A STATE ESTIMATION BASED APPROACH TO GASIFIER CONTROL

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1 A STATE ESTIMATION BASED APPROACH TO GASIFIER CONTROL J.A. Wilson, M. Chew & W.E. Jones School of Chemical, Environmental & Mining Engineering (SChEME University of Nottingham, University Park, Nottingham, NG7 2RD Keywords: Kalman Filter; state estimation; inferential control; soft-sensing; local models. Abstract On-line state estimation techniques provide a means of inferring real-time values for key process variables that cannot themselves be measured directly. Such state estimates can then form a basis for improved process control. Accordingly, we here apply Kalman Filtering (KF to a nonlinear coal gasifier system operating initially under a conventional feedback control strategy. Key unmeasured disturbances to gasifier operation arise in discharge pressure and coal feed quality. We show that by treating both of these variables as unknown process parameters they can be included in an augmented state and parameter vector and estimated reliably by KF. A feedforward control strategy acting on these disturbance estimates, and linked into the existing conventional feedback control system, is shown to enhance system performance to both step and sinusoidal discharge pressure changes and to steps of up to 18% in coal quality. The strategy also proves capable of ramping downstream generated power output with no loss of accuracy relative to the conventional feedback control. 1 Introduction The system under study here is a coal gasifier which forms one part of an integrated power generation system. It was the subject of a previous study (the MEC Benchmark Challenge I in which the academic community was tasked to develop effective strategies for control of the system in the face of a range of disturbances in downstream discharge pressure [1]. Linear dynamic models were provided for the gasifier at the 0%, 50% and 100% output power loads to allow performance testing of alternative control schemes. By approaching control of the gasifier as a chemical engineering process, a successful design was proposed by the present authors [2] which was based on a set of four conventional, single input/single-output (SISO or decentralised control loops. The current Benchmark Challenge II has sought control strategies capable of handling control of the same gasifier, but this time faced with a wider, more testing range of disturbance conditions and with performance measured when applied in simulation to a full, non-linear model of the gasifier. Our 4-loop SISO scheme, with controller tunings adjusted by Dixon to match the now non-linear process model, has been chosen as a performance benchmark. 2 Feedforward action on disturbance estimates Baseline performance of the conventional feedback control system is impressive. Although only a linear control strategy, the PI based controllers perform remarkably well together, even in the face of the non-linearities within the gasifier and its model. Aside from the hard non-linearities imposed on both the range and rate of the manipulated variables there is strong process non-linearity induced by temperature changes (e.g. reaction rates can change by a factor of 2 or 3 for a 10 o C change in gas temperature which here shifts 155 o C between 0% and 100% load. Another key parameter, gas residence time, varies with both freeboard volume in the gasifier vessel (i.e. the volume not occupied by solids and the gas volumetric flowrate (which will itself vary with feed rates as well as gasifier temperature and pressure. Despite these effects however the conventional control holds the plant largely within specified limits. Thus, there seemed little room to enhance performance significantly with some form of non-linear feedback control (though availability of the real time estimates of the gas phase composition shown later, coupled with deeper knowledge of what those chemical species represent and how they connect to the prevailing reaction scenarios, may offer a means of building such a strategy. Instead, we here focus on introducing new feedforward control elements designed to take rapid, co-ordinated action directly on the manipulated variables and in parallel with the existing feedback controls, so as to oppose the effects of the major prevailing process disturbances, in this case downstream pressure P SINK and feed coal quality C Q. While no sensors are available to measure these two disturbance variables directly (though of course a sensor for P SINK could and perhaps should be installed a state estimator could feasibly supply the missing data. To demonstrate the applicability and potential of this as a generic approach to gasifier control we now consider its implementation more specifically in the Benchmark Challenge II gasifier system using the models provided. The form of these models has presented some constraints both in setting up and in evaluating performance of our approach that

2 will be explained later. As a preliminary we first highlight some significant factors affecting the state estimation before outlining implementation and performance of the estimator based feedforward/feedback control scheme itself. 