Panta Rhei More Quality of Traffic by centralized or decentralized - PowerPoint PPT Presentation

Panta Rhei More Quality of Traffic by centralized or decentralized Control ?! Heraclitus All things are in (540 – 480 B.C.) constant flux Prof. Dr.-Ing. Dr. h. c. E. Schnieder Overview Traffic – System view Control arrangements and objectives Control problems, approaches and solutions Braunschweig, 17.08.2009

Panta rhei Traffic and its Contextual Environment politics / law human / society science traffic technology economy ecology Braunschweig, 17.08.2009

Panta rhei Traffic and its Axiomatic System Properties global | local state traffic quality structure behavior system traffic elements traffic processes traffic function traffic organization Braunschweig, 17.08.2009

Panta rhei Hierarchical Structure of Traffic Control Braunschweig, 17.08.2009

Panta rhei Structuring of Traffic Control into Functions and Ressources control function local global control ressources vehicle control ? vehicle navigation level crossing control distributed intersection control fleet dispatching switch control flow control centralized train control traffic guidance truck dispatching Braunschweig, 17.08.2009

Panta rhei - Fundamental decomposition of traffic control into function and ressources StationaryTraffic Behavior at the Fundamental Diagram - traffic flow increases to its global maximum, any further increase in density leads to instability and decrease of flow - behavior expressed by the fundamental diagram may be denoted as suboptimal - collective expression of drivers’ behavior Braunschweig, 17.08.2009

Panta rhei - Fundamental decomposition of traffic control into function and ressources Objectives and Means of Traffic Control increase safety increase capacity and flow quality decrease travel time and confidence global decrease fuel consumption decrease emission homogenization of driving behavior increase stability means indrease driver reliability local increase immediate intervention measurement, control, actuating Braunschweig, 17.08.2009

Panta rhei - Fundamental decomposition of traffic control into function and ressources Traffic Flow Interpretation - Microscopic and Macroscopic Traffic Flow Models single vehicle i real microscopic single vehicle i real position s i_real single vehicle i level position s i_real velocity v i_real position s i velocity v i_real … velocity v i … … macroscopic traffic flow Q level traffic density K average velocity v m Source: tfhrc.gov, stadtentwicklung-berlin.com Braunschweig, 17.08.2009

Panta rhei - Fundamental decomposition of traffic control into function and ressources Traffic Flow Interpretation - Microscopic and Macroscopic Traffic Flow Models highway v a v b x a x b Δs microscopic Q(x 0 ,t) v(x 0 ,t) Q(x 1 ,t) v(x 1 ,t) x 0 x 1 Δx macroscopic Braunschweig, 17.08.2009

Panta rhei - Fundamental decomposition of traffic control into function and ressources Traffic Flow Interpretation - Microscopic and Macroscopic Traffic Flow Models highway v a v b x a x b Δs ADAS uses microscopic control input parameters Q(x 0 ,t) v(x 0 ,t) Q(x 1 ,t) v(x 1 ,t) x 0 x 1 Δx ADAS influences macroscopic traffic characteristic Braunschweig, 17.08.2009

Panta rhei - Fundamental decomposition of traffic control into function and ressources Traffic Flow Interpretation - Microscopic and Macroscopic Traffic Meassures v a v b x a x b Δs 38 v leader Messdaten v ego simuliert v ego Messdaten 36 Geschwindigkeit (m/s) 34 32 30 28 2.2 2.24 2.28 2.32 2.36 2.4 Messzeit [ms] 6 x 10 Q(x 0 ,t) v(x 0 ,t) Q(x 1 ,t) v(x 1 ,t) x 0 x 1 Δx Fundamentaldiagramm, 07.05.2008 Autobahn A2 Richtung Berlin, AS Lauenau 1600 Verkehrsstärke [Fzg/h] 1200 800 400 0 0 10 20 30 Verkehrsdichte [Fzg/km] Braunschweig, 17.08.2009

Panta rhei Fundamental Decomposition of Traffic Control into Function and Ressources control function local global control ressources vehicle control ? vehicle navigation level crossing control distributed intersection control fleet dispatching switch control flow control train control traffic guidance centralized truck dispatching e.g. light-signal system or traffic message signs with induction loops Braunschweig, 17.08.2009

Panta rhei- Centralized traffic control ressources with global control functions Central Problem of Traffic Flow Measurement vehicle positions position vehicle i [m] 0 500 1000 1500 0 10 20 30 40 time[s] 50 60 70 lead vehicle 80 veh. 1 veh. 2 veh. 3 90 veh. 4 veh. 5 veh. 6 100 Road Side Unit Road Side Unit Source: Schick, Peter: Einfluss von Streckenbeeinflussungsanlagen auf die Kapazität von Autobahnabschnitten, Inst. f. Straßen- und Verkehrswesen 2003 Braunschweig, 17.08.2009

