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CHAPTER 3 PLANT-WIDE CONTROL
Reflecting on chemical process control of the 1970’s, the seminal review article by Foss (1973) deplored the gap which existed between the theory of process control and its application. The significant theoretical advances made during that time in optimal control and state estimation were successfully translated for application in the aerospace industry, but these advances were not yet translatable to the chemical process industry. Kestenbaum, Shinnar and Thau (1976) demonstrated how a classical PID controller applied to a chemical process performed better than prevalent optimisation-based design methodologies in the presence of model uncertainties, unmeasured process disturbances, and changing process parameters. The main thesis of Foss (1973) and Kestenbaum et al. (1976) was that the theoretician and not the practitioner was responsible for closing the gap between control theory and the more stringent and rigorous demands of industrial process control. Furthermore, apart from addressing issues such as inclusion of process dynamics and uncertainty in the controller design, the main and most critical issue for theoreticians and practitioners to address for industrial processes was the configuration of the control system. For successful control of any plant, they stated that a systematic framework was required to guide qualitative and quantitative decisions regarding the variables to measure, manipulate, and control (control objective), as well as the relationship between these variables to achieve a specific control objective (control structure) (Stephanopoulos 2014).
The unit-based approach of Umeda, Kuriyama and Ichidawa (1978) decomposes the plant into individual units of operation, generates a control structure for each unit, combines the structures, and then eliminates possible conflicts in the combined control structure. However, as the size of the plant grows, this procedure becomes impractical given the number of conflicts which arise. Also, it does not provide a framework to capture the broad range of objectives for the plant as a whole. As a response to the need for systematic control structure configurations which considers the plant wide objectives, Morari, Arkun and Stephanopoulos (1980) cast the problem in a multi-layer multi-echelon decomposition framework. In the vertical, multi-layer decomposition, the control tasks are decomposed into a series of control tasks with different frequencies. This is similar to the common hierarchical separation of control tasks starting with base layer control, supervisory control, optimisation, and process planning (Seborg, Edgar and Mellichamp 2004). The use of hierarchy representations reduces the complexity of the problem by allowing the designer to address process goals within different ranges of a time-horizon. In Morari et al. (1980), the scope of each layer is determined by a series of quantitative criteria reflecting the sensitivities of the operating objectives to various variables. In the horizontal, multi-echelon decomposition, the control tasks are organized according to different segments of the process. This is based on the sensitivity conveyed by Lagrangian multipliers associated with the interconnections among process sub-systems. The structure of these hierarchical control tasks provide the boundaries of regulatory control tasks (Ng and Stephanopoulos 1996, Stephanopoulos and Ng 2000).
Rather than following a mathematically orientated approach as in Morari et al. (1980), a process orientated approach to control structure configuration is proposed by Luyben, Tyreus and Luyben (1997). Their plant-wide procedure, specifically for chemical process plants, is listed below:
1. Establish control objectives, i.e. determine the controlled variables.
2. Determine the control degrees of freedom by counting the number of independent valves.
3. Establish energy inventory control to remove the exothermic heats of reactions and to prevent propagation of thermal disturbances.
4. Set the production rate using a variable which can increase the reaction rate in the reactor.
5. Ensure product quality and handle safety, operational and environmental constraints.
6. Do inventory control and fix the flow in liquid recycle loops.
7. Check component balances, and return to Step 4 if required.
8. Control individual unit operations.
9. Use the remaining control degrees of freedom to optimise economics or improve dynamic controllability.
The rationale for the order of these steps is as follows: Steps 1 and 2 determine the objectives and the available degrees of freedom. Since the methods of heat removal are intrinsic to heat reactor design, and reactors are considered the heart of any process, Step 3 ensures heat generated by an exothermic reaction is efficiently dissipated. Step 4 determines where the production rate is set. Step 5, where product quality is set, follows Step 4 as the control of product quality is of higher priority than inventory control in Step 6. Variability in inventories is not as critical as ensuring the variability in product quality is as small as possible. After the total process mass balance is satisfied, the individual component balances can be checked in Step 7. If in Step 7 it is evident the choice of throughput manipulator is invalid given other plant-wide control considerations, it is necessary to return to Step 4. The plant-wide control issues are accomplished when Step 7 is completed, such that Step 8 can be used to improve performance of unit operations, and Step 9 can be used to address higher level concerns. From a review of the mathematically and process orientated approaches to plant-wide control, Larsson and Skogestad (2000) proposed a plant-wide control design framework using elements of both these approaches. The framework, which was expanded by Skogestad (2004), distinguishes between economic control and regulatory control by dividing structural decisions into two parts: a top-down and a bottom-up analysis. The aim of the top-down analysis is to define an economic supervisory control structure that achieves close-to-optimal steady-state economic operation (Le Roux, Skogestad and Craig 2016b). The aim of the bottom-up analysis is to define a stable and robust regulatory control structure capable of operating under the conditions imposed by the economic supervisory layer. In comparison to Luyben et al. (1997), Skogestad (2004) combines Steps 1 and 9 since the selection of controlled variables should depend on the plant economics. The procedure is given below:
1. Top-down analysis (to address steady-state operation)
(a) Define the operational economic objective, and determine the steady-state degrees of freedom.
(b) Determine the optimal steady-state operation.
(c) Select the primary controlled variables influencing the economic cost function.
(d) Select the variable responsible for manipulating the process throughput.
2. Bottom-up analysis (to address dynamic operation)
(a) Select the regulatory control structure.
(b) Select the supervisory control structure.
(c) Select the the real-time optimisation structure.
