CONTROLLER-OBSERVER IMPLEMENTATION FOR CYCLE-BY-CYCLE CONTROL OF AN HCCI ENGINE

Transcription

1 Proceedings of IMECE 07 International Mechanical Engineering Conference and Exposition November 11-15, 2007, Seattle, Washington, USA IMECE CONTROLLER-OBSERVER IMPLEMENTATION FOR CYCLE-BY-CYCLE CONTROL OF AN HCCI ENGINE Nikhil Ravi Design Group Dept. of Mechanical Engineering Stanford University Stanford, California Matthew J. Roelle Design Group Dept. of Mechanical Engineering Stanford University Stanford, California J. Christian Gerdes Design Group Dept. of Mechanical Engineering Stanford University Stanford, California ABSTRACT This paper presents experimental cycle-by-cycle control of a single cylinder HCCI engine. The controller is developed from a discrete-time nonlinear model presented in previous work. The model captures the behavior of a gasoline direct-injection engine with an exhaust-recompression strategy used to achieve HCCI. This model is linearized about an operating point so as to enable the synthesis of linear controllers. The model states are represented by the temperature and oxygen content of the retained exhaust, and so are not measurable in practice. Therefore, an observer is used to estimate the states based on a measured ignition proxy. The state estimates are then used by a reference-input tracking controller to track a desired system trajectory. Experimental results show tracking of the model outputs that is comparable to tracking achieved in simulation. The controller is also seen to reduce the cycle-to-cycle variability of combustion significantly, particularly at later combustion phasing. This stabilizes combustion, lowers the instances of misfires, and enables steady operation at points that are normally unstable. NOMENCLATURE A th Arrhenius rate pre-exponential factor E a Activation energy for gasoline EVO Exhaust Valve Opening time EVC Exhaust Valve Closing time IVO Intake Valve Opening time IVC Intake Valve Closing time K th K x Arrhenius threshold value L Estimator n f,k Moles of fuel injected into cylinder during engine cycle k n O2 Moles of oxygen trapped in cylinder at EVC for engine cycle k,k P pk,k Peak pressure on engine cycle k R u Universal Gas Constant T e,k Temperature of trapped exhaust at EVC for engine cycle k V IVC,k Cylinder volume at IVC for engine cycle k V EVC,k Cylinder volume at EVC for engine cycle k u k Input vector on engine cycle k x k State vector on engine cycle k y k Output vector on engine cycle k ψ k Fraction of external EGR for engine cycle k θ pk,k Angle of peak pressure on engine cycle k Deviation of a quantity from nominal operating condition ˆ Estimated value of a quantity INTRODUCTION Homogeneous Charge Compression Ignition (HCCI), with its proven benefits of high efficiency and low NO x emissions [1] is one of the most promising engine technologies for the future. Achieving and controlling the combustion, however, is highly challenging in practice due to the complex dynamics of the process. This is so because of the extreme sensitivity of HCCI to the temperature and composition of the reactant mixture [2, 3]. 1 Copyright c 2007 by ASME

2 Several strategies have been proposed in the past for controlling combustion in an HCCI engine. In [4], it is indicated that the ignition delay and the burn rate can be independently controlled using various fuel mixtures and additives. Dual fuels with different octane numbers are also used to control the combustion timing in [5]. A thermal control system consisting of a preheater to increase fuel-air mixture temperature, a supercharger to increase mixture density and an intercooler to decrease mixture temperature is used in [6] to achieve and control HCCI. [7] and [8] use variable valve actuation to control the mixture properties and affect combustion. In [9], a method combining varying compression ratio to control ignition timing, and supercharging to control load is proposed. This paper presents experimental implementation of a control strategy for HCCI that uses a combination of a variable valve actuation system to control the valve timings and a direct fuel injection system to accurately control the amount of fuel injected into the engine cylinder. The controller is synthesized on the basis of a simple physical model of HCCI described in previous work [10]. The model is based on a description of the fundamental thermodynamics of HCCI. The model specifically captures the behavior of a single cylinder HCCI engine with a gasoline direct injection system, and with HCCI being achieved through an exhaust recompression (trapping) strategy. The model states are chosen so as to represent