9 merican ontrol onference Hyatt Regency Riverfront, St. Loui, MO, US June -, 9 ThB.4 Throttle ctuator Swapping Modularity Deign for Idle Speed ontrol Shifang Li, Melih akmakci, Ilya V. Kolmanovky and. Galip Uloy btract Swapping modularity refer to the ue of common unit to create product variant. companie trive to rationalize engineering deign, manufacturing and maintain procee, modularity i becoming a priority. omponent wapping modularity in control ytem can be achieved by utilizing mart component which can perform control action within the module, and bidirectional network communication. In thi paper we analyze an engine peed control ytem from the perpective of achieving wapping modularity of the throttle actuator. Specifically, we analyze approache to ditribute the optimal controller tranfer function between a throttle actuator time contant dependent portion (which i wappable with the actuator) and throttle actuator time contant independent portion (which doe not need to be changed when the actuator i wapped). Two ditributed controller architecture, with unidirectional and bidirectional communication, are conidered. I. INTRODUTION Swapping modularity occur when two or more alternative baic component can be paired with the ame modular component creating different variant belonging to the ame product family []. There are many advantage to ytem with high component wapping modularity. t preent, the competitive market neceitate product with different upplier, to meet variou tandard and regulation, and with variou level of performance and cot. Swapping modularity enable cutomization of an available product without redeign of the whole ytem. Increaing component wapping modularity can alo horten the engineering time and cot []. ontrol ytem with modularly wappable component can be defined a one where the initial and final configuretion due to a component change operate at their correponding optimal performance [3]. Fig. how a control ytem configuration in which many different type of actuator may be employed. Traditionally, a change in the actuator involve both the actuator and the bae controller. By including the actuator related control algorithm into the actuator component, re-work (in term of control algorithm, oftware and calibration change) can be limited to only the actuator ubytem, thereby making an actuator a modularly Shifang Li (correponding author), Melih akmakci, and. Galip Uloy are with the department of mechanical engineering, Univerity of Michigan, nn rbor, MI, 489-5. email:fli@umich.edu Ilya V. Kolmanovky i with the Ford Reearch and dvanced Engineering, Ford Motor ompany, Dearborn, MI, 48. wappable component, or in a way, a plug-n-play component. With the proliferation of low cot electronic, many control ytem component, uch a enor and actuator, can now incorporate on-board computer (i.e. PU, memory, I/O interface), which enable them to perform component pecific control and diagnotic function and to participate in ditributed controller architecture. Bidirectional communication in networked control ytem (NS) among the mart actuator and enor ha been hown to improve component wapping modularity. e.g., a cae tudy of a drivehaft control with a D motor conidered in [3]. Fig. : ontrol ytem with modularly wappable actuator component. In thi paper we conider a cae tudy of the controller deign for the throttle actuator wapping modularity from the perpective of an automotive engine Idle Speed ontrol (IS). The primary objective of the IS ytem i to regulate the engine peed to a et-point depite torque diturbance due to acceory load (e.g., air conditioning, power teering, alternator, etc.) and due to engagement of the tranmiion. typical IS trategy include a PID control for the air loop, a proportional feedback control for the park loop, and everal feed forward control realizing compenation for acceory load, engine temperature, ambient temperature and barometric preure [4]. pproache to IS baed on modern control theory have been alo conidered, including LQ baed optimization [5], H control [6], and l control [7]. dditional IS improvement are made poible through the preview and feed forward control of known or meaurable diturbance, uch a, for example, air conditioning or power teering load. deign technique, which include lead compenation, feed forward and a diturbance oberver, i preented for IS ytem with minimal park reerve level in [8]. The focu of thi paper i to analyze the wapping modularity of the optimal IS deign for the air path of the engine with repect to the throttle actuator time contant. Specifically, we eek to ditribute an optimal centralized IS into a bae controller part which doe not depend on thi time contant and into a time contant-dependent 978--444-454-/9/$5. 9 7
