Combined Plant and Controller Design Using Decomposition-Based Design Optimization and the Minimum Principle

2010 ◽  
Author(s):  
James T. Allison ◽  
Sam Nazari
Keyword(s):  
Optimal Control ◽  
Design Optimization ◽  
System Design ◽  
Physical System ◽  
Design Problem ◽  
Controller Design ◽  
Minimum Principle ◽  
Optimization Methods ◽  
Optimization Techniques ◽  
Augmented Lagrangian Coordination

An often cited motivation for using decomposition-based optimization methods to solve engineering system design problems is the ability to apply discipline-specific optimization techniques. For example, structural optimization methods have been employed within a more general system design optimization framework. We propose an extension of this principle to a new domain: control design. The simultaneous design of a physical system and its controller is addressed here using a decomposition-based approach. An optimization subproblem is defined for both the physical system (i.e., plant) design and the control system design. The plant subproblem is solved using a general optimization algorithm, while the controls subproblem is solved using a new approach based on optimal control theory. The optimal control solution, which is derived using the the Minimum Principle of Pontryagin (PMP), accounts for coupling between plant and controller design by managing additional variables and penalty terms required for system coordination. Augmented Lagrangian Coordination is used to solve the system design problem, and is demonstrated using a circuit design problem.

scholarly journals Application and benchmarking of a direct method to optimize the fuel consumption of a diesel electric locomotive

2018 ◽  
Vol 232 (9) ◽  
pp. 2272-2289 ◽  
Author(s):  
V Macian ◽  
C Guardiola ◽  
B Pla ◽  
A Reig
Keyword(s):  
Optimal Control ◽  
Direct Method ◽  
Minimum Principle ◽  
Optimization Technique ◽  
Direct Methods ◽  
Optimization Methods ◽  
Computational Time ◽  
Electric Locomotive ◽  
Pontryagin Minimum Principle ◽  
A Direct Method

This paper addresses the optimal control of a long-haul passenger train to deliver minimum-fuel operations. Contrary to the common Pontryagin minimum principle approach in railroad-related literature, this work addresses this optimal control problem with a direct method of optimization, the use of which is still marginal in this field. The implementation of a particular direct method based on the Euler collocation scheme and its transcription into a nonlinear problem are described in detail. In this paper, this optimization technique is benchmarked with well-known optimization methods in the literature, namely dynamic programming and the Pontryagin minimum principle, by simulating a real route. The results showed that the direct methods are on the same level of optimality compared with other algorithms while requiring reduced computational time and memory and being able to handle very complex dynamic systems. The performance of the direct method is also compared to the real trajectory followed by the train operator and exhibits up to 20% of fuel saving in the example route.

scholarly journals Design and optimal control of a tiltrotor micro-aerial vehicle for efficient omnidirectional flight

2020 ◽  
Vol 39 (10-11) ◽  
pp. 1305-1325
Author(s):  
Mike Allenspach ◽  
Karen Bodie ◽  
Maximilian Brunner ◽  
Luca Rinsoz ◽  
Zachary Taylor ◽  
...  
Keyword(s):  
Optimal Control ◽  
Design Optimization ◽  
System Design ◽  
Optimal Controller ◽  
Micro Aerial Vehicle ◽  
Aerial Vehicles ◽  
Aerial Vehicle ◽  
Robust System ◽  
Six Degree Of Freedom ◽  
Allocation Approach

Omnidirectional micro-aerial vehicles (MAVs) are a growing field of research, with demonstrated advantages for aerial interaction and uninhibited observation. While systems with complete pose omnidirectionality and high hover efficiency have been developed independently, a robust system that combines the two has not been demonstrated to date. This paper presents the design and optimal control of a novel omnidirectional vehicle that can exert a wrench in any orientation while maintaining efficient flight configurations. The system design is motivated by the result of a morphology design optimization. A six-degree-of-freedom optimal controller is derived, with an actuator allocation approach that implements task prioritization, and is robust to singularities. Flight experiments demonstrate and verify the system’s capabilities.