physical quantities critical in determining the nature of HCCI combustion - reactant concentrations and temperature. Additionally, the role of the trapped exhaust in determining the phasing and nature of combustion is critical - and therefore the states for the model are picked as the moles of oxygen in the trapped exhaust and the temperature of the trapped exhaust. A linearized version of this model is used as the basis for the development of a linear controller. A caveat to be noted here is that the primary aim of controller development was not the synthesis of an optimal HCCI controller, but rather the validation of the entire model-based control process. Since the states cannot be measured on an engine, an observer is used to obtain an estimate of the states. This observer uses a measurement of the angle of peak pressure (used as an ignition proxy) that is obtained from an in-cylinder pressure sensor. The state estimates are then used by a reference tracking LQR controller to track a desired system trajectory. The outputs controlled are the peak pressure and the angle of peak pressure in an engine cycle, which have been used in the past as representative of the work output and phasing of combustion [8]. This controller-observer system is first tested in simulation and then in experiment. Results show qualitative agreement between the performance of the controller in simulation and experiment. It is seen that the controller is able to track the desired trajectory around a nominal operating point with an accuracy comparable to that achieved in simulation. Some steady state error is seen in the tracking in both simulation and experiment for larger deviations from this point. This suggests that the linearization is valid only within a region around that point. The controller is also seen to reduce the cycle-to-cycle variability of combustion significantly, particularly at a late combustion phasing. In particular, the controller lowers the instances of misfires at points that are unstable in open-loop. Therefore it stabilizes the combustion process, and enables steady operation at points that would otherwise be highly unstable. These results serve to validate the applicability of this simple control model for controlling HCCI. MODEL DESCRIPTION An outline of the model used as a basis for controller development is presented in this section. The complete model has been presented in previous work [10]. Model states The process of combustion is basically dictated by two characteristics of the reactant mixture: reactant concentrations, and mixture temperature. Choosing a set of state variables, therefore, that in some way represent these quantities, would give a fundamental basis for an engine model. Of the two reactants (fuel and O 2 ), the fuel is an input to the system, and is directly controlled through the fuel injector. In HCCI, the trapped exhaust plays a pivotal role. It is the exhaust retained from the previous engine cycle that is used to heat (and dilute) the fresh charge for the current cycle, and is what induces the cycle-to-cycle coupling. This trapped exhaust, therefore, is essentially what carries information about combustion in one engine cycle through to the next. Based on the above observations, the states are chosen as: 1. Moles of oxygen in the products of combustion at EVC, n O2,k 2. Temperature of the trapped exhaust at EVC, T e,k Model inputs and outputs The model assumes the following inputs. 1. Moles of fuel injected in the current cycle, n f 2. Volume at intake valve closure, or the point at which instantaneous mixing between air, fuel and trapped exhaust is assumed to occur, V IVC 3. Volume at exhaust valve closure, or the point at which the states of the system are determined, V EVC and 4. Fraction of external EGR, ψ. This assumes the presence, in addition to exhaust retention, of an external EGR mechanism where some portion of exhaust is routed from the exhaust manifold into the main incoming air stream. It has been shown that diluent concentration affects both the start of combustion time, as well as burn duration [11]. 2 Copyright c 2007 by ASME