actuator controller part. While achieving wapping modularity of a fixed centralized IS i relatively eay with a low order actuator controller baed on pole-zero cancellation, our reult indicate that achieving wapping modularity of an optimal IS, i.e., that perform optimally for each choice of actuator time contant, i comparatively more difficult. In addition, we will demontrate that the bidirectional communication capability can facilitate the development of controller architecture which provide wapping modularity. II. PROBLEM FORMULTION In thi ection the problem formulation to maximize the actuator wapping modularity in a ingle input ingle output (SISO) linear time invariant (LTI) ytem i dicued. The controller deign for wapping modularity include three tep, the centralized controller deign, controller ditribution, and wapping modularity optimization. The key idea i to match the ditributed controller with the centralized controller, while maximizing the wapping modularity. Firt we deign the deired centralized controller de (P) by any controller deign method. Our approach in thi paper i baed on optimization to provide optimal performance of the ytem with each different actuator: min J ( P, ) ubject to gp (, ) σ where the element of the vector P are parameter of the actuator; the element of the vector are the undetermined coefficient of the centralized controller, which are variable of the optimization problem; J i a control-oriented objective function reflecting performance metric, uch a ettling time, control effort, etc; g repreent all the contraint uch a an overhoot limit, tability requirement, etc. Then the centralized controller i ditributed into two component, the bae controller B (x B ) and the actuator controller (x ), where B (x B ) and (x ) are controller tranfer function, or tranfer function matrice, depending on the number of the input and output for each component. The vector x B, x repreent numerator and denominator polynomial coefficient for thee function repectively. The ditributed controller, di (x B, x ), i a function of B (x B ) and (x ). The wapping modularity optimization proce i to maximize the wapping modularity while atifying de (P) = di (x B, x ), to enure that the ditributed controller provide the ame performance a the centralized controller. The variable in the optimization are the coefficient of the actuator controller x, which depend on the parameter of the actuator P, and the coefficient of the bae controller x B, which are independent of P, ince we only change the actuator controller when we wap the actuator. The wapping modularity of the actuator M, i defined in reference to Fig. a follow [3]. Fig. : Illutration of et P for a two parameter ytem. We aume, for the purpoe of illutration, that the actuator ha two parameter P and P, which can change depending on the component. Let P be a connected et of the two parameter including the nominal parameter et p, that atifie de (P) = di (x B, x ), by only changing the controller in the wappable component given a ditribution olution x dit = {x B, x }, i.e., l h P = { p R x [ x, x ]} uch that ( P) = ( x, x ) where p P de di B < ε, p p p p P nd whereε i a very mall poitive number. Then the wapping modularity M i defined a M ( p, xb, x) = dp () correpond to the area (ee Fig. ) in the parameter pace around the nominal value, for which optimal performance can be achieved by changing only the variable x in the actuator controller. That i, for a nominal parameter et of the actuator p, we earch for the bae controller variable x B, and the actuator controller variable x (P), to maximize the wappable parameter et P. P III. THROTTLE TUTOR SWPPING MODULRITY DESIGN FOR IS. IS ytem decription The throttle actuator i modeled a a firt order ytem with a time contant τ, Ga () = τ + () n engine model [9] linearized around an idle peed operating point with the nominal throttle poition, load torque and engine peed et, repectively, a u th, = 3.5 (deg), M L = 3.5 (Nm) and N = 8 (rpm), i ued to obtain the tranfer function from the deviation in the throttle poition (deg) to the deviation in engine peed (rpm), 57.997 td Ge () = e +.545+.8 (3) 73
