田纳西伊斯曼过程在线优化文档

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一个实时优化策略在这里描述,它可以消除传统RTO方法的稳定状态等待要求。为了确保它的成功,四个关键元素—动态模型,在线参数和状态估计,一个全局控制系统,和一个优化算法;这四个部分一定要很好的协同。当传统RTO不能使用时,它尤其有效,并且可以容忍在和系统反应时间相近的时间尺度上出现的干扰。这个策略应用到TE过程,节约了6%的操作花费,相比于没有该方法。
Sometimes the NLP formulation is infeasible. The production rate. The planner also specifies any additional usual reason is that the specified production rate con- equality constraints needed for the current scenario straint cannot be satisfied. For example, this happens For example, if there are large random disturbances when disturbance 6 occurs. Whenever NPsol signals and the reactor pressure and or level repeatedly approach that the nlp is infeasible, we switch automatically from their alarm limits, the planner should decrease the reactor operating-cost minmization to production-rate maximiza- pressure or increase the reactor level constraints to reduce tion the alarm frequency. This will increase operating costs however. On the other hand, if the reactor pressure and 2.4.2 Model update level are always far from the alarm conditions, the planner could move them closer, thereby decreasing costs The model, Eq. 1 and 2, is used for both control and RTO. As shown above, RTO only needs an update of the 2.4.5 Results analysis the model parameters, dxkk, but MMPC requires good estimates of the states as well. The ekf tuning has The optimization calculation provides setpoints for 5 con- to balance the conflicting objectives of steady-state op trolled outputs reactor temperature, %A and % c in the timization and mmPc reactor feed, separator temperature, and purge flowrate. For example, we would like the rto to be insensitive Depending on the objective function, it may also provide to transient(short-term) disturbances. Such disturbances a production rate setpoint unavoidably spread into modeling parameters, however We want the rto to respond to sustained disturbances so dkik fluctuates. The MPC should respond to these To avoid a response to a small or short-term random dis disturbances to minimize short-term variability in its con- turbance we calculate the differcnce between the current trolled outputs, but the RTo should not respond. Be- optimized objective function and that from the previous tween each optimization cycle, modeling parameters are cycle. For the maximum production rate case, if the pre updated 20 times by the eKF. To reduce the effect of dicted change in the optimal production rate is less than short-term variations on the RTO, we filter the parame- twice the production ratc mcasurcmcnt standard devia ters by averaging the 5 most recent values tion, we do not implement the new setpoints. Similarly for the minimum operating cost, if the change in the oper 2.4.3 Model Accuracy Check ating cost is smaller than S 1/h we do not implement the new setpoints. This strategy works well to reduce noise Since the current plant condition is rarely a steady-state, in the setpoints that are manipulated by the rto model validation techniques based on a steady-state as sumption are inappropriate. Instead, we calculate the fol 2.4.6 Update controller setpoints lowing prediction error at each sampling instant: Most of the time, the RTO requests small changes in the ek=yk一yk|k-1 8 setpoints, and we can send them to the control system without modification. There are exceptions, however, es where yt is the measurement vector at sampling period pecially when there is a major production goal change k, and the model prediction of the outputs is yx k-1 such as %G in the product changing from 10 to 50% g(xk k-1,uk-1,dx k-1). Then each component of ek is Setpoints are then filtered to produce ramps with a spec divided by the standard deviation of the corresponding ified maximum rate. For ramping rates and other details measurement noise. A new vector Ek is obtained. Each component of Er reflects the weighted prediction error of that measurement. If one component of Et is too large,or the norm of Et(which we call the prediction error magni- 3 Case Studies tude)is bigger than a threshold, RTO is disabled until the prediction error becomes acceptable. The choice of toler- In this section, we show our simulation results for differ ances on ck is problem-specific. Tests may be needed in ent RTO cases. Each case represents a particular type of order l arrive at tolerances that are small enough to en- challenge in plaut uperation. To successfully run all these sure that RTO always uses a reasonable model, yet large cases, the entire system has to be well coordinated, Thus enough to allow rto to take place. the performance and robustness of each system element is severely tested. Such tests are more"relevant" than arti- 2.4.4 Instructions from planner ficial tests of the components. For example, it is hard to judge whether estimator performance is" adequateun In the te process, the planner specifies the %g in the til its estimates are being used in MMPC and RTO. On product, and indicates whether we should maximize pro. the other hand tests of isolated components help improve duction rate or minimize the operating cost at a fixed understanding and diagnose problcms. Many such tests 2962 Operating cost [S/hr Reactor temperature [c] Feed 1 valve [% Feed 4 valve [ 128 1261 80 124 v 50 120 100 100 Estimated A in feed 4 [%] stimated日 in feec4{ Compressor valve [%] Purge valve 1%] 50 5 Timehri TIme Time(hr) Figure 3: Key variables variation with and without. RTo Figure 4: Key manipulated variables variation for Case 1 for Case #1. Solid line- operating cost with RTO. Dot ted line-operating cost without RTO. Dashed line True steady state optimal operating cost. The simulation mator and controller. The large variation