FUTURE DIRECTIONS REFERENCES Tire modeling and tire parameter estimation are need- [1] L. Wingert, Not to Air Is human. Crane Communications, 2000. [2] N. Normann, Tyre Pressure Monitoring System for all Vehicle Categories. ed to reduce the cost of direct TPMSs and to overcome Crane Communications Inc.: ATZ Worldwide, 2000. the shortcomings of indirect TPMSs. A classical solu- [3] NHTSA, Federal Motor Vehicle Safety Standards [Online]. Available: tion is to model the dependence of tire/road friction on http://www.nhtsa.dot.gov/cars/rules [4] H. Shraim, A. Rabhi, M. Ouladsine, N.K. M’Sirid, and L. Fridman, “Esti- tire pressure, which can then be extracted from the fric- mation and analysis of the tire pressure effects on the comportment of the tion coefficient. Alternatively, one can consider addi- vehicle center of gravity},” in Proc. 9th Int. Workshop on Variable Structure Sys- tional factors that affect tire inflation pressure, such as tems, Italy), June 2006, pp. 268–273. [5] L. Li, F.-Y. Wang, Q. Zhou, and G. Shan, “Automatic tire pressure fault vertical force and vertical deflection [4]. A combination monitor using wavelet-based probability density estimation,” in Proc. IEEE of tire speed and tire height can estimate inflation more Intelligent Vehicle Symp., June 2003, pp. 80–84. precisely than current indirect TPMSs. This approach [6] N. Persson, F. Gustafsson, and M. Drevö, “Indirect tire pressure monitoring using sensor fusion,” in Proc. SAE 2002, Detroit, June 2002, no. 2002-01-1250. needs an additional height sensor or accelerometer, [7] C.R. Carlson and J.C. Gerdes, “Identifying tire pressure variation by non- which is available in vehicles with semi-active or active linear estimation of longitudinal stiffness and effective radius,” in Proc. suspensions. AVEC2002, Japan, 2002. Yet another approach relies on the fact that the reso- nance frequency of the tire changes with respect to pres- AUTHOR INFORMATION sure [5], [6], as modeled by V. Sankaranarayanan ([email protected]) received the Ph.D. degree in systems and control engineering from IIT- Bombay in 2006. He is currently a postdoctoral researcher in ∼ the Mechanical Engineering Department at Istanbul Techni- ωresonance = , m cal University. His research interests include nonlinear con- trol, underactuated systems, sliding mode control, and  where k denotes tire stiffness, k denotes change in tire automotive control systems. stiffness, and m denotes mass acting on the tire. If the Levent Güvenç received the B.S. degree in mechanical tire pressure changes, then the spring constant changes, engineering from Bogaziçi University, Istanbul, in 1985, resulting in a change in the natural frequency. The the M.S. degree in mechanical engineering from Clemson wheel vibration can be measured either by the tire University in 1988, and the Ph.D. degree in mechanical speed or through an accelerometer. Alternatively, tire engineering from the Ohio State University in 1992. Since inflation can be identified through nonlinear identifica- 1996, he has been a faculty member in the Mechanical tion techniques, which rely on tire stiffness changes Engineering Department of Istanbul Technical University, with respect to pressure [7]. where he is currently a professor of mechanical engineer- Due to the U.S. law mandating direct TPMSs, sensor ing and director of the Mechatronics Research Lab and the industries are interested in producing cost-effective solu- EU-funded Automotive Controls and Mechatronics tions. While promising theoretical and practical results Research Center. His research interests include automotive [4]–[7] are available for indirect TPMSs, they have not yet control mechatronics, helicopter stability and control, and appeared in commercial products. applied robust control.

Power Kites for Wind Generation Fast Predictive Control of Tethered Airfoils

BY MASSIMO CANALE, LORENZO FAGIANO, and MARIO MILANESE

he problems posed by electric energy generation from contribution to total energy production within the next fossil sources include high costs due to large demand 15–20 years. Tand limited resources, pollution and CO2 production, Excluding hydropower plants, wind turbines are cur- and the geopolitics of producer countries. These problems rently the largest source of [1]. Unfortu- can be overcome by alternative sources that are renewable, nately, wind turbines require heavy towers, foundations, cheap, easily available, and sustainable. However, current and huge blades, which impact the environment in terms renewable technologies have limitations. Indeed, even the of land usage and noise generated by blade rotation, and most optimistic forecast on the diffusion of wind, photo- require massive investments with long-term amortization. voltaic, and biomass sources estimates no more than a 20% Consequently, electric energy production costs are not yet competitive with thermal generators, despite recent Digital Object Identifier 10.1109/MCS.2007.909465 increases in oil and gas prices.