Panta rhei- Centralized traffic control ressources with global control functions Central Problem of Traffic Flow Measurement – Sampling Theorem 0 500 1000 1500 0 10 20 30 40 time[s] 50 60 70 lead vehicle 80 veh. 1 veh. 2 veh. 3 90 veh. 4 veh. 5 veh. 6 100 Road Side Unit Road Side Unit Road Side Unit Source: Schick, Peter: Einfluss von Streckenbeeinflussungsanlagen auf die Kapazität von Autobahnabschnitten, Inst. f. Straßen- und Verkehrswesen 2003 Braunschweig, 17.08.2009

Panta rhei- Centralized traffic control ressources with global control functions Global and Local Control Functions / Performance Criteria performance criteria ego vehicle collective s end ∫ = → travel time T dt min traffic availability arrival time traffic prediction s σ → 0 min T s end ∫ → 2 min a dt riding comfort homogenity s 0 s end ∫ → fuel consumtion of the Pdt min fuel consumption fleet s 0 ∆ = → p ( s 0 ) 0 distance traffic safety > → overspeed p ( v v ) 0 a Braunschweig, 17.08.2009

Panta rhei - Centralized traffic control ressources with global control functions Traffic Control Objectives and Methodologies considered objective methodologies traffic level local vehicle control • classical control e.g. − state space (Roppenecker et al.) − frequency domain • robust control e.g. distance operational − Sliding Mode Control velocity ego vehicle [Utkin, Slotine] − Quantitative Feedback Theory [Ackermann et al.] − H ∞ -Theory [Isidori et. al] coordination of vehicles by cooperative control • potential fields [Ögren et al.] flow • Sliding Mode Control [Gazi et al.] safety tactical • Ljapunov-based [Jadbabaie et al.] density collective of vehicles / • Receding-Horizon (MPC) [Jadbabaie] quality fleet • graph theory [Baillieul, Fax] congestion • Distributed Consensus [Olfati-Saber, Fax, Murray] • Petri-Net decision making Braunschweig, 17.08.2009

Panta rhei Fundamental Decomposition of Traffic Control into Function and Ressources control function local global control ressources vehicle control ? e.g. by means of robust control distributed intersection control fleet dispatching switch control flow control centralized train control traffic guidance truck dispatching Braunschweig, 17.08.2009

Panta rhei - Distributed control ressources with local control functions Local Control Principles - Sliding Mode Control  for n-th order SISO system − 1 n   d ~ = − ~ = + λ   x x x  definition of sliding surface S(t) s ( x , t ) x d   d t = s ( x , t ) 0  tracking means: S(t)  control law: =  s ( x , t ) 0 equivalent control via:  parameter k by stability criterion: ( n ) = ˆ + ⋅ x f ( x ) b ( x ) u nominal (lin. single track) model = − ˆ F f f model uncertainty λ , η Φ ,  design parameters = J lin. optimization of Braunschweig, 17.08.2009

Panta rhei - Distributed control ressources with local control functions Local Control Principles - Sliding Mode Control • Application e.g. for lateral vehicle-trailer control  max. lateral deviation: • 15 cm – worst case scenario • 11 cm – wind gust at straight ahead driving  stabilizes pendular oscillations due e.g. to cross winds  may be used as a driver assistance system to provide driving safety Example Simulation:  velocity: 190 km/h  straight ahead driving  additionally: disturbance at steering angle as step of 15 deg. at t= 3 s Braunschweig, 17.08.2009

Panta rhei - Distributed control ressources with local control functions Local Control Principles - Quantitative Feedback Theory Specification of performance requirements by means of boundary function Prefilter Controller Plant Sensor Boundary curves Boundary functions ω 1 e.g. control variable ω 2 ω 3 Discretization of frequency Braunschweig, 17.08.2009

Panta rhei - Distributed control ressources with local control functions Local Control Principles - Quantitative Feedback Theory - Robustness Criteria structured unstructured [ ] ( ) ( ) ( ) = + ∆ G s G s 1 s Family of plants 0 M = = = • multiplicative uncertainty with k [ 1 .. 10 ], a [ 1 .. 5 ] und b [ 20 .. 30 ] • direct specification as function ∆ M • in form of virtual templates directly integrated ω 2 into calculation of boundary curves ω 1 ω 3 amplitude (db) ω 4 phase angle ( ° ) Braunschweig, 17.08.2009