuration fails at t = 5 min (Q 2, C A03 ) configuration activated (transmission of disturbance bounds over network no delays) Temperature, T 2 (K) Rate of heat input, Q 2 (KJ/hr) Failure Activating fall back controller (no delays) x 105 Failure Activating fall back controller (no delays) Reactant concentration, C A2 (kmol/m 3 ) Inlet reactant concentration, C A03 (kmol/m 3 ) Failure Activating fall back controller (no delays) Failure Activating fall back controller (no delays)

19 CLOSED-LOOP SIMULATION RESULTS Implementation of fault-tolerant control strategy over network with total delay (fault-detection/communication/actuator activation) of τ D = 2 min & τ D = 3.3 min Temperature, T 2 (K) Rate of heat input, Q 2 (KJ/hr) Failure τ Delay = 3.3 min τ Delay = 2 min x Failure τ Delay = 2 min τ Delay = 3.3 min Reactant concentration, C A2 (kmol/m 3 ) Inlet reactant concentration, C A03 (kmol/m 3 ) Failure τ Delay = 2 min τ Delay = 3.3 min Failure τ Delay = 3.3 min τ Delay = 2 min

20 Tradeoff between: EFFECT OF DELAYS ON FAULT-TOLERANCE Network design (communication logic & delays) Control system design (fault-recovery region, switching logic) (T 2 (0),C A2 (0)) Reactant Concentration, C A2 (kmol/m 3 ) Steady state Failure Switching after τ delay = 2 min Fault recovery region, CSTR Temperature, T 2 (K)

21 Tradeoff between: EFFECT OF DELAYS ON FAULT-TOLERANCE Network design (communication logic & delays) Control system design (fault-recovery region, switching logic) (T 2 (0),C A2 (0)) Reactant Concentration, C A2 (kmol/m 3 ) Steady state Failure Switching after τ delay = 3.3 min Fault recovery region, CSTR Temperature, T 2 (K)

22 CONCLUSIONS Chemical process systems with: Nonlinear dynamics Input constraints Control system failures Integrated approach for fault-tolerant control over communication networks: Design of constrained nonlinear feedback controllers: Design of fault-tolerant supervisory switching laws: Stability regions of control configurations Design of communication logic: Accounting for network resource limitations Effects of delays on fault-tolerance Approach brings together tools from Lyapunov and hybrid systems theory Application to two chemical reactors in series ACKNOWLEDGMENT Financial support from NSF, CTS , is gratefully acknowledged