Department of Systems and Control

Jožef Stefan Institute

Simplified explicit predictive controller

Principal investigator:

Prof. Dr. Stanko Strmčnik

Duration:

May 1, 2009 - April 30, 2012

Funding:

ARRS - Slovenian Research Agency (L2-2342), co-financed by Inea d.o.o.

Abstract:

The aim of the project is to develop a tracking Explicit (parametric) Model-based Predictive Controller (eMPC) suitable for industrial use, and its case-study evaluation in the industrial environment.

MPC is a family of advanced control algorithms based on on-line optimisation of predicted courses of control signals using a process model and respecting constraints on signals. MPC is one of rare advanced methods of control theory that is well established in industry. Due to the high computational demand of on-line optimisation, capable hardware equipment is required and fast sampling is not possible.

With the recently discovered explicit form of MPC the computational load is shifted to the off-line controller design phase. This enables controller implementation on standard industrial automation equipment, and the application niche is extended to processes with fast dynamics.

The existing forms of eMPC originate in basic theoretical research. They are mostly focused on the fundamental problem of regulation of process states to the origin assuming measured states, which is not realistic in practice. In applications, tracking of output reference signals in the presence of various disturbances is typically required. This may be achieved using model augmentation. Unfortunately, the known parameterisation algorithms are not completely reliable when using augmented models, and problems may appear with problems of large dimensions. We will compare variants of tracking controller implementation (tracking error integration or disturbance estimation, with or without steady-state target calculator) and choose the most appropriate one for reliable controller implementation.

We will explore possibilities for decreasing of the computational load in the off-line phase. This is extremely important from the aspect of extending the eMPC field of application. The off-line computational load increases exponentially with the problem dimensions. Due to this the known parameterisation algorithms are not yet useful for multivariate process control or for theoretically more advanced approaches. We will analyse the efficiency of known approaches (merging of polyhedral regions, orthogonal approximation, interpolation, on-line computation and caching of the partition), and also search for new options for forming a simplified partition. One promising direction is a new dual-rate approach where the constraints and future control signal changes are distributed sparsely over the horizon. This should allow fast sampling times without too many regions and poor numerical conditioning.

Closed-loop system analysis with the chosen tracking eMPC will be an important research topic. This is required to ensure reliable and predictable controller performance, as simulation tests cannot cover all possible circumstances. eMPC presents a view of the control law structure that is hidden with conventional MPC. The emphasis will be on local linear analysis of the closed-loop system (LLA). LLA helps analyse the dynamical properties that are important with controller tuning for efficient tracking, rejection of various types of disturbances, noise attenuation and robustness to plant-to-model mismatch (simultaneously). The latter is particularly important as the closed-loop system comprising a state controller and a state estimator may be oversensitive to the modelling error. We will attempt to extend the "Loop Transfer Recovery" (LTR) approach, which systematically solves this problem, for use with eMPC.

During the development phases, the algorithms will be tested in simulation on realistic simulation models of actual plants, most likely with vacuum chamber pressure control and with cooling water temperature control in a CHP unit. For the pilot application in an industrial environment, the most promising eMPC variants will be tested experimentally – firstly using a development environment, and finally using a controller implemented in a PLC.