An Optimal Control Approach to Minimizing Entropy Generation in an Adiabatic IC Engine With Fixed Compression Ratio

2006 ◽  
Author(s):  
Kwee-Yan Teh ◽  
Christopher F. Edwards
Keyword(s):  
Optimal Control ◽  
Entropy Generation ◽  
Compression Ratio ◽  
Combustion Engine ◽  
Optimal Solution ◽  
Combustion Mechanism ◽  
Control Input ◽  
Piston Velocity ◽  
Ic Engine ◽  
Control Approach

Entropy generation due to combustion destroys as much as a third of the theoretical maximum work that could have been extracted from the fuel supplied to an engine. In this paper, an optimal control problem is set up to minimize the entropy generation in an adiabatic internal combustion engine, with the piston velocity profile serving as the control input function. The compression ratio of the engine is fixed, thereby imposing a constraint on the piston motion. The switching conditions for the optimal bang-off-bang control is determined based on Pontryagin's maximum principle. In thermodynamic terms, the optimal solution reduces to a strategy of equilibrium entropy minimization. This result is independent of the underlying combustion mechanism.

An Optimal Control Approach to Minimizing Entropy Generation in an Adiabatic Internal Combustion Engine

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
Kwee-Yan Teh ◽  
Christopher F. Edwards
Keyword(s):  
Optimal Control ◽  
Entropy Generation ◽  
Combustion Engine ◽  
Combustion Mechanism ◽  
Control Input ◽  
Minimum Entropy ◽  
Piston Engine ◽  
Piston Motion ◽  
Thermodynamic State ◽  
Engine Efficiency

Entropy generation due to combustion destroys as much as a third of the theoretical maximum work that could have been extracted from the fuel supplied to an engine. Yet, there is no fundamental study in the literature that addresses the question of how this quantity can be minimized so as to improve combustion engine efficiency. This paper fills the gap by establishing the minimum entropy generated in an adiabatic, homogeneous combustion piston engine. The minimization problem is cast as a dynamical system optimal control problem, with the piston velocity profile serving as the control input function. The closed-form switching condition for the optimal bang-bang control is determined based on Pontryagin’s maximum principle. The switched control is shown to be a function of the pressure difference between the instantaneous thermodynamic state of the system and its corresponding equilibrium thermodynamic state at the same internal energy and volume. At optimality, the entropy difference between these two thermodynamic states is shown to be a Lyapunov function. In thermodynamic terms, the optimal solution reduces to a strategy of equilibrium entropy minimization. This result is independent of the underlying combustion mechanism. It precludes the possibility of matching the piston motion in some sophisticated fashion to the nonlinear combustion kinetics in order to improve the engine efficiency. For illustration, a series of numerical examples are presented that compare the optimal bang-bang solution with the nonoptimal conventional solution based on slider-crank piston motion. Based on the solution for minimum entropy generation, a bound for the maximum expansion work that the piston engine is capable of producing is also deduced.

A Nonlinear Optimal Control Approach for the Vertical Take-off and Landing Aircraft

2021 ◽  
pp. 2150012
Author(s):  
G. Rigatos
Keyword(s):  
Optimal Control ◽  
Control Method ◽  
Nonlinear Optimal Control ◽  
The Body ◽  
Algebraic Riccati Equation ◽  
Control Input ◽  
Time Step ◽  
Control Approach ◽  
Vtol Aircraft ◽  
Optimal Control Approach

The paper proposes a nonlinear optimal control approach for the model of the vertical take-off and landing (VTOL) aircraft. This aerial drone receives as control input a directed thrust, as well as forces acting on its wing tips. The latter forces are not perpendicular to the body axis of the drone but are tilted by a small angle. The dynamic model of the VTOL undergoes approximate linearization with the use of Taylor series expansion around a temporary operating point which is recomputed at each iteration of the control method. For the approximately linearized model, an H-infinity feedback controller is designed. The linearization procedure relies on the computation of the Jacobian matrices of the state-space model of the VTOL aircraft. The proposed control method stands for the solution of the optimal control problem for the nonlinear and multivariable dynamics of the aerial drone, under model uncertainties and external perturbations. For the computation of the controller’s feedback gains, an algebraic Riccati equation is solved at each time-step of the control method. The new nonlinear optimal control approach achieves fast and accurate tracking for all state variables of the VTOL aircraft, under moderate variations of the control inputs. The stability properties of the control scheme are proven through Lyapunov analysis.

