Tao Zeng, Devesh Upadhyay, and Guoming Zhu*

217 IEEE 56th Annual Conference on Decision and Control (CDC) December 12-15, 217, Melbourne, Australia - Tao Zeng, Devesh Upadhyay, and Guoming Zhu* 1 AbstractDiesel engines are of great challenges due to stringent emission and fuel economy requirements. Compared with the conventional turbocharger system, regenerative assisted system provides additional degree of freedoms for the turbocharger speed control. Hence, it significantly improves control capability for exhaust-gas-recirculation (EGR) and boost pressure. This paper focuses on control design for the diesel engine air-path system equipped with an EGR subsystem and a variable geometry turbocharger (VGT) coupled with a regenerative hydraulic assisted turbocharger (RHAT). The challenges lie in the inherent coupling among EGR, turbocharger performance, and high nonlinearity of engine air-path system. A linear quadratic (LQ) controller design approach is proposed in this paper for regulating the EGR mass flow rate and boost pressure simultaneously and the resulting closed-loop system performance can be tuned by properly selecting the LQ weighting matrices. Multiple LQ controllers with integral action are designed based on the linearized system models over a gridded engine operational map and the final gain-scheduling controller for a given engine operational condition is obtained by interpreting the neighboring LQ controllers. The gain-scheduling LQ controllers for both traditional VGT-EGR and VGT-EGR-RHAT systems are validated against the in-house baseline controller, consisting of two single-input and single-output controllers, using the nonlinear plant. The simulation results show that the designed multi-input and multi-output LQ gain-scheduling controller is able to manage the performance trade-offs between EGR mass flow and boost pressure tracking. With the additional assisted and regenerative power on turbocharger shaft for the RHAT system, engine transient boost pressure performance can be significantly improved without compromising the EGR tracking performance, compared with the baseline control. I. INTRODUCTION A regenerative hydraulic assisted turbocharger (RHAT) system is proposed in [1], [2]. A hydraulic system is proposed to be placed between turbocharger center housing as shown in Figure 1. In this new system, a hydraulic turbine is used to spin the turbocharger shaft via high-pressure supply fluid from a tank; a turbo-pump is used to absorb excessive power from the turbocharger shaft while pressurizing the fluid and pumping back into the tank. A driveline pump is also used to recover vehicle kinetic energy during vehicle deceleration mode and pump the fluid into the high-pressure tank. Both the hydraulic turbine and the turbo-pump are packaged inside the turbocharger center housing. The RHAT concept Zeng and Upadhyay are with the Ford Motor Company, Dearborn, MI 48124, USA (e-mails: tzeng6@ford.com and dupadhya@ford.com). Zhu is with the Mechanical Engineering and Electrical/Computer Engineering Departments, Michigan State University, East Lansing, MI 48824, USA (e-mail: zhug@egr.msu.edu). fundamentally changes the operation of a turbocharged engine with reduced turbo lag, engine pumping loss as well as improved surge margin. Compared to traditional electric assisted and regenerative turbocharger, RHAT has a much higher assisting and regenerative capability, and it is also more durable and cost effective [1]. Figure 1. Diesel engine VGT-EGR with regenerative hydraulic assisted turbocharger system By considering only the air-path system, the VGT-EGR-RHAT system has four control inputs and two control outputs. However, the nonlinear multivariable, natural coupling between EGR and boost pressure loops of the diesel engine air-path system and dual objectives make the close-loop control design problem arduous. A good control solution for production application must provide a robust controller that uses minimal ECU computational resources and is simple to implement and calibrate. Most of the existing literature discusses the stability and robustness of controller design for diesel engine air flow regulation. A control Lyapunov function (CLF) based controller design is introduced in [3]. This method is developed based on a simplified model obtained using input-output linearization. Robustness is achieved by using the domination redesign. In [4], a multivariable controller is designed based on input and output