Robust MDSDO for Co-Design of Stochastic Dynamic Systems

2019 ◽  
Vol 142 (1) ◽  
Author(s):  
Saeed Azad ◽  
Michael J. Alexander-Ramos
Keyword(s):  
Dynamic System ◽  
Design Optimization ◽  
System Design ◽  
Design Problem ◽  
Integrated Design ◽  
Problem Formulation ◽  
Robust Design Optimization ◽  
Design Problems ◽  
Embodiment Design ◽  
And Control

Abstract Optimization of dynamic engineering systems generally requires problem formulations that account for the coupling between embodiment design and control system design simultaneously. Such formulations are commonly known as combined optimal design and control (co-design) problems, and their application to deterministic systems is well established in the literature through a variety of methods. However, an issue that has not been addressed in the co-design literature is the impact of the inherent uncertainties within a dynamic system on its integrated design solution. Accounting for these uncertainties transforms the standard, deterministic co-design problem into a stochastic one, thus requiring appropriate stochastic optimization approaches for its solution. This paper serves as the starting point for research on stochastic co-design problems by proposing and solving a novel problem formulation based on robust design optimization (RDO) principles. Specifically, a co-design method known as multidisciplinary dynamic system design optimization (MDSDO) is used as the basis for an RDO problem formulation and implementation. The robust objective and inequality constraints are computed per usual as functions of their first-order-approximated means and variances, whereas analysis-based equality constraints are evaluated deterministically at the means of the random decision variables. The proposed stochastic co-design problem formulation is then implemented for two case studies, with the results indicating the importance of the robust approach on the integrated design solutions and performance measures.

Consistency Constraint Allocation in Augmented Lagrangian Coordination

2010 ◽  
Vol 132 (7) ◽  
Author(s):  
James T. Allison ◽  
Panos Y. Papalambros
Keyword(s):  
System Design ◽  
Design Problem ◽  
Augmented Lagrangian ◽  
Structure Theory ◽  
Additional Element ◽  
Pump Design ◽  
Coordination Strategy ◽  
Ideal System ◽  
Consistency Constraint ◽  
Augmented Lagrangian Coordination

Many engineering systems are too complex to design as a single entity. Decomposition-based design optimization methods partition a system design problem into subproblems, and coordinate subproblem solutions toward an optimal system design. Recent work has addressed formal methods for determining an ideal system partition and coordination strategy, but coordination decisions have been limited to subproblem sequencing. An additional element in a coordination strategy is the linking structure of the partitioned problem, i.e., the allocation of constraints that guarantee that the linking variables among subproblems are consistent. There may exist many alternative linking structures for a decomposition-based strategy that can be selected for a given partition, and this selection should be part of an optimal simultaneous partitioning and coordination scheme. This article develops a linking structure theory for a particular class of decomposition-based optimization algorithms, augmented Lagrangian coordination (ALC). A new formulation and coordination technique for parallel ALC implementations is introduced along with a specific linking structure theory, yielding a partitioning and coordination selection method for ALC that includes consistency constraint allocation. This method is demonstrated using an electric water pump design problem.

scholarly journals Optimal controller design based on minimum principle

2018 ◽  
Vol 173 ◽  
pp. 01001
Author(s):  
Huang Da ◽  
Huang ShuCai
Keyword(s):  
Optimal Control ◽  
Control Theory ◽  
Optimal Control Theory ◽  
Controller Design ◽  
Minimum Principle ◽  
Adaptive Controller ◽  
Control Effect ◽  
Modern Control Theory ◽  
Important Position ◽  
The Ideal

Optimal control theory is the foundation of the modern control theory, the minimum principle in optimal control theory has a very important position, using the minimum principle to design an adaptive controller, the controller integration advantages of the principle of minimum is not affected by the control system of linear or nonlinear constraints, and the end state and free time, is accused of quantity can be controlled and are free to wait for a characteristic, using the minimum controller application example and simulation, the results show that the minimum principle of the designed controller has the ideal control effect.

Consistency Constraint Allocation in Augmented Lagrangian Coordination

2008 ◽  
Author(s):  
James T. Allison ◽  
Panos Y. Papalambros
Keyword(s):  
System Design ◽  
Design Problem ◽  
Augmented Lagrangian ◽  
Structure Theory ◽  
Additional Element ◽  
Pump Design ◽  
Coordination Strategy ◽  
Ideal System ◽  
Consistency Constraint ◽  
Augmented Lagrangian Coordination

Many engineering systems are too complex to design as a single entity. Decomposition-based design optimization methods partition a system design problem into subproblems, and co-ordinate subproblem solutions toward an optimal system design. Recent work has addressed formal methods for determining an ideal system partition and coordination strategy, but coordination decisions have been limited to subproblem sequencing. An additional element in a coordination strategy is the linking structure of the partitioned problem, i.e., the allocation of constraints that guarantee that the linking variables among subproblems are consistent. There can be many alternative linking structures for a decomposition-based strategy which can be selected for a given partition, and this selection should be part of an optimal simultaneous partitioning and coordination scheme. This paper develops a linking structure theory for a particular class of decomposition-based optimization algorithms, Augmented Lagrangian Coordination (ALC). A new formulation and coordination technique for parallel ALC implementations is introduced along with a specific linking structure theory, yielding a partitioning and coordination selection method for ALC that includes consistency constraint allocation. This method is demonstrated using an electric water pump design problem.