scholarly journals A Two-Stage Method for UCAV TF/TA Path Planning Based on Approximate Dynamic Programming

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Hao-xiang Chen ◽  
Ying Nan ◽  
Yi Yang
Keyword(s):  
Optimal Control ◽  
Dynamic Programming ◽  
Path Planning ◽  
Approximate Dynamic Programming ◽  
Optimal Solution ◽  
Planning Problem ◽  
Optimization Approach ◽  
Two Stage ◽  
Control Approach ◽  
Optimal Control Approach

We present a two-stage method for solving the terrain following (TF)/terrain avoidance (TA) path-planning problem for unmanned combat air vehicles (UCAVs). The 1st stage of planning takes an optimization approach for generating a 2D path on a horizontal plane with no collision with the terrain. In the 2nd stage of planning, an optimal control approach is adopted to generate a 3D flyable path for the UCAV that is as close as possible to the terrain. An approximate dynamic programming (ADP) algorithm is used to solve the optimal control problem in the 2nd stage by training an action network to approximate the optimal solution and training a critical network to approximate the value function. Numerical simulations indicate that ADP can determine the optimal control variables for UCAVs; relative to the conventional optimization method, the optimal control approach with ADP shows a better performance under the same conditions.

A Distributed Control Approach for the Boundary Optimal Control of the Steady MHD Equations

2013 ◽  
Vol 14 (3) ◽  
pp. 722-752 ◽  
Author(s):  
G. Bornia ◽  
M. Gunzburger ◽  
S. Manservisi
Keyword(s):  
Optimal Control ◽  
Control Problem ◽  
Distributed Control ◽  
Boundary Control ◽  
Optimal Solution ◽  
Mhd Equations ◽  
New Approach ◽  
Control Approach ◽  
Distributed Control Problem ◽  
Boundary Controls

AbstractA new approach is presented for the boundary optimal control of the MHD equations in which the boundary control problem is transformed into an extended distributed control problem. This can be achieved by considering boundary controls in the form of lifting functions which extend from the boundary into the interior. The optimal solution is then sought by exploring all possible extended functions. This approach gives robustness to the boundary control algorithm which can be solved by standard distributed control techniques over the interior of the domain.

Optimizing Piston Velocity Profile for Maximum Work Output From an IC Engine

2006 ◽  
Author(s):  
Kwee-Yan Teh ◽  
Christopher F. Edwards
Keyword(s):  
Heat Transfer ◽  
Elevated Temperatures ◽  
Optimal Solution ◽  
Nonlinear Program ◽  
Work Output ◽  
Piston Engine ◽  
Piston Velocity ◽  
Ic Engine ◽  
Engine Model ◽  
Set Up

In this paper, an optimal control problem is set up to maximize the work output from a piston engine via piston motion shaping. The empirical heat transfer correlation and global reaction kinetics used in the engine model result in a stiff, non-smooth dynamical system. The algorithm used to transcribe this system to a constrained nonlinear program is described. The optimal solution is obtained using the gradient-based optimization solver SNOPT. At optimality, the total heat transfer loss is lower due to the shorter time spent at elevated temperatures after combustion, leading to a modest increase (less than 3%) in work output as compared to a conventional slider-crank piston engine.

scholarly journals A Lyapunov-Based Optimal Integral Finite-Time Tracking Control Approach for Asymmetric Nonholonomic Robotic Systems