3 State Estimation At Nottingham, on-line State Estimation as a basis for improved process plant operation and control (using Kalman Filtering, KF is a long standing topic of research. Most recently this relates to a generic strategy for control of fixedbed, gas phase catalytic reaction systems [3] where use is made of a sensor array measuring the full temperature profile along the catalyst bed. In the case of the gasifier, examination of the linear model eigenvalues reveals a subset of identical values. One feasible reason for this is that the gasifier model is structured as a stack of mixed cells with burning solid coal/ash falling countercurrent to the rising gas/steam flow. This would be likely to show a temperature profile, thus perhaps enabling almost direct application of our existing profile control approach. However, on closer examination of the gasifier linear models provided, and some of the background information available about their construction [1], it seems that the model is actually composed of two interacting stirred cells, one each for the gas and the solid phases. Both phases operate at a different temperature and the model state is composed of component concentrations or hold-ups within each phase which interact by reaction and transfer between the phases. The fast reactions and high heat evolution in the gas phase make its temperature dynamics exceptionally fast (this is the feature that presents both stability issues in the numerical integrations as well as a need to use very fast sample periods for close control purposes. By contrast, some solid phase components change only over very extended periods, well beyond the timescale of interest in the current study. The repeated eigenvalues arise from the single gas phase residence time (for mixing in the gas phase and the fact that some members in the original 25-state vector are concentrations of chemical species absent from the current study (i.e. neither in the feed nor produced by reaction. This is the reason for the redundancy in the state vector alluded to by several authors previously and most of our work here has been conducted using 17-state reduced order models in implementation. To be sure, all state estimation techniques rely on use of a mathematical process model in some form. In essence the model is needed to define how unmeasured states (or parameters within a model relate to each other and most importantly to the available measurements. State estimation is impossible unless the latter link is in place, i.e. the full state and parameter vector must be completely observable via the measurements. Under this and other well known assumptions, and in the linear case, Kalman provided classical proof of the optimality of the state estimates (in terms of maximum likelihood, minimum error variance etc. delivered by the Kalman Filter. No similar assurances exist for non-linear filtering. Of significance here in applying the KF to the gasifier are the excitability of the plant, the form of the process models and finally the plant observability, each of which is now addressed. 3.1 Excitability In Kalman Filtering excitability is a necessary condition for guaranteed estimate error decay and convergence. It requires every member of the state and parameter vector defining the system to be contaminated with Gaussian process noise at some finite level. In this study the gasifier simulation is deterministic and so to ensure KF convergence we have assigned small but finite covariances for notional noise on both states, parameters and the process measurements. Over the time period of interest in evaluating performance in this study, no divergence problems have arisen. In a real-world application, stochastic behaviour would be present anyway and would be handled in the same manner. 3.2 Process Modelling In a real-world project on advanced control of a gasifier system, the first job to be undertaken by a process engineer would be to develop a suitable process model. To best implement our strategy this would be a dynamic, non-linear, state-space model and its locally linearised partner. And this is effectively what the creators of the Challenge models have already done. Our ideal approach would be to apply an Extended Kalman Filter (EKF which would embed both the non-linear and linearised models into the iterative algorithm at each measurement sample period. While Challenge I linear models are available at 0/50/100% load conditions, only the 100% case matches the Challenge II non-linear model and its corresponding steady state. First therefore we determined valid linear models for the 0% and 50% cases by numerical linearisation using the non-linear model which is available as a Simulink block (i.e. a black box model. Starting at the desired steady state load condition (e.g. at 0% the non-linear model was integrated over a small time increment and the end state noted. Sequential repetition with a small perturbation in each individual state and input variable yields a set of states which can be differenced from the base case to give differentials and hence successive columns in the matrices of the continuous time linear state space model which takes the form X = A X + B U B V (1 U + V Y = C X + D U U + D V V (2 X is the vector of gasifier states, U are the input control actions (i.e. manipulated variables and V=[P SINK C Q ] is the vector of process disturbance inputs, as already explained. Y=[Cv M P T] is the vector of available measurements, being respectively Cv the oultet gas calorific value, and M, P and T the gasifier bed mass, pressure and temperature. A further difficulty is that the non-linear model provided does not allow the level of access we needed for Kalman filtering

3 and its format was also cumbersome to embed within the KF algorithm. Rather than embark on building a new non-linear gasifier model of our own based on experimentation with the Challenge model, we decided to instead adopt a lower level approach which approximates the non-linear model using a set of local models. This is explained further in Section Observability As well as state estimates, our control strategy requires us also to provide estimates of the prevailing disturbance variables (i.e. downstream pressure P SINK and coal quality C Q. By augmenting the state vector with these two variables as unknown, stochastic parameters they can be incorporated for estimation in the standard way. Numerical determination of the necessary linear model matrices has already been explained (Section 3.2. Observability of either the 17thorder gasifier models or the augmented 19 th -order state and parameter