linearization with sliding-model control. It provides a systematic method to regulate the EGR mass flow rate and intake manifold pressure with proper selection of the sliding surface. Different control designs for VGT-EGR are experimentally validated in [5], which shows good tracking performance. A three-input and three-output multivariable control structure is proposed for electrically assisted and regenerative turbocharger in [6]. This paper addresses a systematic approach for closed-loop control design approach that minimizes a cost function consisting of engine performance and emissions during transient operations. The linear quadratic regulator (LQR) is a well-known control design technique that is known for its robustness with gain margin (1/2, ) and phase margin. LQR techniques has been widely investigated in other nonlinear systems [7],[8],[9],[1]. In LQR design routine, weighting 978-1-59-2873-3/17/$31. 217 IEEE 232

matrices can be directly used to tune the closed-loop system performance. It can be used to design multi-input and multi-output (MIMO) controllers for VGT vane position, EGR valve action, and RHAT power for a given cost function. However, LQR control is only applicable for linear systems. Gain-scheduling control is a natural approach to extend the linear control design to a nonlinear system by designing a family of LQ linear controllers over gridded engine operational conditions, and gain-scheduled control for a given engine operational condition can be obtained by interpreting the LQ controllers surround the given operational condition. In this paper, linearized models are obtained from the nonlinear mode over the gridded engine operation conditions and LQ controllers with integral action are designed based on the high fidelity reduced-order nonlinear diesel engine model for both VGT-EGR and VGT-EGR-RHAT systems over a few engine operational conditions. The designed LQ controllers regulate the tracking errors of both EGR mass flow rate and boost pressure down to zero. Control design for different cost functions is proposed by selecting different weighting matrices and it provides to study the trade-off between engine performance and emissions. The proposed MIMO controller is gain-scheduled using engine speed and load (fuel mass) and validated using the nonlinear plant. By comparing with in-house baseline controllers, the proposed controller shows the improved engine performance comparing with baseline controller II. MODEL LINEARIZATION OF DIESEL ENGINE AIR-PATH SYSTEM WITH RHAT A. Model linearization Consider the three-state diesel engine air-path model (1) with the exhaust pressure ( ), boost pressure ( ), and TC shaft speed ( ) as states. Control inputs are VGT vane position ( ), EGR valve position, and RHAT power. In this case, positive hydraulic power is for the hydraulic pump and negative one for the hydraulic turbine. System outputs are EGR mass flow rate ( ) and boost pressure ( ). Control target is to regulate the tracking errors of both EGR mass flow rate and boost pressure down to zero. More detailed engine modeling can be found in [3],[4], [11]. The turbine power model using VGT control as directly input can be found in [12],[13]; and the compressor power model can be found in [14]. The exhaust and intake manifolds are modeled as volumes with ideal gas having constant specific heats. The EGR valve is modeled using the valve flow equations through an orifice, where the effective area is determined experimentally. Volumetric efficiency and temperatures rise are modeled as static nonlinearities. Each of the nonlinear functions in (1) is investigated and validated through experimental data. Developed engine sub-models are calibrated using the steady-state data from a medium duty diesel engine. The model is further validated using transient driving cycle test data as shown in Figure 2. The developed model shows good dynamic behaviors, which is sufficient for control design. Intake pressure [pa] Exhaust pressure [pa] 1.4 1.3 1.2 1.1 1.9 2 1.8 1.6 1.4 1.2 Figure 2. Model validation results A linearized model about an equilibrium point of nonlinear diesel engine air-path model, described by the equations (1), was obtained analytically. The linearized model is in the following form. where, is the states of the plant ( ), is the control inputs ( ). The output available ( ) for feedback. B. Augmented with actuator dynamics Simple actuator dynamics has been added to the plant model and the augmented system is where x 1 5 7 72 74 76 78 8 82 x 1 5 Model predicted Measured Model predicted Measured 1 7 72 74 76 78 8 82,,. Where and are the matrices for the actuator dynamics., and and are the plant matrices in (2), which are corresponding to all the non EGR inputs. Meanwhile, and are the matrices for original the (1) (2) (3) 233

