Advances in Combined Architecture, Plant, and Control Design - PowerPoint PPT Presentation

1 2 3 4 5 6 7 8 9 Advances in Combined Architecture, Plant, and Control Design Daniel R. Herber Final Defense Department of Industrial and Enterprise Systems Engineering University of Illinois at Urbana-Champaign Doctoral Committee: Assistant Professor James Allison Professor Yuliy Baryshnikov Associate Professor Carolyn Beck Professor Harrison Kim November 17, 2017 Urbana, IL, USA 1

1 2 3 4 5 6 7 8 9 Outline 1. Introduction 2. Candidate Architectures through Enumeration 3. Co-Design: Combined Plant and Control Design 4. Scaling of Dynamic Optimization Formulations 5. Direct Transcription and Linear-Quadratic Dynamic Optimization 6. Case Study: Design of Passive Analog Circuits 7. Case Study: Design of Strain-Actuated Solar Arrays 8. Case Study: Design of Vehicle Suspensions 9. Conclusions and Future Work 2

1 Introduction

1 2 3 4 5 6 7 8 9 � Introductory Example end effecter sample ↷ placement path links sample actuators ↷ return path ↷ ↷ joints ground (a) (b) Figure: Task description. Figure: Different architectures. joint 2 joint 1 torque (a) Link length. (b) Cross-section. time Figure: Plant variables. Figure: Joint control trajectories. 3

1 2 3 4 5 6 7 8 9 � Three Design Domains • Architecture • Architecture is defined as the elements contained within a system and their relationships 1 • Component is a common alternative term for element • Architectures with heterogeneous components: electrical circuits 2 , hybrid powertrains 3 , vehicle suspensions 4 , gear trains 5 , and biological networks 6 • Geometric architecture problem: trusses 7 , heat spreaders 8 , and soft robotics 9 • Plant • Generally defined by variables that are generally regarded as time independent • An alternative definition: The plant consists of the quantities fixed during the control design 1 Crawley, et al., 2004; 2 Macmahon, 1994; 3 Bayrak, et al., 2016; 4 Herber, et al., 2017; 5 Pennestri and Valentini, 2015; 6 Trusina, et al., 2009; 7 Bendsøe and Sigmund, 2004; 8 Lohan, et al., 2016; 9 Cheney, et al., 2013 4

1 2 3 4 5 6 7 8 9 � Three Design Domains • Control • Control seeks to govern directly the behavior of a dynamic system, i.e., one which evolves through time • Generally speaking, there are two types of control paradigms: closed loop and open loop • Ambiguity in these delineations • Legacy design paradigms that treat certain parts of the design as separate 1 • Groups based on variables types • Approximations or better representations of design variables in one domain are frequently classified in another domain • Architecture → plant: the SIMP approximation in structural optimization 2 ) 1 Allison and Herber, 2014; 2 Bendsøe and Sigmund, 2004 5

↻ ↻ 1 2 3 4 5 6 7 8 9 � A Design Process for Complete Dynamic System Design • Here we adopt the design process proposed in Ref. 1 for complete dynamic system design • Helps manage the complexity and uncertainty found in combined architecture, plant, and control design problems Stage 1 Stage 2 Stage 3 Plant Control Architecture Architecture Digital Design Design Control Design Co-Design Co-Design with OLC with CLC ↻ Adjust Formulation • Controller architectures could include a basic feedback, hybrid 2 , or model predictive 3 among others 1 Deshmukh, et al., 2015; 2 Lygeros, et al., 2008; 3 Borrelli, et al., 2017 6

1 2 3 4 5 6 7 8 9 � Solution Generation Challenges • Automated candidate architecture generation • Exploring different architectures requires an appropriate conceptual framework that allows for modifications to the appropriate elements in the architecture • However, not all architecture representations are equally useful • Some might produce many infeasible systems or too many candidates • Automated model generation • Given some architecture specification (e.g., a graph), we need to create a suitable model for use in the optimization problems • Certain modeling methodologies support this task such as bond graph modeling [Borutzky, 2010] • Automated optimization problem generation • For different candidate architectures of the same design problem, the optimization problem that predicts its performance may vary • For example, different constraints may be present depending on the components in the architecture 7