case is easy to confirm qualitatively by inspection of the model matrices but a rigorous numerical check poses numerical problems owing to the ill-conditioning of the model matrices (i.e. high condition numbers. We can however demonstrate that the system is observable by simulation. For example, if the open loop non-linear system at 100% load is subject to simultaneous step changes of 0.2 bar in P SINK and +18% in coal quality the disturbance estimates converge, as shown in Figure 1. Minor fluctuation in P SINK as C Q starts to move, and vice versa, shows that the two disturbances can be distinguished properly bar % P SINK Coal Quality Time (s Figure 1: Disturbance estimates with simultaneous steps of 0.2 bar in P SINK and +18% in C Q ( Real; Estimate This is a significant outcome in that both P SINK and C Q (i.e. coal quality in whatever form this parameter is defined as in the non-linear gasifier model can both be estimated simultaneously without the need for additional measurement sensors other than those for Cv, M, P and T. This fact may offer important monitoring or optimisation opportunities on a real power plant system which are quite aside from implications for the local gasifier control of interest here. For example, continuous estimates of coal quality could be fed back to upstream coal handling processes. 3.4 Implementing the Kalman Filter Having reliable estimates for P SINK available, gasifier pressure measured and with a fixed discharge valve position we can use valve pressure difference to infer gas discharge velocity via the familiar square root relationship. Furthermore, with both gas temperature and pressure measured their effects on gas density can also both be compensated using the ideal gas law. This in effect enables us to infer the off-gas mass flowrate which in turn links directly to system power output/load (i.e. the product of gasifier off-gas flow and measured Cv defines current combustion heat release and generated power load. Thus inferred % power load can be used to interpolate between the local models to any prevailing operating point between 0% and 100%. For example we can run a Kalman Filter based on each of the local (linear models simultaneously and then use linear interpolation between the two nearest neighbour state estimates to reach the final state estimate for the current load. Because the local models in use here are linear we can also speed up iteration of the filters by pre-computing the converged Kalman gain matrices (i.e. the Wiener filter for subsequent on-line use. This is the implementation used to generate the results we present here. 4 Feedforward/Feedback Control Strategy With estimates of P SINK and C Q (i.e. V available we can implement feedforward control. From Equation (1 a local model s steady state response to changes in U and V is X=-A -1 B U U-A -1 B V V (3 Substituting into Equation (2 and setting Y=0 we arrive at U=K FF V (4 where K FF =[D U -CA -1 B U ] -1 [D V -CA -1 B V ] (5 Inferred % power load is again used to interpolate between the local model feedforward actions U. These are then added to the existing SISO control system outputs to form the actuator signals. Using these ideal values for K FF gave very oscillatory responses so we introduced a detuning factor α, set by manual trial and error, such that U=α K FF V (6 Starting from zero, we found α=0.4diag[ ] to give acceptable responses in all the tests. The whole estimation and control approach took us about 28 man-days to develop, implement and test (model building aspects excluded. 5 Performance Evaluation 5.1 Disturbances in downstream pressure P SINK Tables 1 to 6 show how the new approach performs when subjected to P SINK step and sinusoidal disturbances at the three

4 load conditions. A periodic violation of the pressure constraint occurs at 0% Load for the sinusoid in P SINK. Responses for the sinusoid at 100% Load are shown in Figure 2(a-d to enable visual comparison of the 4-loop conventional and our feedforward/feedback system performances. (base Cv(J/kg 4.366E E E E+4 Mass(kg Press (Pa 2.003E E E E+4 T (K Table 1.Step change in sink pressure for 100% load condition. (base Cv(J/kg 4.363E E E E+5 Mass(kg Press(Pa 2.003E E E E+5 T (K Table 2.Sine change in sink pressure for 100% load condition. (base Cv (J/kg 4.480E E E E+4 Mass (kg Press (Pa 1.574E E E E+4 T (K Table 3. Step change in sink pressure for 50% load condition. 5 kj/kg -5 4 kg bar Cv (Deviation from 4358 kj/kg Mass(Deviation from kg Pressure (Deviation from 20 bar Temperature (Deviation from K (base Cv (J/kg 4.478E E E E+5 Mass (kg Press (Pa 1.575E E E E+6 T (K Table 4.Sine change in sink pressure for 50% load condition (base Cv (J/kg 4.694E E E E+4 Mass (kg Press (Pa 1.150E E E E+4 T (K Table 5. Step change in sink pressure for 0% load condition. (base Cv (J/kg 4.695E E E E+6 Mass (kg Press (Pa 1.19E+6* 1.137E E E+6 T (K Table 6. Sine change in sink pressure for 0% load condition * Denotes violation of the +0.1 bar constraint K Time (seconds Figure 2 (a-d: 100% load case response for sine variation on P SINK. ( Base, Feedforward In Tables 1-6 the best case performance for each variable is shown in bold face. As can be seen, our estimation based scheme offers significantly improved performance at 100% and 50% loads but at 0% steam flow shuts off, imbalancing the corrective feedforward action. 5.2 Disturbances in coal quality C Q To test resilience to coal quality disturbances we made both positive and negative step changes in C Q while running at the three normal load conditions. In Tables 7-9, where Base refers to the 4-loop conventional system and Feedforward to the estimate-based scheme, results for maximum C Q changes of +/-18% are shown. The best case for each test is again highlighted in bold face. Violation of the temperature constraint occurs at 100% Load but with a milder +/-10% coal quality step no violation occurs, as shown in Table 10.

