2 MPC Based on Step Response Models y2 Time Manipulated variables 789 Figure 2-5 Responses to a Unit Torque Disturbance for Plant #1(nomina model Plant #1) 2 Outp Time Manipulated variables 5678910 Time Figure 2-6 Responses to a Unit Torque Disturbance for Plant #2(nominal model Plant #1)
2 MPC Based on Step Response Models 2-28 Figure 2-5 Responses to a Unit Torque Disturbance for Plant #1 (nominal model = Plant #1) Figure 2-6 Responses to a Unit Torque Disturbance for Plant #2 (nominal model = Plant #1) 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 0 10 Outputs Time Manipulated Variables Time 5 -5 -10 y2 y1 u1 u2 0 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 0 -2 -4 2 Outputs Time Manipulated Variables Time 4 2 0 y2 y1 u1 u2
Application: Idle Speed Control As expected, the nominal performance for both Plant #1 and Plant #2 has deteriorated when compared to the simulations shown in Figure 2-1 and Figure 2-2. A similar effect would be observed if we had detuned the controller which uses plant #2 as the nominal model Simulation #4. The parameter values are the same as in Simulation #3. Instead of using cmpc, we use mpccon and mpcsi m for simulating the closed loop mpcsi m, and cmpc. As we can see, for this example and these tuning Con and parameters, the improvement obtained through the on-line optimization in cmpc is small. However, the difference could be large, especially for ill-conditioned systems and other tuning parameters. For example, by reducing the output horizon to P=80 while keeping the other parameters the same, the responses for Plant 1 found with mpccon and mpcsi m are significantly slower than those obtained with cmpc(Figure 2-8) Solid: cmpc y Dashed: mpccon and mpcsim Time Figure 2-7 Comparison of Responses From cmpc, and mpccon and mpcsi m for
Application: Idle Speed Control 2-29 As expected, the nominal performance for both Plant #1 and Plant #2 has deteriorated when compared to the simulations shown in Figure 2-1 and Figure 2-2. A similar effect would be observed if we had detuned the controller which uses Plant #2 as the nominal model. Simulation #4. The parameter values are the same as in Simulation #3. Instead of using cmpc, we use mpccon and mpcsim for simulating the closed loop responses. Figure 2-2 compares the responses for Plant #1 using mpccon and mpcsim, and cmpc. As we can see, for this example and these tuning parameters, the improvement obtained through the on-line optimization in cmpc is small. However, the difference could be large, especially for ill-conditioned systems and other tuning parameters. For example, by reducing the output horizon to P = 80 while keeping the other parameters the same, the responses for Plant # 1 found with mpccon and mpcsim are significantly slower than those obtained with cmpc (Figure 2-8). Figure 2-7 Comparison of Responses From cmpc, and mpccon and mpcsim for Plant #1 P = inf 0 2 4 6 8 10 -4 -5 -6 -3 Solid: cmpc Time 0 -1 -2 1 Dashed: mpccon and mpcsim Output y1 y2
2 MPC Based on Step Response Models Solid: cmp Dashed: mpccon and mpesim Time Figure 2-8 Comparison of Responses From cmpc, and mpccon and mpcsi m for Plant #1(P= 80
2 MPC Based on Step Response Models 2-30 Figure 2-8 Comparison of Responses From cmpc, and mpccon and mpcsim for Plant #1 (P = 80) 0 2 4 6 8 10 -4 -5 -6 -3 Solid: cmpc Time 0 -1 -2 1 Dashed: mpccon and mpcsim Output y1 y2 -7
Application: Control of a Fluid Catalytic Cracking Unit Application: Control of a Fluid catalytic Cracking Unit Process Description Fluid Catalytic Cracking Units(FCCUs)are widely used in the petroleum refining industry to convert high boiling oil cuts(of low economic value)to ighter more valuable hydrocarbons including gasoline. Cracking refers to the catalyst enhanced thermal breakdown of high molecular weight hydrocarbons into lower molecular weight materials. A schematic of the FCCU studied* is given in Figure 2-9. Fresh feed is contacted with hot catalyst at the base of the riser and travels rapidly up the riser where the cracking reactions occur. The desirable products of reaction are gaseous (lighter)hydrocarbons which are passed to a fractionator and subsequently to separation units for recovery and purification. The undesirable byproduct of cracking is coke which is deposited on the catalyst particles, reducing their activity. Catalyst coated with coke is transported to the regenerator section where the coke is burned off thereby restoring catalytic activity and raising catalyst temperature. The regenerated catalyst is then transported to the riser base where it is contacted with more fresh feed. Regenerated catalyst at the elevated temperature provides the heat required to vaporize the fresh feed as well as the energy required for the endothermic cracking reaction 4. A detailed problem description and the model used for this study ca mamic Simulator for a Model IV Fluid Cata Chem.Eng,17(3),1993, pages275-300 2-31
Application: Control of a Fluid Catalytic Cracking Unit 2-31 Application: Control of a Fluid Catalytic Cracking Unit Process Description Fluid Catalytic Cracking Units (FCCUs) are widely used in the petroleum refining industry to convert high boiling oil cuts (of low economic value) to lighter more valuable hydrocarbons including gasoline. Cracking refers to the catalyst enhanced thermal breakdown of high molecular weight hydrocarbons into lower molecular weight materials. A schematic of the FCCU studied4 is given in Figure 2-9. Fresh feed is contacted with hot catalyst at the base of the riser and travels rapidly up the riser where the cracking reactions occur. The desirable products of reaction are gaseous (lighter) hydrocarbons which are passed to a fractionator and subsequently to separation units for recovery and purification. The undesirable byproduct of cracking is coke which is deposited on the catalyst particles, reducing their activity. Catalyst coated with coke is transported to the regenerator section where the coke is burned off thereby restoring catalytic activity and raising catalyst temperature. The regenerated catalyst is then transported to the riser base where it is contacted with more fresh feed. Regenerated catalyst at the elevated temperature provides the heat required to vaporize the fresh feed as well as the energy required for the endothermic cracking reaction. 4. A detailed problem description and the model used for this study can be found in the paper by McFarlane et al., “Dynamic Simulator for a Model IV Fluid Catalytic Cracking Unit,” Comp. & Chem. Eng., 17(3), 1993, pages 275–300
2 MPC Based on Step Response Models fresh feed feed heater Figure 2-9 Fluid Catalytic Cracking Unit Schematic Product composition, and therefore the economic viability of the process, is determined by the cracking temperature. The bulk of the combustion air in the regenerator section is provided by the main air compressor which is operated at full capacity. Additional combustion air is provided by the lift air ompressor, the throughput of which is adjustable by altering compressor speed. By maintaining excess flue gas oxygen concentration, it is possible to ensure essentially complete coke removal from the catalyst
2 MPC Based on Step Response Models 2-32 Figure 2-9 Fluid Catalytic Cracking Unit Schematic Product composition, and therefore the economic viability of the process, is determined by the cracking temperature. The bulk of the combustion air in the regenerator section is provided by the main air compressor which is operated at full capacity. Additional combustion air is provided by the lift air compressor, the throughput of which is adjustable by altering compressor speed. By maintaining excess flue gas oxygen concentration, it is possible to ensure essentially complete coke removal from the catalyst