1 2 3 4 5 6 7 8 9 � Summary 8

2 Candidate Architectures through Enumeration

1 2 3 4 5 6 7 8 9 � Architectures as Graphs • A variety of different engineering systems can be represented by (undirected) labeled graphs • Labels can be used to represent a (a) Mechanism. variety of concepts • Finding candidate architectures requires the generation of new, useful graphs (b) Vehicle suspension. • Existing approaches have their drawbacks • Generative representations 1 • Enumerative approaches 2 (c) Hybrid powertrain. 1 Chakrabarti, et al., 2011; Schmidt and Cagan, 1997; Hornby, et al., 2003; Starling and Shea, 2005; 2 Macmahon, 1994; Ma, et al., 2009; Bayrak et al., 2016 9

1 2 3 4 5 6 7 8 9 � Graph Structure Space Specification with ( C , R , P ) • A key issue is how to represent the space of graphs of interest • A natural description is a component catalog defined by: • C : labels representing distinct component types (e.g., [ M , K , B ] ) • R : # of replicates for each component type (e.g., [ 2 , 3 , 1 ] ) • P : # of ports for each component type (e.g., [ 1 , 2 , 2 ] ) • The desired graph structure space (a set of all graphs that fulfill a certain set of conditions) is captured by enumerating all perfect matchings (PMs) • Each vertex is a port from ( C , R , P ) • A PM of a graph is where every vertex is incident to exactly one edge Figure: 3 !! perfect matchings for K 4 (general growth is ( n p − 1 )!! ) 10

1 2 3 4 5 6 7 8 9 � Tree Search Enumeration Algorithm • Many of the graphs in a pure PM approach are not unique (i.e., some graphs are isomorphic to each other) • New algorithm is based on the idea that for simple components, the port ordering does not matter , so we are free to always choose the first port of a component when making edges 11

1 2 3 4 5 6 7 8 9 � An Example: Quarter-Car Vehicle Suspension • Many network structure constraints (NSCs) are included to restrict the graphs to ones that are useful • The sprung and unsprung masses must not be directly connected • 4 . 7 × 10 21 adjacency matrices; 2 . 1 × 10 14 PMs; 13,727 unique graphs with the newly developed methods 12

1 2 3 4 5 6 7 8 9 � Enhancements • A number of enhancements have been made beyond the initial publication (see Appendix A) • Includes both general improvements and new network structure constraints • For example, we can break the graph generation procedure into subtasks with appropriate subcatalogs • Improves parallelizability of the generation procedure • Improvements in the vehicle suspension example • Both produce the same set of 13,727 unique, feasible graphs • 1,943,862 (original) vs. 48,408 (enhancements) feasible graphs • 17,903 s (original) vs. 688 s (enhancements) total generation time • Investigating additional enhancements such as a level-order approach where after each edge is created, only the unique graphs are kept (rather than checking for isomorphisms only when all the edges are added) 13

3 Co-Design: Combined Plant and Control Design

1 2 3 4 5 6 7 8 9 � General Co-Design • Focus on combined plant and control design or co-design • With a sequential approach, the plant is optimized initially, followed by the control 1 • Many authors have shown the benefit of a combined strategy rather than a sequential approach 2 • General co-design problems are dynamic optimization problems: � t f min Ψ = L ( t , ξ , x c , x p ) dt + M ( ξ ( t 0 ) , ξ ( t f ) , x c , x p ) (1a) x p , x c t 0 ˙ s.t. ξ − f ( t , ξ , x c , x p ) = 0 (1b) C ( t , ξ , x c , x p ) ≤ 0 (1c) φ ( ξ ( t 0 ) , ξ ( t f ) , x c , x p ) ≤ 0 (1d) • Much of the previous co-design research has focused on specific problem formulations with varying assumptions 3 1 Fathy, et al., 2001; 2 Fathy, et al., 2003; Allison, et al., 2014; Yan and Yan, 2009; 3 Fathy, et al., 2001; Reyer, et al., 2001; Sunar and Rao, 1993; Peters, et al., 2011 14

1 2 3 4 5 6 7 8 9 � Two Solution Strategies • Simultaneous strategy • Solve Prob. (1) directly (a) Simultaneous. • Nested (two-level) strategy • Outer loop optimizes w.r.t the plant • Inner loop optimizes w.r.t the control • The two approaches are only equivalent if for every candidate x † p , there exists a feasible solution to the inner-loop problem (b) Nested. 15