3 In terms of the outputs of the model, what is ultimately desired is that the engine produce the amount of work required, and that combustion occur at the desired phasing. The outputs of the model are therefore chosen as quantities that are representative of these values, but are also easily measurable on an actual engine. These are Pressure (kpa) 1. Peak pressure, P peak, which serves as a proxy for the net work output of the engine 2. Angle of peak pressure, θ peak, which represents the phasing of the combustion event States determined here: 1. Moles of O 2 - n O, k 2. Temperature - Tk Input V EVC, k 2 Input n f, k Input - External EGR ψ Input V IVC, k k Outputs measured here: 1. P pk, k 2. θ pk, k CAD Figure 1. STATES, INPUTS AND OUTPUTS IN THE HCCI MODEL Figure 1 shows a typical HCCI pressure trace, with the locations of the different inputs, outputs and states within an engine cycle. Top dead center after recompression is taken as the 0 crank angle reference. Model summary Based on the above, a two state nonlinear state space model is developed that maps the inputs on one engine cycle to the outputs on that cycle through the states. x k+1 = F(x k,u k ) y k = G(x k,u k ) (1) The states, inputs and outputs are given by where n O2,k and T e,k represent the number of moles of oxygen in the trapped exhaust, and the temperature of the trapped exhaust at EVC, n f,k represents the quantity of fuel injected into the cylinder, V IVC,k and V EVC,k are the cylinder volumes at IVC and EVC respectively, ψ k is the amount of external EGR (as a fraction of the total air entering the cylinder), P pk,k is the peak pressure in a cycle, and θ pk,k is the crank angle at which the peak occurs. A complete description of the model with validation is presented in [10], with analytical expressions for all functions in Eqn. 1. The compression, expansion and exhaust processes are modeled as isentropic. Combustion is assumed to be instantaneous (due to the fast nature of HCCI combustion). The ignition event itself is modeled through an Arrhenius integral, which has been shown to accurately capture the effect of both temperature and reactant concentrations on phasing [2]. The expression is obtained by integrating a global Arrhenius reaction rate equation for the combustion reaction. θth K th = A th e ( RuT Ea ) [ f uel] a [O 2 ] b dt (3) θ IVC The combustion is modeled to begin at θ th, when the integral in Eqn. 3 exceeds a certain threshold, K th. The integration can be simplified by approximating the integrand by its value at TDC, and beginning integration at this point, a justifiable assumption as the value of the integrand is largest at TDC. In this case a linear expression for the phasing θ th is obtained in terms of the Arrhenius threshold. ( ) θth Ea RuT ˆK th = A th e T DC [ f uel] a T DC [O 2] b T DC dθ/ω k θ IVC A th e Ea RuT T DC [ f uel] a T DC [O 2] b T DC (θ th θ T DC ) ω k (4) where ω k is the engine speed. CONTROLLER-OBSERVER SYNTHESIS The above nonlinear model is linearized analytically about an operating point to obtain a linear model of the form shown in Eqn. 5. x k+1 = A x k + Bũ k ỹ k = C x k + Dũ k (5) x k = [ no2,k T e,k ],u k = n f,k V IVC,k V EVC,k ψ k,y k = [ Ppk,k θ pk,k ] (2) In the above linear model, the states, inputs and outputs are represented as normalized deviations from the nominal operating point about which linearization has been performed. The matrices A, B, C and D are functions of that nominal point. 3 Copyright c 2007 by ASME

4 A linear controller and observer can then be synthesized using the above model. An interesting consequence of the particular measurements available for estimation is the fact that the output C matrix for the linear system is poorly conditioned. This is due to the fact that of the two outputs (peak pressure and angle of peak pressure), the peak pressure value is a strong function of the amount of fuel injected in the cylinder, which is an input. This is particularly true once the phasing of combustion - and consequently the other output, the angle of peak pressure - is fixed. Hence the observer uses only the angle of peak measurement to estimate both states. The state estimate generated by the observer is then used by a reference input tracking controller as described in [12]. An LQR controller is used here. The final controller-observer system obtained is shown in Eqn. 6 Table 1. OPERATING POINT AT WHICH CONTINUOUS SIMULATION AND SIMPLE CONTROL MODEL ARE COMPARED Parameter Value Units IVO 80 CAD IVC 220 CAD EVO 480 CAD EVC 6 CAD Mass of fuel injected per cycle 7 mg Peak pressure 75 kpa Angle of Peak Pressure CAD ũ k = K x ˆx k + (N u + K x N x )r k ˆx k+1 = (A LC) ˆx k + (B LD) { K x ˆx k + (N u + K x N x )r k } + Lŷ k = (A LC BK x + LDK x ) ˆx k + Lŷ k + (B LD)(N u + K x N x )r k (6) against experimental data. This model, described in [2, 3], is a continuous time, ten-state model that captures the fundamental thermodynamics of the HCCI process. Valve flows are modeled using compressible flow equations, heat transfer occurs continuously throughout the engine cycle and the combustion event is of finite duration, and is captured by a Wiebe function. Ta- where