The tranfer function from the deviation in the diturbance torque (Nm) to the deviation in the engine peed (rpm) i given a, 37.4 57. td Gl () = e +.545+.8 (4) The delay t d i between the intake troke of the engine and torque production, and correpond to 36 degree of crankhaft revolution. onequently, it i given by 6 t d =.75 (ec) N (5) firt order Padé approximation of the delay ha the form, td t d t.375 d e e = = (6) td t.375 d + e + With thi approximation, a pole-zero pair i added to the delay-free tranfer function, thereby permitting the reulting plant model to be treated with conventional linear control method. B. entralized controller deign The cloed-loop ytem i hown in Fig. 3, Gc () G () a Gt () G () e Fig.3: Feedback control ytem If we conider an objective of maximizing wapping modularity, an actuator controller which ue pole-zero cancellation to cancel the dynamic of the new actuator and maintain the dynamic of the original/nominal actuator, will provide full wapping modularity (within actuator phyical contraint). The hortcoming of uch an approach i that we maintain the repone of the ytem deigned for the original actuator and do not achieve optimality with repect to the changed actuator. It i, thu, of interet to undertand if the optimal centralized controller, which depend on the throttle actuator time contant, can be ditributed with only actuator controller dependent on the actuator time contant. The open loop ytem, including the throttle actuator, i 4 th order, after including the Padé approximation of the delay. The controller i aumed to be 4 th order, a per equation (7)-(9), and include an integrator to enure zero teady tate error: Gc () = S() R() (7) ' 3 R () = R() = ( + r + r + r) (8) 4 3 S () = 4 + 3 + + + (9) The controller deign i formulated a an optimization problem in reference to the repone of the ytem to d = (Nm) load diturbance tep and r = (rpm) et-point, and in reference to controller and cloed-loop pole location: min t (, τ ) ubject to g: M p M p_max g: u umax g3: u umin ' g4: real( root( R )) + e g5: real( root( L )) + e ' g6: mag( root( R )) e g7: mag( root( L )) e where t denote the % ettling time; variable repreent the undetermined controller coefficient,,, 3, 4, r, r, r ; M P repreent the maximum deviation from the idle peed; u i the throttle actuator poition. Since the nominal throttle poition i u th, =3.5 (deg), we limit u to the range [-, ] (deg), and M p to % of the idle peed (8 rpm). ontraint g4, g5 enure the tability of the controller and the cloed loop ytem, while e > enure a tability robutne margin. ontraint g6, g7 enure that the magnitude of the pole of the controller and the cloed loop ytem are not too large to avoid extending the bandwidth into the region where meaurement noie and model uncertaintie are dominant. parameter tudy wa conducted to find the optimal controller coefficient for each time contant of the throttle actuator in the range [.,.]. The coefficient,,, 3, 4, r, r, r can be derived a polynomial function of τ by curve fitting. With the optimal controller, the ytem repone to (Nm) load torque diturbance i hown in Fig. 4. The pole and zero of the optimal controller for each actuator time contant τ are hown in Fig. 5. Fig. 4: Optimal ytem repone to a tep diturbance torque Fig. 5: Optimal controller pole and zero for τ in [.,.] 74
can be een from Fig. 4, the optimal ytem repone change a the value of the time contant of the throttle actuator decreae. Fig. 5 how that ome of the pole and zero of the optimal controller are unchanged for a range of the actuator time contant τ. If we accept an approximation of the pole and zero, i.e., if the pole (zero) for different τ are within the circular region centered at the pole (zero) of the optimal controller correponding to nominal τ =.5, we conider it a unchanged. If we aume the radiu of the circular region i 5% of the abolute value of the pole (zero) for the nominal cae. We oberve the pole p = i unchanged for τ in [.,.], the pole p = -.7 i unchanged for τ in [.3,.8], and the zero z, = -.7±.3i are unchanged for τ in [.3,.]. Now aume the unchanged pole and zero to be fixed at the value for the nominal cae, the approximate optimal controller pole and zero are hown in Fig. 6, and the cloed loop ytem performance baed on the approximate optimal controller are hown in Fig. 7. Fig. 6: pproximate optimal controller pole and zero for τ in [.,.] Fig. 8: ontroller configuration with unidirectional communication hown in Fig. 8, the centralized controller i ditributed into the bae controller B (x B ) and the actuator controller (x ), where B and are both SISO tranfer function and can be aumed to be of different order. For example, if B i 3 rd order and i t order, then 3 x + x + x3+ x4 B = 3 + x + x+ x () 5 6 7 x8+ x9 = + x () From the perpective of computational efficiency and eae of implementation, it i deirable if the two controller are of low order. Thi i epecially deirable for the wappable component. Table decribe the tet cae we ued for our analyi. The cae B4, which can achieve conitent control for each τ by pole-zero cancellation, i included