EGR input in plant (2). Note that only EGR control input presents in matrix D in plant (2), which is the direct input for EGR mass flow rate. With the actuator dynamics, there is no matrix D for system (3). C. Integral action It is desirable to include integral control into the state feedback to eliminate the steady-state error. With model uncertainties presented in the system, the control design must be able to compensate those uncertainties with zero steady-state errors. By augmenting the system with the integral action it is possible for LQR design to choose the integral gain automatically [15]. Define a new system with integral action with time derivatives of outputs as follows. (4) where,,. III. LQR WITH INTEGRAL ACTION (LQI) A. Control design The goal for this control design is to find a linear optimal controller that minimizes the tracking errors of both EGR mass flow rate and boost pressure. The cost function is given below. (5) where. To keep the tracking error small, the integral of the expression and should be nonnegative and small. Matrix shall be positive semidefinite and matrix positive definite, where is 2x2 and 3x3. Note that is the weighting matrix for tracking errors of EGR mass flow rate and boost pressure; and R is the weighting matrix for the derivatives of control inputs. Now the problem is formulated as a standard LQR problem. In this case, we are dealing with the infinite horizon LQR design. In order to guarantee the solution to exist, shall be stabilizable and detectable. Note that as long as the operational condition,, is guaranteed for the engine air-path system, pairs < > and < > are controllable and observable, respectively, for both VGT-EGR and VGT-EGR-RHAT systems. For the standard LQR controller design, the feedback control law is given by: where,, and are obtained by solving matrix algebraic Riccati equation. As a result, the control law can be obtained by integrating from time to t. This control is kind of a PI (proportional-integral) controller with state error and integration of output error defined in (7). (6) (7) In order to implement the LQI design for the nonlinear plant, the equilibrium states value must be subtracted from the states of the nonlinear model and the control inputs are fed by the outputs of the linear controller with equilibrium controls as in (8). The overall control architecture is shown in Figure 3, where is nonlinear plant state vector, is equilibrium state vector that is the desired vector along the regulating trajectory ( ). Tracking errors of EGR mass flow rate and boost ( are used as feedback for the integral controller. The feedforward controls ( are generated from feedforward calibration map based on engine operational condition (, ), which are used to move the nonlinear plant close to the steady-state operational condition. Note that for both assisted and regenerative power, there is no power set-point, leading to =. Figure 3. Proposed linear quadratic regulator for Engine EGR-VGT air-path system B. Weighting selection The diagonal entries of weighting matrix Q are and and are related to the tracking errors of the EGR mass flow rate and boost pressure. In order to tune matrices Q and R for different control design targets, three different evaluation indexes are defined for engine performance, emissions, and RHAT energy. The performance index is defined as the difference between 1 and the normalized accumulated boost pressure tracking error, where the tracking error is normalized to its maximum and minimum range of the a given operational condition for different combinations. The same normalization process is also applied to the emission index used to evaluate the accumulated tracking error of the EGR mass flow rate. Note that after normalization both indexes are ranged between and 1. For the RHAT system, since the assisted and regenerative powers are related to external energy usage, an additional RHAT energy index is defined as the accumulated assisted and regenerative power. This energy index is used to evaluate the RHAT control. For both performance and emission indexes, the highest value represents the best tracking results (minimum tracking errors). The higher the energy index, the less the hydraulic actuation energy used. Frequent hydraulic actuation leads to lower energy cost index. Matrix is used for control inputs weighting. They are related to the VGT vane position, EGR valve position, and (8) 234