r k is the reference input (representing the desired output trajectory), K x is the controller, L is the estimator and N u and N x are matrices obtained from the constraint that the system respond with a zero steady state error to any constant input. The state estimate for the state x k is ˆx k. More details on the controller and observer are presented in [13]. Implementation in simulation 4600 off 4500 on Peak pressure off on LPP Actual trajectory Desired trajectory Peak pressure (kpa) Angle of peak pressure Figure 2. LQR OUTPUT CONTROLLER IMPLEMENTED IN SIMULA- TION - TRACKING OF OUTPUTS The controller-observer pair is implemented on a more complex continuous time simulation model that has been validated Figure 3. TEST APPARATUS 4 Copyright c 2007 by ASME

5 ble 1 shows the characteristics at the particular operating condition about which the nonlinear control model has been linearized for the results shown. At this point, the eigenvalues of the linearized open-loop system are located at (0.4213, ). This indicates that this operating point is stable, as both discretetime eigenvalues lie within the unit circle. This linearized model is then used as the basis for the observer and controller synthesized and implemented in both simulation and experiment. With the controller, the closed-loop system has its eigenvalues at (0.0013,0.0067) - and therefore we expect the system to be much more stable around this point when run closed-loop. Figure 2 shows the tracking achieved in simulation. Both outputs are tracked fairly rapidly, though there is some steady state error. This error can be attributed to the linearization and the lack of a sufficient weight on tracking error in the LQR controller. changes in the exhaust valve timing were weighted much more than changes in fueling. In addition, tracking error was weighted less than the input, so that the input magnitude commanded was maintained within reasonable bounds. Experimental results show that the controller performs fairly reliably over a range of operating conditions around the nominal operating point. Some salient features of the controller performance include 1. Reasonable tracking within a region around the nominal operating point with an accuracy similar to that achieved in simulation 2. Some steady state error when moving further away from that point 3. Speedy response to step changes - of the order of 4-5 cycles 4. Reduction in cyclic variability EXPERIMENTAL IMPLEMENTATION Experimental apparatus The experiments described in this paper were performed on a single cylinder engine. The base engine is a 2001 model year five-cylinder Volvo diesel engine, where just one cylinder is used for conducting tests. The other cylinders intake and exhaust ports are blocked. A spark plug has been added in the head for the active cylinder. Additionally, a Bosch gasoline injector is used in place of the original diesel injector, to directly inject gasoline into the cylinder. Fuel is delivered to the injector at 1500 psig. The intake and exhaust valves (two each) for the active cylinder are controlled with an electro-hydraulic variable valve actuation (VVA) system. The VVA system allows fully flexible actuation of each valve independently. The original diesel piston has been replaced with an aluminium one with a compression ratio of 13:1. The piston geometry is nearly flat with a shallow 2 mm bowl and valve cutouts that are about 0.5 mm deep. In-cylinder pressure is measured used an AVL piezoelectric pressure transducer. This information is used to calculate the outputs - peak pressure and angle of peak pressure - for control. The engine is operated in Matlab s xpc-target environment, with Simulink models used to run, control and collect information from the engine. All experiments described below were performed at 1800 RPM. Experimental results The controller tested in simulation was implemented on the engine testbed described above. The controller was designed so as to use only two inputs - the amount of fuel injected into the cylinder, and the exhaust valve timing. The input cost matrix in the development of the LQR controller was set in such a way that Tracking performance Figure 4 shows the result of a particular test on the engine. The two plots on top show the desired and actual outputs - peak pressure and angle of peak pressure (LPP) - while the plots on the bottom show the commanded inputs - fuel quantity and the crank angle at exhaust valve closure (EVC). Shaded areas show when the controller is on. As seen the engine responds as soon as the controller is switched on, and then subsequently follows the desired system trajectory. There is some