here to invetigate if one can achieve the full range of wapping modularity while guaranteeing optimal control for each τ. TBLE UNIDIRETIONL SE DESRIPTIONS ae ae decription B4 B : 4 th order, : gain B4 B : 4 th order, : t order B3 B : 3 rd order, : t order B B : nd order, : nd order B3 B : t order, : 3 rd order B4 B : gain, : 4 th order The overall ditributed controller with e a the input and q a the output i then given by di ( xb, x ) = B (3) where x B, x are undetermined coefficient of the ditributed controller B and repectively. Only x can depend on actuator parameter. Fig. 7: ytem repone to a tep of diturbance torque with approximate controller hown in Fig. 7, the cloed loop ytem repone with the approximate optimal controller are almot the ame a that with the original optimal controller hown in Fig. 4. Therefore it i acceptable to take the approximate optimal controller for each τ a the deired centralized controller de( τ ). The approximation made here will be employed in tep 3) bellow (i.e., wapping modularity deign), to maximize the actuator wapping modularity.. ontroller ditribution ) With unidirectional communication ) With bidirectional communication The communication network i hown in Fig. 9. Fig. 9: Ditributed controller with bi-directional communication When bidirectional communication between the bae controller and the actuator controller in the mart actuator i introduced, B and become tranfer function matrice, 75
[ ] = (4) B B B = (5) Table how ome of the tet cae to ee the effect of the order ditribution. From a large et of poible olution, we have elected the relatively low-order one that provide good wapping modularity. TBLE BIDIRETIONL SE DESRIPTIONS ae ae decription B B : nd order, B : nd order, : gain, : gain B B : t order, B : nd order, : t order, : gain B B : nd order, B : t order, : gain, : t order B B : gain, B : nd order, : t order, : t order B B : nd order, B : gain, : t order, : t order B B : t order, B : t order, : t order, : t order B B : gain, B : t order, : nd order, : t order B B : t order, B : gain, : nd order, : t order B B : gain, B : t order, : t order, : nd order B B : t order, B : gain, : nd order, : t order B B : t order, B : gain, : t order, : nd order B B : gain, B : gain, : nd order, : nd order By analyzing Fig. 9 and uing the notation preented in (4)-(5), the equation repreenting individual ignal are u = y + e (6) ca B ac B y = u (7) ac ca q = u (8) ca Equation (6)-(8) can be rewritten in matrix form a uca B B e y = ac (9) uca q = [ ] y () ac Therefore the ditributed controller with e a input, q a output i given by B B di ( xb, x ) = [ ] ( x, x ) = di B B B () D. Swapping modularity optimization Fig. illutrate the et P for the cae where the actuator can be repreented uing only one parameter (i.e. τ). The wapping modularity meaure i a real number repreenting the range of thi parameter for which wappable modularity i achievable. Fig. : Illutration of et P for a one parameter ytem The optimization problem to maximize wapping modularity i formulated a follow, ( τ τ ) max max min xb x x ubject to: h: de ( τ ) = di ( xb, x ) g: tability of each ditributed controller g:. τ. Note that the deign variable in thi optimization problem are x B and x (τ). Thi optimization problem wa olved numerically uing the following tep: a) Initialize x B and x b) Vary τ about the nominal value τ =.5, to find the maximum and minimum value of τ that atify the contraint h, g and g, by varying x only, for a fixed x B. ompute M = max τ min τ c) Repeat tep b), chooing different value for x B ; ompute and tore M (x B ) d) Determine maximum of M with repect to tried x B To initialize x B and x, one may olve the equality contraint h (matching the pole and zero) for the nominal value of τ=τ. Step c) and d), to earch for different x B for M (x B ) and then maximize M with repect to x B, repreent a nonlinear optimization problem. If we make ue of the information that, for a certain range of τ, the pole and zero of the centralized controller de ( τ ) are contant, a illutrated in ection B, it i poible to predict an upper bound on the maximum M (x B ) that can be achieved. For example, if the ditributed controller di( xb, x ) ha a zero, which i determined by x B only, i.e., it cannot be manipulated by x, then thi zero ha to be equal to one of the contant zero of de( τ ) in order to achieve wapping modularity. Since that zero of de( τ ) i only contant for a certain range, then thi range put an upper bound on the maximum M we can achieve. In thi way, we may terminate the earch for x B, if we obtain the predicted upper bound on M. In our cae, the predicted upper bound on M x x 76
