In search of Uniform and Equable Motion Three term (PID) control A history and some thoughts on current practice Page 1
The story 1. Early engines were batch devices with sequence controls 2. The interest in displacing water and wind mills meant an interest in uniform and equable motion 3. The engine governor emerged and exposed the principals of dynamics and of proportional and integral action 4. Meanwhile P+I enters the process world 5. The application to IC engines is widespread 6. How about PID control for research? 2
Mentions 1. Stuart Bennett (Sheffield) - https://www.shef.ac.uk/acse/staff/sb 2. Colleagues (for use of slides and material) Zhijia Yang Dezong Zhao Ed Winward 3. Our students and particularly Tyson Cheung. 4. Our Loughborough technical team 3
A parallel form https://en.wikipedia.org/wiki/pid_controller
Newcomen s environment World of intense commercial activity Water was the nuisance factor in mining and agriculture Cornish mines presented a substantial market The principal energy source was South Wales coal Harveys of Hayle was to become one of the great steam engine suppliers http://www.geevor.com/ (Geevor mine web site)
Henry Ford Museum Guide Newcomen s 1712 engine
Watt s double acting engine
Windmills and making flour gerald-massey.org.uk/windmills 8
The centrifugal governor Already established patented in 1787 by Thomas Mead Matthew Boulton suggested to James Watt to use as an engine governor Watt had already been working on the new throttle actuator gerald-massey.org.uk/windmills 9
Watt s governor en.wikipedia.org/wiki/lap_engine A proportional controller and known to suffer from offset Stuart Bennett, 10 A History of Control Engineering, 1800-1930
Pump governors Pump regulators may have been invented by James Watt Continued to be developed in spite of the progress of the mechanical governor Two particular aspects Integral action Actuating force Stuart Bennett, A History of Control Engineering, 11 1800-1930
Siemens and Maxwell The Siemens brothers arrive in the UK to commercially exploit William Siemen s new governor Maxwell motivated by the dynamics of governor behaviour Governors were also needed in scientific equipment Maxwell s analysis presented in February 1868 not as lucid as usual Routh picks up the ideas and works with them Stuart Bennett, A History of Control Engineering, 12 1800-1930
Maxwell s analysis dd dddd dddd MM dddd = PP RR FF dddd dddd VV In the steady state, left hand side vanishes so that dddd dddd = VV + PP RR FF William Siemens already used the terms: Moderator for a governor demonstrating droop Governor for an isochronous (constant speed) controller. Moderator dd dddd dddd BB dddd = FF dddd dddd VV In the steady state, dddd dddd = VV Governor J C Maxwell, On Governors, Philosophical Transactions of the Royal Society (20 th February 1868) 13
Maxwell and Jenkins In 1861 the British Association for the Advancement of Science appointed a committee to establish electrical standards Resistance measurements required the precise rotation of a coil Fleeming-Jenkins governor was conceived for this purpose It includes integral action. Fleeming Jenkin s governor (Stuart Bennett, History of Control Engineering 14
Mid 20 th century and the diesel governor Medium speed diesel engines in a wide variety of applications marine, power railway traction Seminal paper on governors came from an unusual source. Paxman, AEC, University of Cambridge (Donald Welbourn) Main impact appears to have been a substantial reduction in test bed usage D. B. Welbourn, D. K. Roberts, and R. A. Fuller, Governing of Compression-Ignition Oil Engines, Proceedings of the IMechE, June 1959 173: 575-604 15
The Ardleigh Type 222 governor 1 pp 0 DD 2 + 2ζζ pp 0 DD + 1 xx = μμ gg sin pppp Ardleigh later Regulateurs Europa 16
Achieving PI functionality μμ gg TT NN TT NN + TT SS + 1 TT NN + TT SS. 1 DD ωω ee TT NN = rr γγrr 3 rr 2 TT SS = 1 ααrr 1 αα γγ rr 1, rr 2, rr 3 are all geometrical factors αα, γγ are respectively flow co-efficients with dimensions LL TT LL 17
The PID controller in a process setting uu ss = KK 1 + 1 sstt ii + sstt dd ee ss Usually a PI controller will stabilise a plant so long as TT ii is chosen well Actuating devices scaled 0-100% 1/K is defined as the proportional band (PB) N% PB gives N% output for a 100% error Reset time is the time taken for a 100% error to create 100% output uu ss = KK 1 + 1 sstt ii ee ss Clarke, D W PID algorithms and their computer implementation Trans Inst MC, 6, 6, 1984