steady state error that we observe. The order of magnitude of the error is the same as in simulation. Also, due to the higher weight placed on valve motion, most of the cycle-by-cycle control is done by the fuel injection, while the valve control really becomes important only while switching from one point to another. Speed of response Figure 5 shows a zoomed-in view of the response when the controller is switched on. As seen, the response is extremely quick, and the engine reaches the new steady state point in a space of about 4-5 cycles. Reduction in cyclic variability One of the big advantages of applying cycle-by-cycle control to the HCCI process is its effect on cyclic variability. HCCI is an inherently dynamic process. This is due to the effect that the combustion phasing on a particular engine cycle has on the trapped exhaust temperature (through heat transfer). This affects the mixture temperature on the next cycle, and subsequently the phasing of combustion on that cycle. This dynamic effect can be compensated for by using a controller based on a model that captures this behavior. Figure 6 shows the results from a test where the engine is switched between open and closed-loop modes several times. This operating condition is fairly unstable open-loop, particularly due to the late phasing of combustion. The dynamics at 5 Copyright c 2007 by ASME

6 Peak pressure (bar) Fuel quantity commanded per cycle (mg) Measured peak pressure Desired peak pressure LPP (CAD) EVC (CAD) Measured LPP Desired peak pressure Open loop Figure 4. Closed loop control Control of HCCI - output tracking Fuel quantity commanded per cycle (mg) Peak pressure (bar) Measured peak pressure Desired peak pressuree Figure 5. LPP (CAD) EVC (CAD) Measured LPP Desired peak pressure Open loop Closed loop control SPEED OF RESPONSE OF CONTROLLER this point are such that the combustion process is highly oscillatory from cycle to cycle, with early phasing on one cycle causing late combustion on the next due to heat transfer effects, and vice versa. However, when the controller is switched on, we see a drastic reduction in the peak-to-peak variability of both peak pressure and angle of peak pressure. This is achieved through a minimum of control effort - with practically no change in the exhaust valve timing, and just small variations in fuel quantity. However, due to the predictive nature of model-based control, these small variations in fuel quantity on a cycle-by-cycle basis are actually sufficient to prevent the oscillatory behavior from setting in. The effect of the controller on the net work output of the engine can be seen in Fig. 7. Though this quantity is not directly 6 Copyright c 2007 by ASME

7 Peak pressure (bar) Fuel quantity commanded per cycle (mg) Measured peak pressure 372 Desired peak pressure 370 LPP (CAD) 360 Measured LPPP 358 Desired ed peak pressure EVC (CAD) Open loop Closed loop control Figure 6. REDUCTION IN CYCLIC VARIABILITY controlled, there is a marked decrease in the variation of the indicated mean effective pressure (IMEP) when the controller is turned on. In particular, there are several instances in the openloop case where the engine is misfiring, as evidenced by the points showing a negative value for the IMEP. These instances are non-existent in closed-loop mode. Therefore the controller, by reducing cycle-by-cycle variation, is actually able to prevent misfires at points that are otherwise unstable, and therefore enables more steady operation at these points. P pk,k (bar) P pk,k 1 (bar) IMEP (bar) Figure 8. PEAK PRESSURE LAG PLOT - OPEN LOOP Figure 7. Open loop Closed loop control REDUCTION IN CYCLIC VARIABILITY - IMEP This effect of reducing process variation can also be seen in the lag plots shown in Fig.s 8 and 9. These plots show the P pk,k (bar) Figure 9. P pk,k 1 (bar) PEAK PRESSURE LAG PLOT - CLOSED LOOP 7 Copyright c 2007 by ASME

8 peak pressure on cycle k as a function of the peak pressure on cycle k 1. In open loop, there is a lot more dispersion in these values. There are also several points that lie right at the motoring peak-pressure barrier of about 24 bar, which indicates misfires. In closed loop, however, there is much less variation, and the engine does not misfire. Whatever variation exists is also more white and more centered around the mean peak pressure at this operating point, which is about 35 bar. CONCLUSIONS The results presented in this paper show the value of modelbased control in controlling the HCCI combustion process. The complex dynamics of exhaust-recompression HCCI are captured through two states - the oxygen content and temperature of the trapped