RHAT power, respectively, and is chosen as. The reason for the selection is that slow VGT action leads to slow exhaust pressure dynamics; and as a result, it makes the EGR mass flow rate easy to regulate. Weighting Matrix used for tracking boost pressure and EGR mass flow rate are tuned using a coefficient sweep of and. This study is used to obtain different control performance indexes. The selection range for the normalized entries ( and ) of matrix are between 1 and 1. The simulations are conducted under different based on a small step perturbation around the baseline engine speed and torque (in term of fuel injection). For example, a small step change at 1 rpm with 2 mg/cc fuel mass is simulated around a light load engine operational condition at 8 RPM engine speed with 2 mg/cc fuel mass. Note that linearized model at this local operational condition is used for both VGT-EGR and VGT-EGR-RHAT system study. weighting. This is because the external power can be used to control boost pressure, rather than use VGT. In other words, the boost pressure control can be partially independent of exhaust manifold property. Hence, the EGR weighting has less influence on boost pressure tracking, compared with the VGT-EGR case. For the large value, EGR control improves the tracking performance of the EGR mass flow rate as expected; and large results in large energy input from RHAT. Both Figure 4 and Figure 5 show the physical meaning and trade-offs of VGT-EGR-RHAT system. The results also show that, optimal EGR and best boost pressure tracking cannot be achieved at the same time for the conventional VGT-EGR system. Figure 4. Normalized indexes with normalized matrix Q matrix for VGT-EGR control design First, the conventional VGT-EGR control design is investigated. With the defined performance and emission indexes, simulation results for different weighting matrix in terms of and are shown in Figure 4. The simulation results clearly show the trade-off relationship between the two design targets. Note that and are penalty coefficients for tracking errors of EGR flow rate and boost pressure, respectively. Large leads to low EGR tracking error, and in other words, results in a tight EGR tracking error bound. The same works for. The Higher value will lead to the designed controller to put more control effort on correcting boost pressure error than EGR mass tracking error. The combination of and will lead to different VGT position and EGR controls. Second, control design for VGT-EGR-RHAT is performed using the proposed method at engine operational condition of 8 rpm and 2mg/cc fuel mass. With the assisted power on TC shaft, extra energy is used to drive the compressor for improved boost pressure response. The VGT vane position does not need to be closed to build up high exhaust pressure for turbine power extraction, and it can be used for both EGR mass flow and boost pressure regulation. As shown in Figure 5, the performance index is mainly dependent on boost pressure Figure 5. Normalized indexes with normalized matrix Q for VGT-EGR-RHAT control design IV. RESULTS FROM CONTROLLER IMPLEMENTATION Baseline control is chosen as a two-siso controller developed inside of Ford. The baseline control is a gain-scheduling PID (proportional-integral-derivative) controller that is commonly used in automotive industry to control nonlinear systems due to its simplicity and easy access to on-line calibrations. The current in-house baseline controller has two independent control loops: one for EGR mass flow rate tracking and other for boost pressure tracking. EGR valve position is used to track target EGR mass flow rate; and the VGT vane position is feedback-controlled for tracking the boost pressure by regulating the vane position. MIMO controllers are designed for both VGT-EGR system and VGT-EGR-RHAT systems at four operational conditions. They are 8 rpm with 2 mg/cc, 8 rpm with 35 mg/cc, 12 rpm with 2 mg/cc, and 12 rpm with 35 mg/cc. For the VGT-EGR system, the goal is to track the EGR mass flow rate and boost pressure. The controller for best engine performance with and and the controller for the best emissions with and are simulated using the nonlinear plant (1). For simplicity, these two controllers are called performance and emission controllers, respectively. For VGT-EGR-RHAT system, additional attention is paid to the hydraulic actuation 235