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2367
Author(s):  
Khalid A. Alattas ◽  
Saleh Mobayen ◽  
Wudhichai Assawinchaichote ◽  
Jihad H. Asad ◽  
Jan Awrejcewicz ◽  
...  
Keyword(s):  
Optimal Control ◽  
Equilibrium Point ◽  
Sliding Mode ◽  
Design Procedure ◽  
Robotic Systems ◽  
Control Input ◽  
Control Lyapunov Function ◽  
Terminal Sliding Mode ◽  
Control Approach ◽  
Precise Control

This study suggests a control Lyapunov-based optimal integral terminal sliding mode control (ITSMC) technique for tracker design of asymmetric nonholonomic robotic systems in the existence of external disturbances. The design procedure is based on the control Lyapunov function (CLF) approach. Hence, the output tracking problem is solved by combining the ITSMC with optimal control. The CLF synthesizes a nonlinear optimal control input for the nominal system. Once the control system’s states lie far away from the operating point, it is activated to drive them toward the equilibrium point optimally. However, on the condition that the system perturbations are the main factor, the ITSMC would be designed to take over in the vicinity of the equilibrium point. Accordingly, the control goals, such as robustness and precise control, are warranted in the perturbed system. The usefulness of the suggested method is demonstrated with a wheeled mobile robot via a simulation study.

scholarly journals Comparing the Potentiality of Propane, Propanol and Octane Fuel Using in SI Engine Based on Energy-Exergy Analysis

2021 ◽  
Vol 9 ◽  
pp. 45-53
Author(s):  
Md Mizanuzzaman Mizan
Keyword(s):  
Compression Ratio ◽  
Combustion Engine ◽  
Empirical Relation ◽  
Fundamental Equation ◽  
Spark Ignition ◽  
Operating Conditions ◽  
Spark Ignition Engine ◽  
Si Engine ◽  
Ic Engine ◽  
Single Cylinder

From the beginning of IC engine era, it is trying to improve the performance and efficiency of internal combustion engine. In this study, numerically analysis on combustion of Propane, Propanol and Octane in SI engine have been done thoroughly and presented to assess the potentiality and highlighted the comparison. For this analysis thermodynamic engine cycle model is developed for numerical analysis. Mathematical models considering fundamental equation and empirical relation are implemented in a single cylinder 4 stroke spark ignition engine (system) with the help of FORTRAN 95 to find out heat losses, friction losses, output parameter etc.  Single cylinder four-stroke spark-ignition (SI) engine is considered as system. In this study, different working parameters like 8 and 12 compression ratios with three different rpm 2000, 4000 & 6000 are considered for simulation. This study shows the different comparisons of energy-exergy content (%), as example of exhaust gas 35.08 & 17.82, 37.02 & 19.22, 37.79 & 19.79 for Octane (at compression ratio 8 and 2000, 4000, 6000 rpm) etc., which explains the potentiality content and the potentiality losses in different process like combustion, mixing of gases etc. It also shows for the fuel propane and propanol in similar way with changing different operating conditions. Maximum inside cylinder temperature, 1st law and 2nd law efficiencies were determined for the fuels with respect to different compression ratio and engine speed.

Optimal Control of the Integrated Marketing-Production Planning Problem

2018 ◽  
pp. 349-370
Author(s):  
Jill Reid ◽  
Lotfi Tadj
Keyword(s):  
Optimal Control ◽  
Production Planning ◽  
Optimal Solution ◽  
Inventory Level ◽  
Planning Problem ◽  
State Variables ◽  
Periodic Review ◽  
Integrated Marketing ◽  
Control Approach ◽  
Production Planning Problem

We consider in this paper the integrated marketing – production planning problem and propose an optimal control approach to derive the optimal solution. The state variables are the inventory level and the stock of goodwill and the control variables are the production rate and the advertising rate. Both cases where the firm adopts a continuous-review and a periodic-review policy are considered. The optimal states and controls are obtained explicitly. Illustrative examples are presented. Sensitivity analysis shows the effect of some system parameters on the optimal solution.

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