of the operating starts with disturbance #1 on. At t=20 hour, disturbance cost in the beginning is mainly due to the transient in the #2 occurs. At t=60 hour, disturbance #1 is removed. At purge valve, which is needed to control reactor pressure t=100, disturbance #2 is removed The optimizer has little impact at first because the opti ating cost only changes by 2% when disturba On the other hand, the operating cost is ver of this work in order to tune nce #2. It 40% incre the system to achieve the overall performance shown in the optinal steady-state cost. The reason is that b is a the following cases, but space limitations prevent their non-condensible inert, and can only be removed by purg inclusion here ing, which is the dominant term in the cost function. The RTO is crucial here to provide new setpoints. As shown 3.1 Case 1-Feed composition sustained in Fig 3, in less than 20 hours, disturbance #2 is fully disturbances recognized. The RTo calls for nearly double the original purge rate(Fig. 4). The operating cost increases accord The first case involves Mode 1, which minimizes the oper- ingly. In this period, the rto gives the optimal operating ating cost under fixed production rate and a 1: 1 G: H mass cost as 148s /hr. which is 9%o higher than the true optimal ratio in the product. At the beginning of the simulation, operating cost.(see Table disturbance#1 occurs. This causes a step change in the At t =60, when disturbance #1 is removed, the esti A/C feed ratio in feed #4, while B composition is con- mator quickly detects the A composition change(Fig 3) stant. After t= 20 hours, disurbance #2 occurs, which But now the RTO finds a totally different optimal condi- causes a step change of b composition in feed stream 4, tion. The reactor temperature target increases by about while A/C ratio is kept constant. At t= 60, disturbance 3 C, and the compressor valve goes from closed to about #1 is removed, and at t= 100, disturbance #2 is re- 65 open. a g in reactor feed increases by 4%.As moved. From t= 100 until the end of the simulation Ricker [4 argued, there are two very different local opti (t= 140), there are no disturbances mal points in the tE process. Depending on the operating The objective is to see whether the estimator can condition, both have the possibility to be the global op- quickly identify the feed composition change, which is timum. They are distinguished by the compressor valve unmeasured, even when there are multiple disturbances. opening. When the compressor valve is fully open, there When the estimator performs well, we expect the RTo is lower product loss. Otherwise, the purge loss is lower to supply near-optimal setpoints for the controller. As At t= 100, disturbance #2 is removed. Now there shown in Fig. 3, the estimator identifies the change of a is no disturbance. After another 20 hours, the estima omposition in stream 4 within about 5 hours, As shown tor changes the B% in stream 4 back to the correct value in Fig. 4, feed 1 is increased and feed 4 decreases slightly of 0.5. The operating cost starts to decrease. But the to compensate for the reduced A in feed 4. Disturbance operating strategy does not return to the initial condi- #1 is easily rejected. Most of the work is done by the esti- tion. The RTO settles into a local optimum instead of 2963 the global optimum. This illustrates a potential pitfall 200- Operatng cost (sh, Production rate(m a/hr. 1 in RTO, Exsiting NlP solvers cannot guarantee that the solution of a non-convex problem is globally optimal. The impact on cost is negligible in this case, but could be large in general 州 Table 1: Operating cost comparison for Ca 100 ime period(hr)0-2020-6060-1001001400-140 Disturbance +t 1,2 Inen B in purge [ %] 卫one G in product [% True Optimum 101 36140 103 S.S. Optimum 103148 143 103 Mean W rto 147 1287 Mean W/O RTO 150 166 Table I compares true optimum, steady state optimum 25 found by RTO, and the average cost for each period with 50 and without RTo. The true optimum is found by direct Time(hr.) steady-state optimization of the TE code [4. The steady state optimum is the cost achieved by RTo at the new figure 5 Key variables variation for Case 2. Solid line- steady-state following each disturbance result with the RTo, Dashed line true steady state The final two rows in Table 1 indicate the economic optimal result. The simulationstart from Mode l to Mode potential of RTo. Mean values of operating cost are com- 3. At 40 hour instant, Mode 6 is requested. G: H ratio is puted for each period and for the entire run. The val- 90: 10 ues labeled "without RTo are the results obtained when RTO is disabled and all setpoints are held constant at their initial conditions. The control strategy is otherwise controller when the setponts change dramatically. In the identical. The dotted line in Fig 3 and 4 shows the op base case, G H ratio is 50: 50. Downs and Vogel propose erating cost when RTO is off. The dashed line is the true two other product mixes where the G: H ratio can be either steady-state optimum of the plant for the given distur 90:10ori0:90 bances Figs. 5 and 6 show the simulation result for a g: h ra As shown in Table 1, for the whole 140-hour period, tio of 90: 10. The initial condition is Mode l with a G: H compared to the true optimum, the operating cost with ratio of 50: 50. We start the simulation by asking the G: H the Rto is only 5%higher. The major loss is in the period ratio to change to 90: 10 with a fixed production rate. We with both disturbances #1 and #2. When considering the also ask the rTo to minimize the operating cost. This is steady-state optimum found by the RTO, all losses are less Mode 3 in the tE process. At t= 40, we