Early developments The earliest process control devices emerged in the early 20 th century The late 19 th century had seen a growing demand for instrumentation and automation Foxboro and Taylor Instrument both emerged during this period The modern pneumatic control is a testimony to the early beginnings Foxboro 43AP controller
The pneumatic PI controller Modern Control Engineering Ogata, 1997 20
Practical considerations and the D term 1. Adding feedforward 2. Bump-less transfer from manual to automatic control 3. Avoidance of derivative (and proportional) kick 4. Measurement conditioning and filtering 5. Rate limits for start-up of a new process 21 21
The D term 1. Provide phase lead 2. Simply adding a D term could improve phase margin and decrease gain margin sstt 3. Apply a term, DD where typically αα = 0.1 1+ααααTT DD 4. Velocity feedback apply derivative of feedback alone 5. Set-point filter progressively apply a set point change Li, Y, Ang, K H, Chong, G C Y, PID Control Systems Analysis and Design, IEEE Control Systems Magazine 26 (1), pp32-41 22
A PI loop with feedforward vv ss KK ff ee ss KK + + 1 1 + sstt ii Control, uu ss = K 1 + 1 sstt ii ee ss With feedforward, control, uu ss = K 1 + 1 sstt ii ee ss + KK ff vv ss
The PID controller A practical implementation ww ss + K uuu ss Limiter uu ss - + + ff ss 1 1 + sstt ii yy ss 1 + sstt dd Total action on yy ss is uu ss = K 1 + 1 sstt ii 1 + sstt dd yy ss Zeros at 1 TT ii, 1 TT dd Clarke, D W PID algorithms and their computer implementation Trans Inst MC, 6, 6, 1984
Non-interacting form of controller L1 provides de-saturation L2 provides a secondary limit Clarke, D W PID algorithms and their computer implementation Trans Inst MC, 6, 6, 1984 25
Tuning the PID controller Tuning methods emerged from the efforts made by the instrumentation suppliers Ideas were emerging in the 1930s Fulscope 100 from Taylor was the first PID controller (announced in 1939) Most significant result came from the Taylor Instrument Company Ziegler and Nichols papers (1942 and 1943) Cohen and Coon (1953) J G Ziegler and N B Nichols, Optimum Settings for Automatic Controllers, Trans ASME, 64, 1942 26
The effect of tuning Clarke suggests following PI tuning rules produces a toolively controller But the PID rules place two zeros on the real axis and guarantee stability. Increasing gain for simple plant, 1 1+ss 3 Using the Z-N PI tuning rule Place zero at 1.2 TT uu = 0.33 Clarke, D W PID algorithms and their computer implementation Trans Inst MC, 6, 6, 1984
Effect of tuning on disturbance rejection Richard Dorf Modern Control Systems 12 th Edition
PID - a short summary 1. Form of control that emerged in both the engine and process sectors in a quite different form 2. Much of PID literature is process oriented but there is substantial carry-over 3. The PID algorithm is well documented, well supported by tuning rules and can be adapted to multi-variable situations 29
The diesel engine Electronic control unit Inlet manifold Common rail EGR valve Injectors Intercooler EGR cooler VNT control Exhaust manifold Turbocharger Fuel tank Inlet air temperature Mass air flow meter Catalyst
The Challenge 1. Rapid iteration 2. Relative ease of adjustment and tuning 3. Reliable known algorithms with understood properties 4. Open to analytical and experimental approaches 31 31
Diesel Fuel Path Control(1) Two loop engine speed control system with CA50 and Alpha control system (control structure) Page 32
Diesel Fuel Path Control(1) Two loop engine speed control system with CA50 and Alpha control system Page 33
Diesel Fuel Path Control (2) 2I2O P max and IMEP Control Control structure Page 34
Diesel Fuel Path Control (2) 2I2O P max and IMEP Control Control authority Engine Speed: 1100rpm Variation of Pmax and IMEP with the two inputs: m1 and m2 Page 35
Diesel Fuel Path Control (2) 2I2O P max and IMEP Control System Control results: step response Cylinder 2 IMEP step response Cylinder 2 P max step response Engine Speed: 1100rpm Page 36
Evaluation of ETA hardware and controls The benefits of ETA Easily integrated into existing Turbine or VGT system Ability to improve the engine response to fast load increase Facilitates conversion of extra exhaust energy into electricity Some of the hallenges Thermal management Control scheme Mechanical installation Number 1 Engine Lab at Loughborough
Air Path System (with ETA) Three control inputs: 1) EGR valve position 2) VGT vane position 3) ETA torque demand Implementation of control system of the test engine 38
