Pressure and Friction Observer-Based BacksteppingControl for a VGT Pneumatic Actuator

Salah Laghrouche, Fayez Shakil Ahmed, and Adeel Mehmood

Student : YI-AN,CHEN 4992C085

IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 22, NO. 2,

MARCH 2014

I. INTRODUCTIONPNEUMATIC actuators are commonly used in high powerpositioning applications in automobile systems, such asturbocharger control (waste-gate and VGT), exhaust gas recirculation(EGR), and variable intake manifolds [1]. Although not as precise as electric motors [2], [3], they have the advantages of high power-to-size ratio, low maintenance cost, light weight, and the availability of pneumatic sources in the engine[4], [5]. These advantages come at the price of more friction and nonlinearity due to air compressibility and aerodynamic forces etc. In presence of these traditional drawbacks, precise and robust control strategies are required to use pneumatic actuators effectively.

II. SYSTEM MODELINGThe pneumatic actuator regulates the quantity of exhaustgas entering into the turbine by adjusting its vanes. This system (Fig. 1) consists of two parts, an EPC and a pneumatic actuator. The EPC regulates the air mass-flow in the pneumatic actuator, which varies the pressure in the actuator and produces a linear motion in the diaphragm. This is converted into rotation via a unison ring that actuates the VGT vanes. Detailed working and modeling of this system have been published in [19] and [20]. In this section, we will briefly review the results of these articles and present complete model.

A. Actuator Mechanics

III. SLIDING MODE ESTIMATION AND OBSERVATION

While commercial actuators are equipped with positionsensors only, velocity can be estimated by using robust differentiatorsor finite time observers. In this paper, we haveestimated velocity from measured position using the robustfixed time convergent differentiator. In this way, the velocityis assumed to be known after a certain interval, and is usedfor the pressure and friction state observer design.

A. Robust Fixed Time DifferentiatorReal-time differentiation is an obstacle in control implementation.Angulo et al. [30] have developed a uniform fixed timedifferentiator that converges in two phases. The first phaseguarantees uniform convergence of the derivative estimatefrom any initial condition, to a neighborhood of the real valuein a fixed maximum time duration tu. In the second phase,the differentiator takes the form of the robust differentiator[31], which then guarantees finite time convergence from theneighborhood, exactly to zero, in finite time t f. After theperiod tτ = tu + t f , the derivative estimate can be consideredas the real derivative for all t > tτ . For a given signal x1whose derivative x2 is bounded by the Lipschitz constant L,the first-order differentiator is given as for 0 ≤ t ≤ tu

B. State ObserversTo design the pressure observer, we first define the error offunction f (u, x4) for observed and actual pressure, given asfollows:f. = a1 + a2 x4 + xˆ4 ε4 = f˜ε4 (8)where f. = f (u, x4)− f (u, xˆ4). From (3), f˜ < 0 for all valuesof input u. The observer is designed using sliding mode,

IV. BACKSTEPPING CONTROL DESIGNThe controller has been developed using backsteppingmethod, which is a recursive procedure based on Lyapunov’sstability theory [34]. In this method, system statesare chosen as virtual inputs to stabilize the correspondingsubsystems.Step 1: According to the control objective given inSection II, the following error function is chosen:s1 = λe1 + ˙e1 (19)where e1 = x1 − xref is the tracking error. The term λ is apositive constant and xref is the reference signal to be tracked.The error function dynamics are˙s1 = ˙x2 − [ ¨ xref − λ (x2 − ˙xref )] (20)

V. LYAPUNOV ANALYSISIn this section, we will demonstrate the exponential convergenceof the closed-loop controller–observer system. Let usrecall VO, the Lyaponov function associated with the observeras given in (17), and its derivative from (18)

Fig. 8. Positioning at Ptrb = 0, 1500, and 3000 mbar.Remark 2: When implemented on a discrete-time controlsystem, the velocity estimation error, due to sampling, willbe proportional to the sampling period T [31]. Therefore,according to Levant, the term x2 in (16) will be replaced byx2 + O(T ). In this case, the observation error (ε3, ε4) willnot converge to zero exactly, but to a neighborhood of zerothat is proportional to the sampling time. This is because thederivative of the Lyapunov function (18) will take the form

VI. EXPERIMENTAL RESULTSThe experiments were performed on an industrial turbocharger(GTB1244VZ) mounted on the test bench of acommercial diesel engine DV6TED4 (shown in Fig. 5). Themaximum displacement of the VGT actuator is 16.4 mm,which allows movement of the vanes in the range of 48°.Its integrated potentiometric position sensor provides measurementswith an accuracy of 0.1 mm. The test benchis equipped with a pressure sensor for measuring actuatorpressure and a force sensor on the actuator shaft for measuringthe total resistive force. These measurements were used forvalidation of the observer. The low-pass bandwidth of thelatter does not permit us to capture the pulsating effects ofexhaust gases, therefore the mean effect of the aerodynamicforce was obtained. The controller output was calculated

using the observer values, whereas the measured values ofpressure and force were used for validating the observers lateron. National Instruments CompactRIO was used to implementthe controller and to record data and measurements.

The controller parameters were tuned to obtain the best tradeoffbetween response time and saturation limits, such that for astep reference of maximum possible displacement (16.4 mm)at 3000 mbar turbine pressure, the controller output wouldnot exceed the voltage limit of 12 V (i.e., 100% PWM). Thesampling frequency was fixed at 1 kHz, which is the nominalfrequency used in commercial automobile computers (ECUs).The exhaust air pressures (turbine inlet pressures) at whichthe controller was evaluated were 0, 1500, and 3000 mbar,resulting in three different conditions of the aerodynamicsforce.

The estimated resistive force was validated, as shown inFig. 6. The force was generated by running the engine at140 Nm load torque and varying the turbine inlet pressure,

VII. CONCLUSIONIn this paper, an adaptive output feedback controller waspresented for controlling the electropneumatic actuator of adiesel engine VGT. The controller was developed using backsteppingmethod. Friction and aerodynamic force were consideredand modeled as a composite resistive force by parameterizingthe aerodynamic force as a function of turbine inlet pressure.Both forces were then combined through a modificationof the LuGre model. The states that are unavailable for measurementwere observed using sliding mode observers. Lyapunovanalysis showed that the complete closed-loop systemi.e., the system states, controller, and observers converge exponentially.Experimental results showed the effectiveness of thiscontroller.

quantizing errors introduced by the bus limitations of themicroprocessors may induce observation and estimation errors.In future works, we aim to integrate dynamic adaptive laws inthe controller to make it robust against modeling uncertaintyand parametric drifts. Implementation issues in relation withcommercial ECUs, such as memory and calculation powerrequirements will also be addressed in detail.

VII. CONCLUSION