ask the rto to than 2% except for the period with both disturbances#1 maximize the production for the same product composi- and #2. In this period, the Rto chooses a local minmum, tion. The D feed valve(Fig. 6)immediately responds to where the compressor valve is almost closed Fig. 3). Note the production setpoint change, and it saturates. This in- that the Rto settles in a local minimum at the end of dicates that the production rate is hitting its upper limit simulation. The cost penalty is very small. The low operating cost is due to minimum purge ios Compared with simulation without the RtO, we have The optimal b in the purge changes from 25% to about about 7% savings in the operating cost for the whole sim- 45%. Si ince there is only 0.5 mole b in stream 4, the ulation. The major saving comes from the period with buildup of b in the inventory is very time-consuming. In disturbance #2 only. Here, the rto quickly identifies a the early part of the simulation, the purge valve is almost new global optimum, which is in the vicinity of the true completely closed. The control system does this to in- optimum. The 7% savings is not dramatic, because the crease the B composition in the system. This causes a simulation starts from a near-optimal condition. The con- temporary reduced operating cost in the early part of the troller configuration is designed to provide near-optimal simulation. The true optimal production rate is virtually operation even when RTo is off identical to the one achieved by the RTO. The operating cost for the maximum production rate region is about 2% 3.2 Case 2- Product mix change higher than the true operating cost. The MMPC strategy used here responds much faster Another interesting case is a product composition change. than the result reported by Ricker [5], where itt took more The challenge here is to see whether RtO can define re- than 15 hours to completely change the product composi- alistic setpoints for a condition far from the initial oper- tion. Here, it takes less than 5 hours, showing that MMPC ating point. A secondary problem is the stability of the and RTo work very well together 2964 Reactor pressure伙P °a Reactor temperature [c] of the TE code. The difference is usually smaller than 5%, which includes both dynamic loss( due to short-term 2960 upsets)and non-optimal steady state losses(model error and failure to converge to a global optimum. Overall RTO typically saves 3-6% in operating cost compared to the results with near optimal(but constant)setpoints. 220 100 Reactor leval [ D feed vahe[‰ References [1]James J. Downs and Ernest F. Vogel. A plant-wide industrial process control problem. Computers and Chemical Engineering, 17(3): 245-255, 1993 [2] H. Lee. Recent advances in model predictive control 100 50 and other related areas. In Chemical Pracess Control Time(hr,) T meth CPCV. 1996 Figure 6 Key controlled and manipulated variables vari- [3] K. R Muske and J. B. Rawlings. Nonlinear moving ation for Case 2 with G: H ratio as 90: 10 horizon state estimation. In Methods of Model based Process Control, pages 349-366, 1995 4 Conclusions 4] N. L. Ricker. Optimal steady-state operation of the tennessee eastman challenge process. Computers 8 The difficult part of the modeling is to choose a correct Chemica! Engincering, 19 (9): 949-959, 1995 set of inputs, outputs, states, and modeling parameters Before constructing a model, the needs of control and op- 15] N. L. Ricker and J. H. Lee. Nonlinear model predic- timization must be carefully evaluated. For exanple the tive control of the tennessee eastman challenge pro- model used here neglects fast valve dynamics. This is cess. Computers Chemical Engineering, 19(9): 961 possible because the lower-level control system provides 981,1995 flow control. The valve dynamics are important when (61 N. L. Ricker and J.H. Lee. Nonlinear modeling tuning these controllers, but have virtually no impact on and state estimation for the tennessee eastman chal- the upper level controllers, which operate at a much lower samp ling frequency lenge process. Computers 6 Chemical Engineering, 19(9):983-1005.1995 a dynamic model is of little use if it cannot adapt to changing plant conditions. We use an extended Kalman [7] Ming Yan. Multi-objective, Plant-wvide Control and filter(ekF) to estimate states and parameters. The ma Optimization of Chemical Processes. PhD thesis, Uni- jor difficulty in designing the estimator is to choose the versity of Washington, 1996 best measurement set. This decision is strongly coupled to the model accuracy issue If the model of a specific [8 Ming Yan and N L. Ricker. Multi-objective control of output is inadequate, one should not use its measurement the tennessee eastman challenge process. In Proceed- for model correction. For example, in the present work ings of the 1995 American Control Conference, pages we found that h in the purge and %o e in the product 245-249,1995 frequently exhibited large prediction errors. There was no obvious way to improve the model in this respect. If these errors were heavily weighted, the EKF spread them over all outputs. When we reduced the weight on these two innovations, the bias in other variables dropped dra matically, and overall performance improved The rTo strategy proposed here outperformed the con ventional strategy in which the plant must achieve near- steady operation between each optimization cycle. The present strategy can execute much more frequently, when a sustained disturbance occurs, the plant goes the new optimum rapidly The RTo results are also very close to the true opti mal values, which can be obtained by direct optimization 2965

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