Recovering from a Gradual Degradation in MPC Performance

Transcription

1 Preprints of the The International Federation of Automatic Control Furama Riverfront, Singapore, July 1-13, 212 Recovering from a Gradual Degradation in MPC Performance Mohammed Jimoh*, John Howell** *School of Engineering, College of Science and Engineering, James Watt South Building, University of Glasgow, Glasgow G12 8 QQ, UK. ( m.jimoh.1@research.gla.ac.uk) **School of Engineering, College of Science and Engineering, James Watt South Building, University of Glasgow, Glasgow G12 8 QQ, UK. (Tel: +44() ; John.Howell@Glasgow.ac.uk) Abstract: Anecdotal evidence suggests that Model Predictive Control (MPC) performance sometimes deteriorates in commercially operated plants. When deterioration occurs, the operators are sometimes quick to switch off the MPC. Given the significant benefits of MPC, it is important that means should be fashioned to exploit its full potential when these events arise. In this paper a situation is hypothesised in which a CSTR operator has been sold a MPC, which subsequently begins to perform badly. The situation is examined to discover a suitable, acceptable recovery path. Keywords: model predictive control, supervisory control, prediction horizon, control horizon 1. INTRODUCTION There is anecdotal evidence to suggest that Model Predictive Control (MPC) performance sometimes deteriorates in commercially operated process plants (Huang et al 2). The MPC is commissioned by specialist engineers who visit the plant to set-up the MPC. Sometime later, the operators start to observe difficulties. Again anecdotal evidence suggests that this deterioration sometimes derives from actual shift operators interfering with MPC settings (i.e. because they know better). However stories also allude to process drift or to operating at points removed from that at which the MPC was commissioned. Whatever the cause, in all circumstances a key question for the operators is to decide whether there is a preferable MPC configuration, whether they themselves can return the MPC performance to previous levels, whether they require specialist support, or whether they should simply switch the MPC off. The scenarios described here may seem very obvious or even trivial to seasoned MPC engineers, yet anecdotal evidence of such occurrences abound. This paper is part of a wider study to develop a recipe for MPC maintenance, to help the operators diagnose and recover from reported MPC problems such as wrong CV and MV selection, wrong regulatory configurations, process drifts, and effects of measured and unmeasured disturbances, amongst others. MPC is an advanced form of control that is mostly used in process industries. Its practical implementations and the underlying principles and designs have been widely presented and discussed. The design of step response MPC (Seborg et al 24), transfer function MPC (Maciejowski 22) and state space MPC (Maciejowski 22, Wang 29) are among many publications on MPC design. Nikolaou (21) provides a detailed synthesis of theory and industrial needs of MPC. The industrial applications of MPC are also reported in Froisy (1994), Qin & Badgwell (23), and Gao et al (23). A Continuous Stirred Thermal Reactor (CSTR) based investigation is described here, which attempts to draw out some of these issues. The CSTR itself is just a vehicle to explore ideas. A situation is hypothesised here in which a CSTR operator has been sold a MPC, which subsequently begins to perform badly. Taken from Luyben (199), the CSTR in question has particularly difficult properties, because it is open-loop unstable. In essence, the MPC as configured should never have been sold. The aim is to help the operator reach this conclusion, and choose a more suitable configuration. For convenience this study has been carried out using MATLAB s SIMULINK (version 7.5) and Model Predictive Control (Version 3.2) toolboxes, although clearly the actual MPC would be implemented on the plant using a commercial control product. Such toolboxes are grey in their transparency, and at this stage the authors are unclear as to whether their diagnostic recipe could be applied using these tools. The next section gives the basic MPC algorithm, the description of the CSTR process and dynamics, an overview of the installed MPC configuration, and the nature of degradation that is envisioned. In section 3 the diagnosis and recovery strategies are given. The final section gives conclusions arising from the study. IFAC, 212. All rights reserved. 679