exhaust. A model based on these states then serves as a useful platform for the development of control strategies. Here, a simple linear controller and observer have been used to control an HCCI engine around a nominal operating point. The results demonstrate two significant benefits of applying cycle-by-cycle closed loop control. First, the system is able to track a desired output trajectory reasonably within a range of conditions. More importantly, though, the controller is able to reduce the cyclic variation that is natural to HCCI, particularly at points that are prone to misfires and unsteady combustion when run open-loop. This reduction in combustion variability also prevents misfires. The controller is able to effect this reduction in variation through a minimal amount of control effort. By enabling steady operation at points that are otherwise unstable, the controller effectively widens the operating possibilities of the HCCI engine. FUTURE WORK Future work will focus on using this model-based control approach to develop better controllers for HCCI. Some of the issues with the particular controller presented here, such as the steady state error due to the linearized treatment of a nonlinear system, will be addressed. Additionally, it was seen here that one of the measurements used for state estimation, peak pressure, did not give much information about the states. Future work will investigate the extent to which these estimation challenges impact controller performance. Acknowledgements The authors would like to thank the General Motors Corporation and the Robert Bosch Corporation Research and Technology Center for their technical and financial support of this work, and in particular, Dr. Chen-Fang Chang, Dr. Man-Feng Chang, Dr. Jason Chen, Dr. Jim Eng, Dr. Tang-Wei Kuo, Dr. Paul Najt, Dr. Jun-Mo Kang, Dr. Nicole Wermuth, Dr. Jean-Pierre Hathout, Dr. Jasim Ahmed, Dr. Aleksandar Kojic and Dr. Sungbae Park. REFERENCES [1] Caton, P. A, Simon, A. J., Gerdes, J. C., and Edwards, C. F., Residual affected homogeneous charge compression ignition at low compression ratio using exhaust reinduction. International Journal of Engine Research [2] Shaver, G. M., Gerdes, J. C., Jain, P., Caton, P. A, and Edwards, C. F., Modeling for Control of HCCI Engines. Proceedings of the 2003 American Control Conference, pp [3] Shaver, G. M., Roelle, M. J., and Gerdes, J. C Modeling Cycle-to-Cycle Coupling in HCCI Engines Utilizing Variable Valve Actuation. Proceedings of the 2004 IFAC Symposium on Advances in Automotive Control, pp [4] Tanaka, S., Ayala, F., Keck, J. C., Heywood, J. B., Two-stage ignition in HCCI combustion and HCCI control by fuels and additives. Combustion and Flame, Volume 132, Number 1, pp [5] Bengtsson, J., Strandh, P., Johansson, R., Tunestl, P., and Johansson, B., Closed loop combustion control of homogeneous charge compression ignition (HCCI) engine dynamics. International Journal of Adaptive Control and Signal Processing, 18, pp [6] Martinez-Frias, J., Aceves, S. M., Flowers, D., Smith, J. R., and Dibble, R., HCCI engine control by thermal management. SAE paper [7] Agrell, F., Angstrom, H-E., Eriksson, B., Wikander, J., and Linderyd, J., 2003 Integrated simulation and engine test of closed loop HCCI control by aid of variable valve timings. SAE transactions 2003, vol. 112, no. 3, pp [8] Shaver, G. M., Gerdes, J. C. and Roelle, M. J., Physics-Based Closed-Loop Control of Phasing, Peak Pressure and Work Output in HCCI Engines Utilizing Variable Valve Actuation. Proceedings of the 2004 American Control Conference, pp [9] Zhili, C., and Mitsuru, K., How to put the HCCI engine to practical use: Control the ignition timing by compression ratio and increase the power output by supercharge. SAE transactions 2003, vol. 112, no. 4, pp [10] Ravi, N., Roelle, M. J., Jungkunz, A. F., and Gerdes, J. C., A physically based two state model for controlling exhaust recompression HCCI in gasoline engines. Proceedings of the 2006 ASME International Mechanical Engineering Congress and Exposition, IMECE [11] Atkins, M. J., and Koch, C. R., The effect of fuel octane and diluent on homogeneous charge compression ignition combustion Proceedings of the Institution of Mechanical Engineers - Part D, 2005, pp [12] Franklin, F. F, Powell, J. D, Emami-Naeini, A., Feedback Control of Dynamic Systems, 3rd Edition. Addison Wesley Publishing Company, pp Copyright c 2007 by ASME

9 [13] Ravi, N., Roelle, M. J., Jungkunz, A. F., and Gerdes, J. C., Model based control of exhaust recompression HCCI. Proceedings of the 2007 IFAC Symposium on Advances in Automotive Control at Monterey, California 9 Copyright c 2007 by ASME