wa alway achievable, frequently, jut for the tarting value of x B. E. Reult and dicuion We conider the range of the time contant of the actuator a [.,.]. Note that, for thi range, full wapping modularity correpond to M =., and implie that any actuator with τ in the range [.,.] can be ued to achieve optimal performance by making change only to the gain x of the actuator controller. value of M =, indicate that the optimal performance can only be achieved for the nominal value of the time contant, τ =.5. ny internal value of M, like.5, correpond to a certain range of τ, in which the actuator ha wapping modularity. Table 3 how the modularity reult for the cae decribed in Table, with the configuration in Fig. 8. Table 4 how the modularity reult for the cae decribed in Table, with the configuration in Fig. 9. TBLE 3 EFFETS OF ONTROLLER DISTRIBUTION WITH UNIDIRETIONL OMMUNITION ae M (range) B4, B4, B3 (.5-.5) B, B3.5 (.8-.3) B4. (.-.) The reult in Table 3 how that for the configuration with unidirectional communication, when the order of the actuator controller i of or 3, the wapping modularity i.5. Only when all the control, except a gain, i moved to the actuator, can we achieve full range wapping modularity. Note that if our objective were to match the performance of a fixed centralized controller, the olution in the B4 cae with a firt order actuator controller may exit, a thi cae include an actuator controller baed on pole-zero cancellation. But the olution for matching the optimal centralized controller doe not exit in thi cae. TBLE 4 EFFETS OF ONTROLLER DISTRIBUTION WITH BIDIRETIONL OMMUNITION ae M (range) B, B, B (.5-.5) B, B.5 (.8-.3) B, B,,.8 (.-.3) B, B, B B. (.-.) The wapping modularity reult for the bidirectional communication configuration are hown in Table 4. We can achieve larger wapping modularity when the order of the actuator controller i of, in cae B, and we have many controller configuration to achieve larger wapping modularity, compared to the unidirectional communication configuration. IV. SUMMRY ND ONLUSION pproache to achieving wapping modularity for an engine peed control ytem with repect to change in the throttle actuator time contant have been analyzed. It ha been hown that an optimal centralized controller can be ditributed between an actuator controller and a bae controller, where only the actuator controller depend on the throttle actuator time contant. With uch a ditributed controller implementation, a throttle actuator and it controller can be wapped without touching the oftware or the calibration of the bae controller in uch a way that the performance of the cloed-loop ytem i automatically configured to be optimal for the new throttle component. omparing to the unidirectional communication configuration, the bidirection-al communication capability provide extra flexibility in developing ditributed controller architecture which enhance wapping modularity. In thi paper we focued on a cae tudy for achieving wapping modularity of the engine peed control with repect to the throttle actuator time contant. imilar approach can be followed to analyze the pathway to achieving wapping modularity with repect to other component and parameter, including throttle actuator time delay, intake manifold volume, engine diplacement volume and/or engine inertia. REFERENES [] K. Ulrich and K. Tung, "Fundamental of Product Modularity," in Iue in Deign/Manufacture Integration, SME, New York, 99, pp. 73-79. [] M. akmakci and. G. Uloy, "Bi-directional communication among "mart" component in a networked control ytem," in merican ontrol onference, 5. Proceeding of the 5, 5, pp. 67-63 vol.. [3] M. akmakci and. G. Uloy, "Improving omponent Swapping Modularity Uing Bi-directional ommunication in Networked ontrol Sytem," IEEE/SME Tran. Mechatronic, (in pre). [4] D. Hrovat and J. Sun, "Model and control methodologie for I engine idle peed control deign," ontrol Engineering Practice, vol. 5, pp. 93-, 997. [5] M. bate and V. DiNunzio, "Idle peed control uing optimal regulation," in SE paper, 99. [6]. arnevale and. Mochetti, "Idle peed control with H-infinity technique," SE paper, 993. [7] K. Butt, N. Sivahankar, and J. Sun, "Feedforward and feedback deign for engine idle peed control uing l optimization," in merican ontrol onference, 995. Proceeding of the, 995, pp. 587-59 vol.4. [8]. Gibon, I. Kolmanovky, and D. Hrovat, "pplication of diturbance oberver to automotive engine idle peed control for fuel economy improvement," in merican ontrol onference, 6, 6, p. 6 pp. [9] I. Kolmanovky and D. Yanakiev, "Speed gradient control of nonlinear ytem and it application to automotive engine control," Journal of SIE, vol. 47(3), 8 77