energy. Therefore, two sets of controllers for VGT-EGR-RHAT system are designed within the same operating range as the VGT-EGR case. The two sets of controllers are designed with high and low energy indexes. The high energy index controller uses relative low RHAT energy for both hydraulic turbine and hydraulic pump with weighting matrix entries ; and the low energy index controller uses relative high RHAT energy with A transient operational profile located inside the envelop of light load operational region is simulated for different control design. A bilinear interpolation is used to schedule the local linear controller gain based on engine speed and fuel quantity. The simulation results for five different control designs are shown in Figure 6. The VGT-EGR control design for emission has better EGR mass flow rate tracking performance (less tracking error) than the VGT-EGR control design for performance and baseline control; see Figure 6.b. However, the emission controller for VGT-EGR system shows poor tracking performance for the boost pressure compared to the performance and baseline controllers as shown in Figure 6.a. For the emission controller, the VGT closes less aggressively for boost pressure tracking, which leads to large boost pressure tracking error. Since large weightings are used for both EGR and boost pressure tracking for the performance controller, the VGT-EGR performance controller provides improved boost pressure tracking performance over the emission and baseline controllers. For the VGT-EGR-RHAT low energy index controller (with high assisted and regenerative power), RHAT aggressively assists the turbocharger at the initial tip-in stage as shown in Figure 6.f. The gas turbine mass flow rate increases as the TC speed goes up due to RHAT assistance, leading to quick reduction of exhaust pressure. This leads to aggressive VGT closing action to build up exhaust pressure to maintain the EGR mass flow rate; at the same time, EGR closing action keeps the tracking error of the EGR mass flow rate. Then, the exhaust manifold pressure increases due to increased air mass flew into the exhaust manifold. Since less energy is needed for the low energy index case, the VGT vane opens to reduce the exhaust pressure. With increased boost pressure and exhaust pressure, both VGT vane and EGR valve open, leading to a constant pressure drops between exhaust pressure and intake pressure as shown in Figure 6.c. The small pressure different across EGR valve maintains the EGR mass flowing with minimum pumping loss. Hence, the low energy index controller has the best fuel efficiency due to reduced pumping loss, which is based on the assumption of the free kinetic energy recovery. For the high energy index controller (with low assisted power), VGT action is to build up exhaust pressure to drive the compressor for boost pressure tracking. With the increased exhaust pressure, EGR valve closes to reduce the effect of higher exhaust pressure and to track the desired EGR mass flow rate during tip-in. With coordinated control for the VGT-EGR-RHAT, it improves engine boost pressure tracking performance as well as EGR mass flow rate tracking. By comparing the five control validation results shown in Figure 7, the proposed MIMO control design provides a good approach to manage the trade-offs between EGR mass flow rate and boost pressure, compared to the baseline controller. With the additional assisted and regenerative power on the TC shaft for the VGT-EGR-RHAT system, transient performance can be further improved without compromising EGR tracking performance, compared with the VGT-EGR system. Pressure tracking error [hpa] VGT position 5-5 -1-15 -2-25 -3 75 7 65 6 55 5 45 4 a. Boost pressure tracking error [hpa] Baseline VGT-EGR emission VGT-EGR performance VGT-EGR-RHAT with low energy index VGT-EGR-RHAT with high energy index d. VGT position e. EGR valve position Figure 6. Closed-loop simulation results for baseline, VGT-EGR, and VGT-EGR-RHAT controllers EGR MFR tracking error [kg/h] EGR valve positon 8 6 4 2-2 -4-6 -8 14 12 1 8 6 4 b. EGR MFR tracking error [kg/h] Pressure hpa [pa] Hydraulic actuation normalized power 16 x 14 14 12 1 8 6 4 2 1.5 1.5 -.5-1 -1.5 c. Pressure difference across EGR valve f. Hydraulic actuation power [kw] VGT-EGR-RHAT with low energy index VGT-EGR-RHAT with high energy index 236

