Closed-loop validation

Similarly to the closed-loop validation of the scheduling and control interaction section the closed loop-validation of the unified approach is presented. For the validation we fix the

design to two different engine sizes and compare the results. Note that the demand of thermal and electrical power in both cases is identical. Figures 7.11 and 7.12 presents the operational scheme performance for an engine size of 1500cc. Similarly the closed-loop validation for the system with 2500cc engine size is presented in Figures 7.13 and 7.14. The format of the results is identical to Figures 7.7 and 7.8.

Figure 7.11: Closed-loop validation results for the simultaneous, design dependent scheduling and control of the cogeneration unit (process level). The mode of operation and set-points are determined by the scheduling problem. Heat recovery driven operation for 20s ≠ 30s, 60s≠70s, 100s≠110s and 120s≠130s, power production driven, otherwise. Top Left: water temperature (system output) set-point tracking; Top Right: water flow rate (optimal action or system disturbance otherwise); Bottom Left: power output (system output) set-point tracking (coordinated or schedule defined set-point); Bottom Right: valve position (optimal action) (Engine size: 1500cc)

It is obvious that for the same demand, the design dependent, control aware scheduling formulation requires different operating mode switches from the control scheme and provides different set-points. This proves the importance of considering all three aspects simultane- ously.

7.3 Concluding remarks

In this Chapter we presented a framework for the simultaneous process scheduling and control via multi-parametric programming via the PAROC framework. We also set the basic

Figure 7.12: Closed-loop validation results for the simultaneous, design dependent scheduling and control of the cogeneration unit (surrogate model level). The mode of operation and set-points are determined by the scheduling problem. Heat recovery driven operation for 20s ≠30s, 60s≠70s, 100s≠110s and 120s≠130s, power production driven, otherwise. Top: Heat storage schedule and surrogate model; Bottom: Power generation level schedule and surrogate. (Engine size: 1500cc)

procedure for the inclusion of the design into the formulation thus targeting simultaneously the unified design, scheduling and control problem. The framework was applied on a domestic cogeneration system. After the development of an advanced, design dependent, control scheme, we developed a control aware model that was utilized to derive and solve offline (i) the economic, design dependent, scheduling problem and (ii) the design dependent surrogate QP model. The different optimization levels were cross-validated against the original model of the process and their performance was assessed. The importance of multi-parametric programming and the PAROC framework in our approach is essential as (i) it allows for the decomposition of the problem into smaller more tractable problems, (ii) it provides an explicit map of all possible optimal solutions and (iii) it is based on a validated, model based procedure.

Figure 7.13: Closed-loop validation results for the simultaneous, design dependent scheduling and control of the cogeneration unit (process level). The mode of operation and set-points are determined by the scheduling problem. Heat recovery driven operation for 20s ≠ 30s, 40s ≠ 50s, 60s ≠ 70s, 80s ≠ 90s, 100s ≠ 110s and 120s ≠ 130s, power production driven, otherwise. Top Left: water temperature (system output) set-point tracking; Top Right: water flow rate (optimal action or system disturbance otherwise); Bottom Left: power output (system output) set-point tracking (coordinated or schedule defined set-point); Bottom Right: valve position (optimal action) (Engine size: 2500cc)

Figure 7.14: Closed-loop validation results for the simultaneous, design dependent scheduling and control of the cogeneration unit (surrogate model level). The mode of operation and set-points are determined by the scheduling problem. Heat recovery driven operation for 20s≠30s, 40s≠50s, 60s≠70s, 80s≠90s, 100s≠110s and 120s≠130s, power production driven, otherwise. Top: Heat storage schedule and surrogate model; Bottom: Power generation level schedule and surrogate. (Engine size: 2500cc)

Chapter 8

Conclusions and future work

8.1 Conclusions

The aim of this thesis was to address the aspect of integration among process design, control and operational optimization. On this basis, a decomposition model based method was introduced which utilizes multi-parametric programming. First, the PAROC framework and prototype software platform was presented. A domestic CHP unit was mathematically modeled and used as the test bed for a variety of optimization problems. This CHP model was used for (i) advanced control studies, (ii) integrating design and control optimization, (iii) integrating a receding horizon optimization based scheduling formulation with advanced control and (iv) addressing the integrated problem of scheduling, control and optimization in a simultaneous fashion. In summary the following were shown.

• The PAROC framework: A model based framework was introduced in order to formulate, solve and validate a variety of receding horizon policies (including control, estimation and scheduling problems). The diversity of the model was showcased as well as its major characteristics which can be summarized as: (i) its ability to produce explicit optimization policies, a so-called map of solutions, (ii) its closed-loop valida- tion capabilities and (iii) its compatibility with advanced modelling and optimization software which enables the incorporation of advanced control strategies into highly accurate model simulation tools.

• Simultaneous design and advanced control optimization: A decomposition method via multi-parametric programming was presented. The decomposition method is based on the ability to derive explicit control expressions that are design dependent, via an approximation step, and incorporate them into a design dynamic optimization

formulation. It is based on a single ‘high fidelity’ model and can provide validation of the design dependent control scheme prior to the design optimization step.

• Simultaneous scheduling and control: The aspect of simultaneous scheduling and control was addressed via the formulation and solution of control aware scheduling problems. The scheduling solution was synchronized with the control solution via the formulation of a surrogate quadratic program. The ability to solve these classes of problems offline was of vital importance as it (i) reduced the online computation time and (ii) provides the ability to incorporate the actions within an overall design optimization problem.

• Simultaneous design, scheduling and control: Addressing the three problems simultaneously was discussed in the final part of the thesis. It was shown that design dependent control and design dependent control aware schedules can be formulated and validated based on the same process model. It was also shown how different designs can affect the optimal schedule and consequently the optimal control strategy.