5 Base Feedforward Base Feedforward Cv(J/kg 18.21E E E E+3 Mass(kg Press(Pa 0.277E E E E+5 Temp(K 279(* 415.8(* Table 7. for 100% load case when C Q changes +/-18% (* Denotes violation of the +1K constraint Base Feedforward Base Feedforward Cv(J/kg 16.52E E E E+3 Mass(kg Press(Pa 0.32E E E E+5 Temp(K Table 8. for 50% load case when C Q changes +/-18% Base Feedforward Base Feedforward Cv(J/kg 13.09E+3 3.2E E E+3 Mass(kg Press(Pa 0.23E E E E+5 Temp(K Table 9. for 0% load case when C Q changes +/-18% +10% Coal Quality -10% Coal Quality Base Feedforward Base Feedforward Cv(J/kg 12.19E E E E+3 Mass(kg Press(Pa 0.265E E E E+5 Temp(K Table 10. for 100% load case when C Q changes +/-10% 5.3 Load ramping In tune with use of the local models for estimation, the feedforward actions against P SINK and C Q swings are linearly interpolated (on the inferred % Load between actions calculated separately using the local models at 0%, 50% and 100% Load. To execute a 50% to 100% load ramp we input the corresponding set point ramps to the Cv, M, P and T SISO controllers as well as in P SINK. While the KF estimated value for P SINK provokes some transient feedforward action the time profiles settle quickly to matching those with the conventional SISO strategy alone, as Figure 3 shows in terms of deviation in % load from the desired load ramp. Worthy of note is the fact that at the end of the manoeuvre the load has not met the 100% target. This is because the slow solid component compositions have been disturbed in the process and the target load will only be achieved later once these have settled. Although outside the scope of this study, there is a further potential application for estimation here in relation to load ramping. Because the %load condition can be estimated, this 4 % Time(s could be used as the measurement in a feedback servo control strategy designed specifically to produce an accurate ramp in gasifier output. 6 Conclusions A state estimation based feedforward system has been introduced for improving on the conventional control of a gasifier. It has been shown feasible to reliably estimate the two primary disturbances affecting the gasifier (sink pressure and coal quality from the available measurements using Kalman Filtering. Lacking a suitable non-linear model, the estimated % load can be used to linearly interpolate between local linear models at three operating points as a means of implementing both estimation and feedforward control. This approach improves on the response of the conventional SISO control system in most cases. Inferior performance arises when a manipulated variable s limit is hit causing imbalance between the feedforward actions. At a more general level this study has also allowed us to identify other potentially useful applications for state estimation in gasifier systems. Acknowledgements The authors are grateful to acknowledge the support of CONACyT in enabling M Chew to contribute to the work presented. References Deviation from the load set point ramp Figure 3: Deviation from target 50% to 100% load ramp ( Base, Feed forward [1] R. Dixon, Pike A.W. & Donned M.S. The ALSTOM Benchmark Challenge on gasifier control Proc. Instn. Mech. Eng., Part I, J Syst and Cont Eng, 214, (16, pp , (2000. [2] B. N. Asmar, W. E. Jones & J. A. Wilson. A process engineering approach to the ALSTOM gasifier problem, Proc. Instn. Mech. Eng., Part I, J of Syst and Cont Eng, 214, (16, pp , (2000. [3] M. Chew, W. E. Jones & J. A Wilson. On Control of Whole Temperature Profile in an Autothermal Tube- Cooled Fixed Bed Catalytic Reactor. Proc. ESCAPE- 14, Elsevier, pp (2004