(Additional guidelines on decisions specific to each step are provided by Minasidis, Skogestad and Kaistha (2015).) The plant-wide control design framework of Skogestad (2004) is applied by Downs and Skogestad (2011) to industrial processes operated by the Eastman Chemical Company. It is noted that since the dawn of the holistic approach to process control design, the variety of frameworks to address the design problem illustrates the difficulty in finding a unified approach. At least from the industrial perspective of J. Downs, one of the original proposers of the “Tennessee Eastman challenge problem” (Downs and Vogel 1993), the procedure outlined by Skogestad (2004) is adequate to design a controller capable of optimising the process economics of a plant (Downs and Skogestad 2011).
The aim of this chapter is to construct a control strategy for a comminution circuit to achieve operational goals determined by the economic objectives of the larger mineral processing plant. The control strategy is developed according to the plant-wide control design procedure outlined by Skogestad (2004). The chapter is organised according to the top-down and bottom-up analysis steps listed above.
TOP DOWN ANALYSIS
Operational economic objective
The questions to answer in this step are: what is the scalar cost function which defines the economic objective of operation, and what are the available dynamic and steady-state degrees of freedom to achieve this economic objective? Given the mineral processing plant economic objective defined in (2.6)
The economics of the plant are primarily determined by its steady-state behaviour. In general the steady-state degrees of freedom are the same as the economic degrees of freedom. Identifying the dynamic degrees of freedom is generally easier than identifying the economic (steady-state) degrees of freedom. However, it is the number of economic degrees of freedom (NSS) and not the variables themselves which is important to determine. NSS gives the number of controlled variables to be selected in the third step of the top-down analysis (Skogestad 2012).
NSS is determined by subtracting the number of manipulated and controlled variables with no economic steady-state effect (N0) from the number of dynamic degrees of freedom (ND). Since there are six manipulated variables, it means ND = 6:
• Mill ore feed-rate (MFO)
• Mill inlet water flow-rate (MIW)
• Mill ball feed-rate (MFB)
• Sump feed water flow-rate (SFW)
• Cyclone feed flow-rate (CFF)
• Mill rotational speed (fc)
The liquid levels in tanks generally form part of the variables with no economic steady-state effect.
There are four levels throughout the circuit to consider:
• Total charge filling in the mill (JT )
• Ball filling in the mill (JB)
• Mill slurry volume
• Sump slurry volume (SVOL)
As discussed in Section 2.1, JT , JB and the mill slurry volume can all affect TP, PSE and Pmill .
Therefore, these three levels in the mill remain crucial steady-state degrees of freedom to define. At the sump, SVOL has no economic steady-state effect and can be controlled through either SFW or CFF. This means N0 = 1. Consequently, there are five steady-state degrees of freedom NSS = ND?N0 = 6?1 = 5:
Optimal steady-state operation: Grindcurves
Once the cost function is identified, the question is what are the operational conditions for optimal steady-state operation? In other words, how should the set-points be chosen for optimal circuit operation? The optimal steady-state of operation for the single-stage grinding mill circuit is primarily determined by the operating performance of the mill. The main mill performance indicators are Pmill QS and y. The quazi-static curves of Pmill , QS and y as functions of JT and fc are called grindcurves and can be used to determine the optimal steady-state operating region of a mill (Van der Westhuizen and Powell 2006, Powell et al. 2009).
CHAPTER 1 INTRODUCTION
1.1 PROBLEM STATEMENT
1.1.1 Context
1.1.2 Research questions
1.2 CONTRIBUTION AND PUBLICATIONS
1.3 ORGANISATION
CHAPTER 2 COMMINUTION: PROCESS DESCRIPTION AND ECONOMIC OBJECTIVES
2.1 COMMINUTION PROCESS: SINGLE-STAGE GRINDING MILL CIRCUIT
2.1.1 Process description
2.1.2 Controlled and manipulated variables
2.1.3 Additional circuit variables
2.1.4 Disturbances
2.2 RELATIONSHIP BETWEEN COMMINUTION AND SEPARATION
2.2.1 Separator concentrate grade and recovery
2.2.2 Effect of cyclone product flow-rate (CPF) and density (CPD) on recoverygrade curve
2.2.3 Effect of cyclone product particle size estimate (PSE) on recovery-grade curve
2.3 MINERAL PROCESSING PLANT REVENUE
2.3.1 Net smelter return
2.3.2 Comminution and separation cost
2.4 CONCLUSION
CHAPTER 3 PLANT-WIDE CONTROL
3.1 TOP DOWN ANALYSIS
3.2 BOTTOM-UP ANALYSIS
3.3 CONCLUSION
CHAPTER 4 MODEL PREDICTIVE STATIC PROGRAMMING
4.1 MILLING CIRCUIT MODEL DESCRIPTION
4.2 OUTPUT TRACKING USING MODEL PREDICTIVE STATIC PROGRAMMING
4.3 NON-LINEAR MPC
4.4 SIMULATION
4.5 DISCUSSION
4.6 CONCLUSION
CHAPTER 5 STATE AND PARAMETER ESTIMATION FOR A GRINDING MILL
5.1 OBSERVER MODEL FOR A GRINDING MILL
5.2 OBSERVABILITY OF STATES AND PARAMETERS
5.3 OBSERVER DESIGN
5.4 SIMULATION
5.5 RESULTS AND DISCUSSION
5.6 CONCLUSION
CHAPTER 6 CONCLUSION
6.1 PLANT-WIDE CONTROL
6.2 MODEL PREDICTIVE STATIC PROGRAMMING
6.3 STATE AND PARAMETER ESTIMATION
6.4 FUTURE WORK
APPENDIX A
APPENDIX B
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