Figure 7. Comparison of different control designs V. CONCLUSION In this paper, a systematic control design approach for a diesel engine air-path subsystem with assisted and regenerative turbocharger is proposed. Linear quadratic integral (LQI) controllers are designed for the linearized models over the gridded engine operational conditions for tracking EGR (exhaust-gas-recirculation) flow rate and boost pressure, and gain-scheduling control for a given operational condition is obtained by interpreting the LQI controllers around the operational condition. The gain-scheduled control strategy is implemented for the nonlinear air-path system. Comparing to the baseline VGT-EGR controller, this approach provides a method of designing the VGT and EGR controller with tracking performance trade-off between EGR flow rate and boost pressure by tuning LQI weighting matrices. Using the dual-loop baseline single-input and single-output controller, the designed multi-input and multi-output controllers show improved tracking performance for both EGR mass flow rate and boost pressure and trade-off characteristics between engine performance and emissions through weighting selection. With the added regenerative hydraulic assisted turbine system, the VGT-EGR-RHAT controller further improves the transient engine performance without compromising EGR tracking performance due to additional power on the turbocharger shaft, compared with both baseline and VGT-EGT controllers. Future work is to extend the controller design for the entire engine operational conditions with detailed hydraulic system dynamics and validate the designed gain-scheduling controller in experiments. [3] M. Jankovic, and I. Kolmanovsky, Robust nonlinear controller for turbocharged diesel engines. The proceedings of 1998 American Control Conference, 1998 [4] D. Upadhyay. Modeling and Model based Control Design of the VGT-EGR System for Intake Flow Regulation in Diesel Engines. PhD diss., The Ohio State University, 21. [5] M. Van Nieuwstadt, I. Kolmanovsky, and P. Moraal. Coordinated EGR-VGT control for diesel engines: an experimental comparison. No. 2-1-266. SAE Technical paper, 2. [6] Z. Yang, E. Winward, D. Zhao, and R. Stobart, Three-input-three-output air path control system of a heavy-duty diesel engine. IFAC-PapersOnLine, 49(11), pp.64-61. [7] P. Kapasouris, M. Athans and H.A. Spang, Gain-Scheduled Multivariable Control for the GE-21 Turbofan Engine Using the LQG/LTR Methodology. American Control Conference, 1985 (pp. 19-118). IEEE [8] I. Masar and E. Stöhr, Gain-scheduled LQR-control for an autonomous airship. 18th International Conference on Process Control. [9] M. Brasel, Gain-scheduled multivariable LQR controller for permanent magnet synchronous motor. Methods and Models in Automation and Robotics (MMAR), 214 19th International Conference On (pp. 722-725). IEEE. [1] K.Z. Ostergaard, P. Brath, and J. Stoustrup, Gain-scheduled linear quadratic control of wind turbines operating at high wind speed. In 27 IEEE International Conference on Control Applications (pp. 276-281). IEEE. [11] J. Wahlström, and L. Eriksson, Modelling diesel engines with a variable-geometry turbocharger and exhaust gas recirculation by optimization of model parameters for capturing non-linear system dynamics. Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, 225(7), pp.96-986 [12] T. Zeng, D. Upadhyay, H. Sun, and G. Zhu. Physics-based turbine power models for a Variable Geometry Turbocharger. American Control Conference (ACC), 216 (pp. 599-514). [13] T. Zeng, G. Zhu, Control-Oriented Turbine Power Model for a Variable Geometry Turbocharger. Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, p.954471772996. [14] T. Zeng, D. Upadhyay, H. Sun, and G. Zhu, A generalized compressor power model for turbocharged internal combustion engine with reducing simplicity. ASME Dynamic System Control Conference, Oct, 216. [15] M. Tomizuka and E. Dan, On the optimal digital state vector feedback controller with integral and preview actions. Journal of Dynamic Systems, Measurement, and Control 11.2 (1979): 172-178. REFERENCES [1] T. Zeng, D. Upadhyay, H. Sun, E. Curtis, and G. Zhu, Regenerative hydraulic assisted turbocharger. 217 ASME Turbo Expo., submitted for publication. [2] H. Sun, D. Hanna, M. Levin, E. Curtis, and F. Z. Shaikh, Ford Global Technologies, LLC, 214. Regenerative assisted turbocharger system. U.S. Patent 8,915,82. 237