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Author: Ramprasad Yelchuru, PhD student, NTNU, Trondheim, Jan 2008 - Dec 2011.
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Background:

Selecting appropriate controlled variables is a key issue in Plantwide Control area
to operate the plant close to optimum in the presence of disturbances.
The PROST Group, NTNU, Trondheim have piloted self optimizing control ideas to address 
the controlled variables selection problem in Plantwide control

The files in this folder are to solve self optimizing control problem defined in

	I. J. Halvorsen, S. Skogestad, J. C. Morud, V. Alstad, Optimal selection
	of controlled variables, Ind. Eng. Chem. Res. 42 (2003).

This problem for a full H with given measurement set is solved as a constrained QP in 

	V. Alstad, S. Skogestad, E. Hori, Optimal measurement combinations
	as controlled variables, Journal of Process Control 19 (2009) 138-148.

Incorporating a structure in H while selecting controlled variables as c = Hy is very important.
To find c s as combinations of measurements with (decentralized) block diagonal/triangular H are
non-convex. Hence, we propose a few new ideas and convex approximation methods.
 
In my PhD, I solved these problems using MIQP formulations with structured H 
(block-diagonal/decentralized or triangular) and standard cplex solvers. We proposed two 
convex approximation methods.

    	R.Yelchuru and S. Skogestad, “Optimal controlled variable selection with structural 
	constraints using MIQP formulations”, IFAC Congress, Milano, Aug 28-Sep 2, 2011. 

	R.Yelchuru and S. Skogestad, “Optimal controlled variable selection for individual 
	process units in self optimizing control with MIQP formulations”, American 
	Control Conference, San Francisco, California, USA, June 29-July 1, 2011.


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Details of the programs and data files in this folder:

Prerequisite: 
You should have the freely available IBM ILOG CPLEX solver (IBM academic initiative) 
installed in your computer.


cplex_main_structuredH_final.m  - The main script file to find a full H matrix with 
				a structured H (block-diagonal or triangular) with 
				i number of optimal  measurements 


cplex_main_structuredH_Triangular_final.m   - The main script file to find a triangular
			        H matrix that meets structural constraints with 
				i number of optimal  measurements 

cplex_miqp_decentralized_final.m- function to find optimal i measurement subsets 
				with block diagonal structure in H	


cplex_miqp_decentralized_less_final.m	- function to find optimal i measurement subsets 
				with block-diagonal H structure that meets structural constraints


HBlkDiag.m, 
HBlkDiag_cong_D.m, 
HBlkDiag_congress.m	 	- functions to impose constraints on structured H (block-diagonal,
				 traingular) in cplex solver based routines				


OriginalData.mat		- The data for binary distillation column case study

				This case study details can be found in: 
				S. Skogestad, Dynamics and control of distillation columns:
				 A tutorial introduction, Chemical Engineering Research 
				and Design 75 (1997) 539 - 562. 


EvaporatorData.mat		- The data for the evaporator case study
				
				This case study details can be found in 
				V. Kariwala, Y. Cao, S. Janardhanan, Local self-optimizing 
				control with average loss minimization, 
				Ind. Eng. Chem. Res. 47 (2008) 1150-1158.


VectorizationProcedure.pdf	- Describes the procedure to vectorize the matrix based
				optimization problem to vectorized optimization problem.
				
				The approach in the pdf is used in developing the functions
				cplex_miqp_full_final.m	and cplex_miqp_full_structure.m