1066-033X/07/$25.00©2007IEEE DECEMBER 2007 « IEEE CONTROL SYSTEMS MAGAZINE 25 FIGURE 1 Kite surfing. Expert kite-surfers drive kites to obtain ener- FIGURE 2 KiteGen small-scale prototype of a yo-yo configuration. gy for propulsion. Control technology can be applied to exploit this The kite lines are linked to two electric drives. The flight of the kite is technique for electric energy generation. controlled by regulating the pulling force on each line, and energy is generated as the kite unrolls the lines.

THE KITEGEN PROJECT generated energy [4]. This yo-yo configuration is under the To overcome the limitations of current tech- control of the kite steering unit (KSU, see Figure 3), which nology, the KiteGen project was initiated at Politecnico di includes the electric drives (for a total power of 40 kW), the Torino to design and build a new class of wind energy drums, and all of the hardware needed to control a single generators in collaboration with Sequoia Automation, kite. The aims of the prototype are to demonstrate the abil- Modelway, and Centro Studi Industriali. The project focus ity to control the flight of a single kite, to produce a signifi- [2], [3] is to capture wind energy by means of controlled cant amount of energy, and to verify the energy tethered airfoils, that is, kites; see Figure 1. production levels predicted in simulation studies. The KiteGen project has designed and simulated a The potential of a similar yo-yo configuration is investi- small-scale prototype (see Figure 2). The two kite lines are gated, by means of simulation results, in [5] and [6] for one rolled around two drums and linked to two electric drives, or more kites linked to a single cable. In [5] and [6], it is which are fixed to the ground. The flight of the kite is con- assumed that the angle of incidence of the kites can be trolled by regulating the pulling force on each line. Energy controlled. Thus, the control inputs are not only the roll is collected when the wind force on the kite unrolls the angle ψ and the cable winding speed, as considered in [4] lines, and the electric drives act as generators due to the and in this article, but also the lift coefficient CL. rotation of the drums. When the maximal line length of For medium-to-large-scale energy generators, an alter- about 300 m is reached, the drives act as motors to recover native KiteGen configuration is being studied, namely, the the kite, spending a small percentage (about 12%, see the carousel configuration. In this configuration, introduced in “Simulation Results” section for details) of the previously [7] and shown in Figure 4, several airfoils are controlled by their KSUs placed on the arms of a verti- cal-axis rotor. The controller of each kite is 2 designed to maximize the torque exerted Onboard Sensors Kite Ground Sensors on the rotor, which transmits its motion to (Kite Position and Speed) W (Wind Speed and Direction, an . For a given wind 1 Line Strength) direction, each airfoil can produce energy ◦ 5 for about 300 of carousel rotation; only a 3 6 Lines 7 small fraction (about 1%, see the “Simula- 6 Control tion Results” section for details) of the Software generated energy is used to drag the kite ◦ against the wind for the remaining 60 . Actuation Unit 4 (Electric Drives and Winches) According to our simulation results, it is estimated that the required land usage FIGURE 3 Scheme of the kite steering unit. The kite steering unit, which provides auto- for a kite generator may be lower than a matic control for KiteGen, includes the electric drives, drums, and all of the hardware current of the same power by a needed to control a single kite. factor of up to 30–50, with electric energy

26 IEEE CONTROL SYSTEMS MAGAZINE » DECEMBER 2007 production costs lower by a factor up to 10–20. Such poten- tial improvement over current wind technology is due to several aerodynamic and mechanical reasons [8], [9]. For example, 90% of the power generated by a 2-MW three- blade turbine with a 90-m rotor diameter is contributed by only the outer 40% of the blade area, corresponding to about 120 m2. This dependence is due to the fact that the aerodynamic forces on each infinitesimal section of the blades are proportional to the square of its speed with respect to the air, and this speed increases toward the tip of the blades. In KiteGen, the tethered airfoils act as the outer portions of the blades, without the need for mechanical support of the tower and of the less-productive inner blade portions; see Figure 5. Indeed, a mean generated power of 620 kW is obtained in the simulation reported in Figure 16 FIGURE 4 KiteGen carousel configuration concept. Several airfoils for a single kite of 100-m2 area and 300-m line length. are controlled by the kite steering units placed on the arms of a ver- Figure 5 shows that the torque exerted by wind forces at tical axis rotor. The airfoils’ flight is controlled so as to turn the rotor, the base of a ’s support structure increases with which transmits its motion to an electric generator.

