Control-oriented modeling, validation, and interaction analysis of turbocharged lean-burn natural gas variable speed engine

Abstract

Accurate modeling and control of the gas exchange process in a modern turbocharged spark-ignited engine is critical for the control and analysis of different control strategies. This paper develops a simple physics-based, five-state engine model for a large four-stroke spark-ignited turbocharged engine fueled by natural gas that is used in variable speed applications. The control-oriented model is amenable for control algorithm development and includes the impacts of modulation to any combination of four actuators: throttle valve, bypass valve, fuel rate, and wastegate valve. The control problem requires tracking engine speed to provide propulsive power, differential pressure across the throttle valve to prevent compressor surge, air-to-fuel ratio to restrict engine emissions. Two validation strategies, open-loop and closed-loop, are used to validate the accuracy of both nonlinear and linear versions of the control-oriented model. The control models are able to capture the engine dynamics within 5%–10% error at most of the engine operating points. Finally, the relative gain array (RGA) is applied to the linearized engine model to understand the degree of interactions between plant inputs and outputs as a function of frequency for various operating points. Results of the RGA analysis show that the preferred input-output pairing changes depending on the linear plant model as well as frequency. Therefore, a coordinated controller is ideal to tackle the control problem in question.

Robust model-based switching MIMO air handling control of turbocharged lean-burn SI natural gas variable speed engines

“…As discussed in Rayasam et al, 34 the above system has significant coupling from inputs to outputs which necessities the design of a controller that does not ignore the input-output interactions.…”

“…where x GT , i denotes the i th cycle-averaged state estimated by the truth-reference GT-Power model, x linear , i denotes the corresponding state estimated by the linear model used for controller synthesis. 34…”

“…The non-linear dynamic model is then linearized at five operating points (shown in Table 2) using Taylor's expansion up to first order terms to obtain a linear state-space model (shown in equation ( 2)) that covers the entire operating range of interest. The reader should refer to Rayasam et al 34 for detailed derivations of these models. The linear models derived for controller synthesis are scheduled only based on engine speed since the load torque is expected to be around the equilibrium value of load torque considered for that engine speed.…”

“…However, modern engines are complex, can operate over a wide operating region, and are highly non-linear due to incorporation of multiple actuators for which there exists a large amount of interaction between multiple outputs (controlled outputs) and multiple inputs (actuator settings). 34 With continuous development of new technology and more complex engine architectures to increase efficiency, controller design needs to be efficient if any additional parameter needs to be controlled. Therefore, control strategies which cover the entire operating range of the engine, are robust, and easily tunable while taking into account the multivariate interactions between inputs and outputs and controls all outputs in a coordinated fashion is necessary to achieve effective closed-loop performance of the system.…”

“… μ -synthesis and DK -iteration methods are used to compute a robust linear H ∞ controller. MIMO controller is chosen to tackle the control problem in consideration as the results in Rayasam et al 34 showed the following: there is no particular input-output pairing that is suitable for all operating conditions; a coordinated controller is the ideal controller for this engine due to the interaction between inputs and outputs. Therefore, the controller development focuses on improving the output tracking performance as much as possible and maximizing fuel economy is not the main objective of the MIMO controller.…”