2 Furama Riverfront, Singapore, July 1-13, THE PROCESS AND ITS CONTROL The process involved in a CSTR is non-linear, multivariable and highly coupled. A description of the process flow, its dynamics and the basic MPC algorithm is given in this section. 2.1 The Process The CSTR has an impeller that continuously stirs the reactant to ensure perfect mixing (figure 1). The reaction in the CSTR is non-isothermal, is irreversible and exothermic. The exothermic reaction occurs at an appropriate temperature T hence the use of a controller is vital. The reactant feed is introduced to the reaction tank at a flowrate of F, with feed temperature T and feed concentration C A. FO, CA, T Fj, Tj Tj V2 V, T, CA Fig. 1: Flow diagram of the CSTR unit The set of nonlinear differential equations used to describe the non-isothermal CSTR are given in equations 1 to 4. The nominal steady-state values as well as the parameter values are shown in table 1. The equations and the values are taken from Luyben (199). V Fj F...(1)...(2)...(3) Table 1: Variables and parameter values of the CSTR model Symbol Description and units Nominal values F Reaction Product flowrate ( /h) 4. F j Cooling water flow rate () 49.9 F Fresh Feed Flow rate () 4. C A Fresh Feed concentration.5 (Ib.mol A/ ) T Ambient Temperature ( o R) 53. V Reactor holdup volume ( ) 48. C A Reaction product concentration.245 (Ib.mol A/ ) T Reactor absolute Temperature ( o R) 6. T j Cooling water temperature ( o R) T jo Cooling water initial temperature ( o R) 53. V j Cooling water volume ( ) 3.85 E Activation Energy (Btu/Ib.mol) 3,. U Overall heat transfer coefficient 1. (Btu/h ft 2 o R) C p Heat capacity of process liquid.75 (Btu/Ibm o R) ρ Density of process liquid (Ibm/ ). α Frequency factor (h -1 ) 7.8x1 1 R Universal gas constant (Btu/Ib mol 1.99 A h Heat transfer area (ft 2 ) 2. λ. Heat of reaction (Btu/Ib mol) - 3,. C j Heat capacity of cooling liquid 1. (Btu/Ibm o R) ρj Density of cooling water (Ib/ ) MPC Control Algorithm The model in the MPC is obtained by linearizing the stabilised CSTR SIMULINK model, at nominal values of V set and Tj set (48 and o R respectively). The state space linear model is written as:...(5)...(6) Propagating the prediction for P steps ahead from the current kth sampling time is performed by:...(4) 2.2 The CSTR Dynamics At its nominal operating point, the open loop process has one pole at the origin (resulting in the integrating loop F - V) and another in the right half plane. The steady-state operating point of table 1 cannot be maintained with open loop control. In open loop simulation, the reaction essentially stops; product concentration tends to (feed concentration) and the reactor temperature T drops. It is obvious that without the use of controllers, the reactor volume (V) will either overflow or dry up unless F is controlled, and the desired product concentration will not be unachieved. (7) 68