KiteGen Project Perspectives t present, a small scale yo-yo prototype has been real- on a cart riding on a circular rail will be considered. To col- Aized (see Figure S1). This system can generate up to lect the energy produced by the wagon motion, the wheels 40 kW using commercial kites with characteristic area up to of the cart are connected to an alternator. Such a proto- 10 m2 and line length up to 800 m. The prototype is under type is expected to produce about 0.5 MW with a rail test (see Figure S2). Preliminary tests show that the radius of about 300 m. According to scalability, a platoon amount of energy predicted by simulation is confirmed by of carts, each one equipped with a kite steering unit, can experimental data. be mounted on the rail to obtain a more effective wind A new KiteGen prototype is expected to be built in the power plant. This configuration can generate, on the basis next 24Ð36 months to demonstrate the energy-generation of preliminary computations, about 100 MW at a produc- capabilities of the carousel configuration. In particular, a tion cost of about 20 €/MWh, which is two to three times carousel structure with a single kite steering unit mounted lower than from fossil sources.

FIGURE S1 The first KiteGen prototype. Based on the yo-yo con- figuration, KiteGen can generate up to 40 kW using commercial kites with characteristic area up to 10 m2 and line length up to 800 m. Preliminary tests show that the amount of energy predict- FIGURE S2 KiteGen small scale prototype flying tests. This pic- ed by simulation is confirmed by experimental data. A new Kite- ture shows the kite motion and line developing during the trac- Gen prototype is expected to be built in the next 24 to 36 months tion phase. The kite steering unit is mounted on a light truck for to demonstrate energy-generation capabilities of the carousel easy transportation to locations with favorable wind conditions. configuration. This picture was taken on a hill near Torino.

DECEMBER 2007 « IEEE CONTROL SYSTEMS MAGAZINE 27 the height of the tower, the force is independent of the line Wind Industry Association Web site [10], it follows that, length in KiteGen. Due to structural and economical limits, it for a site such as Brindisi, in the south of Italy, a 2-MW is not convenient to go beyond the 100–120 m height of the wind turbine has a mean production of 4000 MWh/year. largest turbines commercially available. In contrast, airfoils To attain a mean generation of 9 TWh/year, which corre- can fly at altitudes up to several hundred meters, taking sponds to almost 1000-MW mean power, 2250 such towers advantage of the fact that, as altitude over the ground increas- are required, with a land usage of 300 km2 and an energy es, the wind is faster and less variable; see Figure 6. For exam- production cost of about 100–120 €/MWh. In comparison, ple, at 800 m the mean wind speed doubles with respect to 100 the production cost from fossil sources (gas, oil) is about m (the altitude at which the largest wind turbines operate). 60–70 €/MWh. Simulation results show that a KiteGen Since the power that can be extracted from wind grows with capable of generating the same mean energy can be the cube of the wind speed, the possibility of reaching such realized using 60–70 airfoils of about 500 m2, rotating in a heights represents a further significant advantage of KiteGen. carousel configuration of 1500-m radius and flying up to The carousel configuration is scalable up to several 800 m. The resulting land usage is 8 km2, and the energy hundred megawatts, leading to increasing advantages production cost is estimated to be about 10–15 €/MWh. over current wind farms. Using data from the Danish SYSTEM AND CONTROL TECHNOLOGIES NEEDED FOR KITEGEN Wind Tower KiteGen Control Design The main objective of KiteGen control is to maximize energy generation while preventing the airfoils from falling to the ground or the lines from tangling. The control problem can be expressed in terms of maximizing a cost function that pre- dicts the net energy generation while satisfying constraints on the input and state variables. Nonlinear model predictive control (MPC) [11] is employed to accomplish these objec- tives, since it aims to optimize a given cost function and fulfill Forces Exerted by Wind constraints at the same time. However, fast implementation is needed to allow real-time control at the required sampling FIGURE 5 Comparison between wind turbines and airfoils in energy production. In wind towers, limited blade portions (red) contribute time, which is on the order of 0.1 s. In particular, the imple- predominantly to power production. In KiteGen, the kite acts as the mentation of fast model predictive control (FMPC) based on most active portions of the blades, without the need for mechanical set membership approximation methodologies as in [12] and support of the less active portions and the tower. [13] is adopted, see “How Does FMPC Work ?” for details.

