Saturday , June 10 2023

A Simulator for the Multi-model Control of Diesel Engines

Faculty of Automation and Computer Science, UPB, Bucharest
313 Splaiul Independentei, Bucharest, Romania,

Abstract: It was proposed and designed a modern configuration control type multicontroler-multimodel (MM) that pilots nonlinear combustion process of the diesel engine, needed to adjust the pressure in the intake manifold and air flow circulating through the compressor. The MM simulator developed by the authors allows the implementation of control systems represented by pairs (Mi, Ci) with the Mi candidate closest to the current operating point of the process and the paired controller Ri, for controlling the key parameters of the combustion process. The proposed configuration is built with robust controllers and thus is able to ensure superior performance, tolerance to nonlinearities and parametric/ structural perturbations in the system.

Keywords: Diesel engine, dynamic models, optimal control, robust control, MM simulator.

>>Full text
Silviu CÎRSTOIU, Dumitru POPESCU, A Simulator for the Multi-model Control of Diesel Engines, Studies in Informatics and Control, ISSN 1220-1766, vol. 23 (4), pp. 381-386, 2014.


Multi-model control strategy for nonlinear systems configuration is a relatively new approach. In recent studies, one can find an ever increasing interest for management control of nonlinear processes or multimode operations, as diesel engines can only be roughly approximated by a single global model. The first works that have proposed solutions and methods suitable for this type of processes, relying mainly on the construction of adaptive-robust systems using classical algorithms are those of Balakrishnan and Narenda in the 90s[1]. Later detailed studies and positive results were presented by Athans (2006) who used the concept of multimodel control and demonstrated the effectiveness of this approach, with the risk of additional computation and implementation effort. The principle of building an MM configuration is the same, and is based on known identification procedures of Mi models and design of control algorithms Ci, the differences are mainly due to the selection mode and command switching.

Studies by Petridis, Kehagias and Toscano use the multicontroler-multimodel (MM) configuration for systems with nonlinear static characteristics and Landau and Karimi use the so-called Cloe (Closed Loop Output Error) procedure, adjusting the parameters in an MM control structure [6]. Later studies have appeared on the use of neural networks and fuzzy logic systems, involved in the development of MM structures.

Research by the authors has been focused on proposing and testing control configurations MM for nonlinear processes implemented on certain applications designed to control the combustion process parameters in the diesel engines.

Following the preliminary results obtained in the paper, the proposed solution consists of a control structure (MM) in a robust version, to be tolerant to nonlinearities and disturbance regime of the diesel engine combustion.

The management configuration used here contains control loops (feedback) with pairs of models, robust controllers designed for the pre-specified operating points of the nonlinear characteristic of the process, caused mainly by the variation engine load and actuators behavior.

We fix three possible operating points and for the designed (Mi, Ci), i = 1,2,3, systems, presumably linearized model Mi is disrupted in parameters and/or structure, there is a robustness analysis of systems in closed loop and adjust the nominal command but for all operating points preset. An adaptive strategy MM structure occurs when the engine is in operation between two operating points.

The multimodel control structure designed is shown in the Figure 1:


Figure 1. Multi model control structure


  • ysp – reference measure
  • e – the error between actual and desired output
  • u – command
  • d – disturbance
  • U – disturbed command
  • y – the controlled output of the process
  • yi – i model output
  • y – yi  – difference between process output and i model output.

The supervising module must choose the right model and control algorithm for the engine functioning point. Thus we define the model error, calculated at each sampling moment and which represents the difference between output yi and output y for the same u value of the applied command.


The used criteria for selection of the closest model of the current process operating point is a square criteria built with the help of the model error, as in:
where α >0and β >0are the criteria ponderation factors, and γ >0is the forgiveness factor which ensures its action window limitation over the model error ε i(k).

The α, β and γ parameters choice depends on the systems’ characteristics, being:

  • α= 1 and β = 0, for fast response systems:
  • better performances in detecting the process parameters modification,
  • disturbances sensitivity,
  • α= 0 and β = 0, for slow response systems,
  • weak performances in detecting the process parameters modification,
  • good performances in detecting the process parameters modification.

The MM structure is configured for the proper version for controlling faster systems encountered in the case of controlling the working parameters of the diesel engine.

For each identified Mi model was computed a Ci regulator (controller) that meets the objectives and performance requirements; so we provide the set of pairs (Mi, Ci), corresponding to the possible nominal operating points Pi. For Ci control algorithms, robust correction was applied.


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