3 Furama Riverfront, Singapore, July 1-13, 212 The quadratic cost function to be solved optimally at every kth step is given by: (8) The unconstrained solution of the cost function is given as: (9) where (1) In the equations above, P is the prediction horizon, M is the control horizon, and r is the vector of set-point at kth step. Advanced MPC incorporates features for handling measured disturbances, blocking, state estimation and constraints, amongst others. 2.4 The installed MPC The CSTR was stabilised by using two PI controllers. The first is a PI level controller LC that is used to control the volume V of reactant in the tank by manipulating the flow rate of reactant product F. The other is a temperature controller TC used to control the temperature Tj of the cooling jacket by manipulating the flow rate Fj of coolant. The PI controller settings are shown in table 2. Table 2: PI settings for the stabilizing controller Loop Proportional Gain Integral TC F-V -5 2 Fj-Tj -1 2 Fig. 2: MPC as supervisory controller on a CSTR The configured MPC was tested by applying small perturbations to the disturbance inputs (figure 3), while step changing set-points. As can be seen in Figures 4 and 5, the controlled variables V and C A performed very well Perturbations in Feed flowrate (F) Perturbations in Feed Concentration (CA) It is assumed that a supervisory MPC was implemented on the stabilised plant using MVs V set and Tj set and CVs V and C A, and with MPC parameters given in table 3. The work of Grosdidier et al (1993) shows how the model of MPC as supervisory controller may be obtained. The constraints on V set and Tj set are hard and for safety reasons are not allowed to drift far from their nominal values. Table 3: MPC Simulation Parameters for CSTR control Name Symbol Value Sampling Interval Ts.1 hr Prediction P 3 Horizon Control Horizon M 3 Input weights iw [, ] Output weights ow [1, 1] Constraint on Vset Constraint on Tjset The MPC supervisory configuration setting is shown in figure 2. ib.mol A/ R Perturbations in Feed Temperature (T) -5 Fig. 3: Trend of perturbations in disturbance inputs Figure 4 shows that the MPC controller is able to make the two CVs track the set points even in the presence of perturbations in the disturbance inputs. Figure 5 shows the trend of the manipulated variables from the MPC and the PI controllers. The MV responsible for controlling the variable C A is Fj. 681

4 ib.mol A/ Furama Riverfront, Singapore, July 1-13, Volume (V) Concentration (CA) might also be operated at a point away from its nominal values and disturbances might differ from those observed at testing. These factors may cause the MPC to degrade drastically and become immune to correction via tuning by the plant operators. A situation is envisioned here where the heat transfer coefficient U is reduced by 2% (from 1 to 12 Btu/h ft 2 o R), while the plant is subjected to perturbations in the disturbance inputs higher than those observed at commissioning (figure 6). As can be seen in figures 7 and 8 the plant s performance degrades sharply and the MPC no longer keeps the product concentration at the set point. The plant becomes unstable and the MPC breaks down Perturbations in Feed flowrate (F) Fig. 4: Trends of reference and controlled V and CA Vset (MPC MV1).1 Perturbations in Feed Concentration (CA) ib.mol A/ Tjset (MPC MV2) 4 Perturbations in Feed Temperature (T) R F (PI output1) R Fig. 5: Trends of manipulated inputs (MPC and PI outputs) 2.5 Process Degradation Fj (PI output2) Process drift may occur when process parameters such as heat transfer coefficients (U) change over time. For example material might build-up on the surface of the jacket, reducing the overall heat transfer coefficient significantly. The plant Fig.6: Trend of perturbations in disturbance inputs 3.1 Diagnosis 3. DIAGNOSIS AND RECOVERY When faced with this situation, the operator might embark on a series of checks. a) Check the effect of changing MPC parameters such as manipulated variable weights, prediction and control horizons on the performance. b) Check cases of limit violations on the controlled variables. c) Check the performance of the PI controllers. The well-supported operator might have computer tools: for instance controlled variable limit violations can be diagnosed from the plots of the MV and CV Lp targets (Jiang et al, 212). These plots can also help to reveal possible problems in the performance of PI controllers. 682