H ∞ Optimal Repetitive Controller Design for Stable Plants

1997 ◽  
Vol 119 (3) ◽  
pp. 541-547 ◽  
Author(s):  
T. E. Peery ◽  
H. O¨zbay
Keyword(s):  
Optimal Control ◽  
Control Problem ◽  
Design Problem ◽  
Controller Design ◽  
Delay System ◽  
Weighting Functions ◽  
Stability Robustness ◽  
Finite Dimensional ◽  
Repetitive Controller

The repetitive controller design problem is studied for stable plants in the framework of the H∞ optimal control. For a given nominal repetitive controller, first stability robustness is optimized by solving a finite dimensional H∞ control problem. Then the nominal design is modified in an optimal way so that the performance is improved while keeping the robustness level approximately the same. This problem is formulated as a two block H∞ problem involving a delay system and two weighting functions. The resulting controller can be implemented by adding a few blocks to the existing nominal design. An example is given to illustrate the numerical aspects of this approach.

Cyber Physical System Design

2015 ◽  
pp. 38-60
Keyword(s):  
Mathematical Modelling ◽  
Design Optimization ◽  
System Design ◽  
Dynamic Systems ◽  
Physical System ◽  
Cyber Physical Systems ◽  
Cyber Physical System ◽  
Large Set ◽  
Temporal Semantics ◽  
Model Based

A large set of CPS physical processes are referred to as Cyber Physical System community. This CPS community deals with the modelling and design optimization of CPS. The network elements that are model-based emphasize control over system with various temporal semantics. Model-based design is a great technique for CPSs and are mainly used for developing mathematical modelling to plan, examine, prove, and certify dynamic systems. This is described in ten fundamental steps. This design methodology helps in assessing the development of CPS. Due to difficulty and nonexistence of accurate and technical tools, the three necessary elements in the strategy and study of existing and forthcoming cyber-physical systems are also explained in the chapter.

Optimization Methods Applied to Selecting Support Positions in Fixture Design

1991 ◽  
Vol 113 (4) ◽  
pp. 412-418 ◽  
Author(s):  
R. J. Menassa ◽  
W. R. DeVries
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Objective Function ◽  
Design Problem ◽  
Optimization Methods ◽  
Design Criterion ◽  
Optimization Techniques ◽  
Fixture Design ◽  
The Finite Element Method ◽  
Numerical Examples

This paper proposes optimization techniques to assist in the design and evaluation of fixtures for holding prismatic workpieces. This formulation of the fixturing design problem takes into account deflection of the workpiece subjected to assembly or machining loads. Using the minimization of the workpiece deflection at selected points as the design criterion, the design problem is determining the positions of the fixture supports. The Finite Element Method is used for calculating deflections that are the basis for the design objective function, and the Broyden-Fletcher-Goldfarb-Shanno optimization algorithm is used to determine the fixture support positions. In this paper the proposed objective function is developed and the method is illustrated with three numerical examples.

Multidiscipline Design Optimization

1988 ◽  
Vol 41 (6) ◽  
pp. 257-262 ◽  
Author(s):  
Garret N. Vanderplaats
Keyword(s):  
Design Optimization ◽  
Design Problem ◽  
State Of The Art ◽  
Optimization Techniques ◽  
Conceptual Level ◽  
Considerable Research ◽  
Single Discipline ◽  
Basic Approaches ◽  
The Individual ◽  
Formal Optimization

While formal optimization techniques are seeing increasing use within individual disciplines, application of this technology to the more general multidiscipline design problem is less common. This is due to both the inherent complexity of multidiscipline design and the fact that design is traditionally separated along discipline lines. The application of optimization to multilevel and multidiscipline design is discussed here. It is seen that, computationally, multilevel design within a single discipline and multidiscipline design across disciplines have similar features, and so are generally treated the same. Multidiscipline optimization at the conceptual level is first discussed and it is seen that this has been done successfully for some time. Then the more general case is discussed where formal mathematical decomposition of the larger problem is required to make optimization practical. Here, the state of the art is still relatively undeveloped. Two basic approaches are briefly described to indicate the concepts, and a simple example is offered. The key idea in persuing the multidiscipline design problem is that the optimum system is seldom the sum of optimum components. It is necessary to properly account for the coupling that exists among the subsystems, while still allowing the individual designer to work with relative freedom within his discipline. It is concluded that to achieve this, considerable research remains ahead.

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