Area Cientıfica de Controlo Automacao e Informatica IndustrialInstituto Superior TecnicoTechnical University of Lisbon

Progress Report

Isaıas Tavares

Date: March 16th, 2012Subject: TitleSupervisors: Jose BorgesProject term: January 2012 – March 2012E-mail:

Outcome of the previous meeting

Task 1: Improvement of Simulink implementation of CLLM

Summary of Activities

• Predictive Control (result improvement)

In this report two controller perspective was presented as well as the simulation resultachieve using Nuhcc model developed by Nabais. These controller perspective are ModelBased Predictive Controller based on local models from Composite Local Linear Models andother is Nonlinear Model Based Predictive Controller from nonlinear models namely CLLM,FM and ANN with Branch and Bound.

• Model Based Predictive Controller based on local models from Composite Local LinearModels.

Table 1: Values of the configuration parameters of the NMBPC for each internal model.Controller Internal Models physical limitations Hc Hp n ∆umax Pi Qi

MPC with CLLM constrained 1 2 3 ∝ 0.01× (umax − umin) 100 1

MPC with CLLM unconstrained 1 2 3 ∝ 0.01× (umax − umin) 100 1

Table 2: Performance of the controller.Controller Internal Models Physical limitations MSE CPUtime (sec)

MPC with CLLM constrained 1.5959× 10−4 178.6086

MPC with CLLM unconstrained 1.5959× 10−4 175.4286

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Progress Report Isaıas Tavares 2

• Nonlinear Model Based Predictive controller from nonlinear models namely CLLM, FMand ANN with Branch and Bound.

Table 3: Values of the configuration parameters of the NMBPC for each internal model.Controller physical limitations Hc Hp n ∆umax Pi Qi

NMBPC with CLLM constrained 1 2 15 ∝ 0.01× (umax − umin) 100 1

NMBPC with CLLM unconstrained 1 2 15 ∝ 0.01× (umax − umin) 100 1

NMBPC with FM constrained 1 2 3 ∝ 0.01× (umax − umin) 100 1

NMBPC with ANN constrained 1 2 3 ∝ 0.01× (umax − umin) 100 1

Table 4: performance of the controller.Controller Internal Models Physical limitations MSE CPUtime

NMBPC with CLLM constrained 6.4444× 10−4 201.1563

NMBPC with CLLM unconstrained 4.864× 10−4 212.1701

NMBPC with FM constrained 0.0021 1.1136×103

NMBPC with ANN constrained 1.5959× 10−4 1.7179× 105

Unconstrained control actions for NMBPC with FM and ANN are presented here be-cause it’s result are not good enough. CUPtime is the compute time measured duringsimulation and it is not the real time.

Next Weeks Activities

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Appendix A

Write theoretical concept about controller implemented on water canal system.

• Control in Water Canal System

Different control methodologies were also applied to canals systems, Heuristic mono-variable methods proposed by rogers1995, originating in hydraulics, this method hasshown some constraints such as being tuned in a full simulation, thus limiting theiruse in real time due to its mathematical tool. PID proposed by shand1971, is one ofthe most used controllers in canal systems. Based on Linear Multivariable PID con-troller, many of these controllers are tuned based on the placement of the poles usingSISO transfer functions. Predictive control proposed by sawadogo1992, rodellar1993,ruiz1998 and pages1998, was implemented based on the minimization of a cost functionJ . Fuzzy control proposed by bouillot1994, was implemented in canals systems andonly had good performance in SISO systems. Model inversion proposed by falvey1987,is based on the inversion of nonlinear models from finite-order, it has problems dueto the inversion of oscillatory diffusive dynamics. In respect to Optimization methodsproposed by sabet1985, if the optimization is nonlinear it will be susceptible to errorsand disturbances, very limited for real-time control. However, this approach has theadvantage when applied to canal systems in that it allows the choice of multivariable

Progress Report Isaıas Tavares 3

control structures and the proposed decentralized control. Robust control proposed byschuurmans1997, tested by some authors was designed as a good tool when it is subjectto unknown disturbances and model errors in the presence of nonlinear effects. Nonlin-ear Control proposed by coron1999, given as one of the most difficult approaches from atheoretical point of view, but presents many advantages in controlling nonlinear effects.Further contributions are presented in [?].

The MPC can efficiently manage multiple systems when constraints are taken intoaccount, brouwer. The predictive controller was used by Begovich1997, to control thewater level downstream of canals. To specify the reference, he used simple linear modelsidentified by data-driven identification tools.

Appendix B

Write theoretical concept about nonlinear model based predictive controller.

• Predictive Controller

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References