5 ib.mol A/ Furama Riverfront, Singapore, July 1-13, Volume (V) Concentration (CA) d) Check whether the correct variables (MVs and CVs) are used in the MPC design A useful aid in doing this might be a small computer simulation of the model incorporated into the MPC. We imagine that the operator has this: Figure 9 shows model step response plots. These might help to confirm his understanding that C A is highly correlated and coupled with T and Tj. It also shows that the steady-state gains of T and Tj are much higher than that of C A. The combination of the two factors implies that T and Tj are much highly affected by changes in Fj compared with effect of Fj on C A. It also implies that C A is dependent on T or Tj, and that it is sufficient that by controlling any of them, C A is also controlled. A second useful aid might now be a computer simulation of the MPC: the operator might experiment with switching CVs, and in doing this the operator might find that performance is now improved..5 Fig. 7: Trends of reference and controlled V and CA for the degraded performance 55 Vset (MPC MV1) Tjset (MPC MV2) R F (PI output1) Fj (PI output2) Fig. 8: Trends of manipulated inputs (MPC and PI outputs) for the degraded performance Changes in the MV weights and in the prediction and control horizon values did not improve the performance. Also from the simulation plots, there are no cases of constraint violation. Although the operator would not be an expert modeller, it is quite likely that he would understand the workings of his plant. It is quite possible that he would question the MPC structure: Fig. 9: Step response plots for the CSTR MPC model 3.2 Recovery In light of the above diagnosis, the proposed recovery involves that T is used as a CV instead of CA, while still maintaining the initial PI configurations. The objective function in the optimisation level can be programmed to set the reference temperature (Tref) to values corresponding to the required CA values. The trends from the implementation of the proposed MPC configuration are shown in figures 1 and Alternatives Clearly, the MPC dynamic model differed from the plant model in this particular scenario. Both vendors and theoreticians might therefore add e) check the quality of the MPC dynamic model. 683

6 Model quality evaluation requires expert revalidation since this may involve obtaining open-loop data with pseudorandom binary excitation (PRBS) and/or data sampled under routine operation (Huang et al 2). Such activities are costly, which is perhaps why operators might choose to switch off the MPC instead. Again operator access to a simulation tool might encourage them to open up a dialogue with vendors once more. ib.mol A/ Fig.11 Trends of V and T for the corrected performance R Furama Riverfront, Singapore, July 1-13, 212 R Concentration (CA) Temperature (T) Vset (MPC MV1) 59 4 Tjset (MPC MV2) 3 1 F (PI output1) Fj (PI output2) CONCLUSIONS The simulation results show that some degradation in MPC performance can be caused by choices made during the design stage. Even when using MPV as supervisory controller for lower level PI controllers, the choice of CV is very important. Whilst this is somewhat obvious to seasoned MPC engineers, it may be unclear to most plant operators. In situations where the design of the MPC allows the operator to select what variables to include as CV, the knowledge of information presented in step response plots allow them to make informed decisions. ACKNOWLEDGEMENT Mohammed Jimoh wishes to acknowledge the support and funding of the PETROLEUM TECHNOLOGY DEVELOPMENT FUND (PTDF), Nigeria, for this work REFERENCES Froisy, J. B. (1994). Model Predictive Control: Past, Present and Future. ISA Transactions, volume (33), pp Gao, J. et al (23). Performance Evaluation of Two Industrial MPC Controllers. Control Engineering Practice, volume (11), pp Grosdidier P. et al (1993). FCC Unit Reactor-Regenerator Control. Computer Chemical Engineering, volume (17), No 2, pp Huang, B., et al (2). An Investigation into the Poor Performance of a Model Predictive Control System on An Industrial CGO Coker. Control Engineering Practice, volume (8), pp Jiang H. Et al (212). Model analysis and performance analysis of two industrial MPCs. Control Engineering Practice, vol. 2, pp Luyben, W. L. (199). Process Modelling, Simulation and Control for Chemical Engineers, McGraw-Hill Publishing Company, New York. Maciejowski, J. M. (22). Predictive Control with Constraints, Peason Education Limited, England. Nikolaou, M. (21). Model Predictive Controllers: A Critical Synthesis of theory and industrial needs Control Engineering Practice, volume (26), pp Qin, S. J. & Badgwell, T. A. (23). A Survey of Industrial Model Predictive Control Technology. Control Engineering Practice, volume (11), pp Seborg, D. E. et al (24). Process Dynamics and Control, John Wiley and Sons Inc., USA. Wang, L. (29). Model predictive Control System Design and Implementation Using Matlab, Springer-Verlag Publishing, London, UK Fig. 12: Trends of manipulated inputs (MPC and PI outputs) for corrected performance 684