ETA and Fuel Consumption(1) Delta Pressure = EXP-MAP 1) Delta pressure increases with the increased VGT vane position 2) Delta pressure drops a little at low VGT vane position and then evolves to increase a little at high VGT vane position when ETA swept from generation to motoring 1) Fuel rate strongly correlated to delta pressure 2) At low VGT vane position, small increase of delta pressure caused by ETA generating mode results in bigger fuel rate increment (deteriorated efficiency) 39
ETA and Fuel Consumption(2) When EGR valve open (engine test results-delta pressure & MAP) When EGR valve open, the area of the shape of delta pressure related to MAP formed by different ETA and VGT becomes smaller because of the reduced delta pressure (it can be remembered as like a paper falling to the desk) 40
ETA and Fuel Consumption(3) When EGR valve open (engine test results-fuel rate & delta pressure) 1) When EGR valve opened wider, the maximum delta pressure becomes smaller and the fuel rate is more sensitive to delta pressure change which is caused by ETA especially when ETA is generating 2) The total area formed by fuel rate and delta pressure for all feasible VGT, EGR and ETA combinations can be simplified as a triangular area 41
3I3O Square Control Structure Selection (2) Three PI Controllers Decoupler Complete multi-variable controller 42 Such structure is the simplest decoupling multi-variable controller
3I3O Control System Implementation (1) Use looptune or systune MATLAB function 43
3I3O Control System Implementation (2) Gain-scheduling techniques were used for engine transient 44
3I3O Control System Engine Test Results (1) Setpoint tracking performance Three controlled variables Three control variables Engine Torque 45
Fast Starting Strategy Investigated by Toyota Motor Corporation to improve stop-start quality Utilises compressed cylinder for restart 50% Starting energy reduction 63% Cranking time reduction 10dB sound reduction Assisted Direct Start Strategy Kenji Kataoka, Kimitoshi Tsuji, Crankshaft Positioning Utilizing Compression Force and Fast Starting with Combustion Assist for Indirect Injection Engine, SAE Technical Paper 2005-04-11, DOI: 10.4271/2005-01-1166
Deploying a PID Controller Constant Deceleration Trajectory Speed Profile ωω tt = ωω tttttt tt ssssssss tt + ωω tttttt Crank angle profile θθ tt = ωω tttttt 2 tt ssssssss tt 2 + ωω tttttt tt 47
Implementing a PID Controller Control Input dddd tt uu tt = KK pp ee tt + KK ii ee ττ dddd + KK dd 0 dddd Application Dynamic Lookup table for reference speed Low speed control loop Controller Gains Tuned iteratively Increasing KK pp increased tracking performance KK dd and KK ii were found to decrease performance Initiation Speed reduced the peak control input - engine initially has high angular momentum tt
The results a benchmark assessment 14 PID Controlled Shutdown 12 10 8 6 4 2 0 Stop Time [s] Error [Degrees] Max Acceleration Fluctuation [100 rad/s] Peak Torque [danm] Net Energy Usage [kj] Uncontrolled PID
Observations and question PI and PID controls Simple Available Practical aspects covered Tuning rules developed Heuristics Provides a benchmark Open source Why so few examples? Github - Arduino - RPi What makes for a good real-time kit? 1 Could we easily modularise both algorithms and tuning? 1 LI, Y, Ang, K H and Chong, G C Y PID Control Analysis and Design IEEE Control Systems Magazine (26) 1,pp32-41 50
Summary (1) 1. The origins of control for uniform motion echo in today s control solutions 2. PID is widely understood familiar to most engineers - but not that well understood 3. But surrounded by a kind of folklore that has been dispelled in at least some of the process industry 4. Provides an excellent basis for quick implementations - tuning accessible heuristics accessible 51 51
Summary (2) 1. How do we access the best practice? 2. How do we choose the right analytical approach? Through modelling Through experiment and design 3. By making the controller easier we emphasise the physical solution 4. Understanding the dynamics remains our central interest 52 52
A concluding thought The change from ponderous beams to uniform and equable motion was not the result of a process of gradual improvement Rather it was through the use and adaptation of existing devices to meet the practical problems as they arose Stuart Bennett The Search for 'Uniform and Equable Motion': a study of the early methods of the control of the steam engine University of Sheffield, Department of Automatic Control, Research Report No 20. (Can be downloaded.) 53