Model Identification Optimizing performance for Kite- 3,000 Gen relies on predicting the behav- 2,800 ior of the system dynamics as 2,600 accurately as possible. However, 2,400 since accurately modeling the 2,200 2,000 dynamics of a nonrigid airfoil is 1,800 challenging, model-based control 1,600 design may not perform satisfacto- 1,400 rily on the real system. In this case,

Altitude (m) 1,200 methods for identifying nonlinear 1,000 systems [14], [15] can be applied to 800 derive more accurate models. 600 400 Sensors and Sensor Fusion 200 0 The KiteGen controller is based on 3579111315feedback of the kite position and Wind Speed (m/s) speed vector, which must be mea- sured or accurately estimated. Each FIGURE 6 Wind-speed variation as a function of altitude. These data are based on the average airfoil is thus equipped with a pair European wind speed of 3 m/s at ground level. Source: Delft University, Dr. Wubbo Ockels. of triaxial accelerometers and a pair

28 IEEE CONTROL SYSTEMS MAGAZINE » DECEMBER 2007 How Does FMPC Work? . f − fˆ ≤ sup f˜ − fˆ = E( f ), (S3) he fast model predictive control (FMPC) approach intro- p p f˜∈FFS Tduced and described in [12] and [13] is based on set mem- bership techniques. The main idea is to find a function fˆ that approximates the exact predictive control law ψ(tk) = f (w(tk)) where E( f ) is the (guaranteed) approximation error. to a specified accuracy. Evaluating the approximating function A function f ∗ is optimal approximation if is faster than solving the constrained optimization problem con- . ∗ sidered in MPC design. r p = E( f ) = inf E( f ), fˆ To be more specific, consider a bounded region W ⊂ R8

where w can evolve. The region W can be sampled by choosing where the radius of information r p gives the minimal L p approxima-

w˜ k ∈ W, k = 1,...,ν, and computing offline the corresponding tion error that can be guaranteed. Defining exact MPC control given by . ¯ ˜ f (w) = min ψ, min ψk + γ w −˜wk ,(S4) ˜ k=1,...,ν ψk = f (w˜ k), k = 1,...,ν. (S1) . ¯ ˜ f (w) = max −ψ, max ψk − γ w −˜wk ,(S5) ˜ k=1,...,ν The aim is to derive, from these known values of ψk and w˜ k and from known properties of f , an approximation fˆ of f over W, along with a measure of the approximation error. Neural yields the function networks are used in [S1] for such an approximation. However, 1 neural networks have limitations, such as the possibility of f ∗(w) = [ f (w) + f (w)],(S6) 2 local minima during the learning phase and the difficulty of sat-

isfying the constraints in the image set of the function to be which is an optimal approximation in the L p(W) norm for all approximated. Moreover, no measure of the approximation p ∈ [1, ∞] [13]. Moreover, the approximation error of f ∗ is point- error is provided. To overcome these drawbacks, a set mem- wise bounded as bership approach is used in [12] for MPC with linear models. 1 Based on sampled data and a priori information about f , the |f (w) − f ∗(w)|≤ |f (w) − f (w)|, for all w ∈ W 2 approach finds a feasible function set in which the true function is guaranteed to lie. An optimal approximation, along with and is pointwise convergent to zero [13] approximation error, is derived based on this set. In the case of

KiteGen control it is assumed that f ∈ Fγ , where Fγ is the set lim |f (w) − f ∗(w)|=0, for all w ∈ W,(S7) of Lipschitz functions on W with Lipschitz constant γ . Note that ν→∞ stronger assumptions cannot be made, since even in the sim- ple case of linear dynamics and a quadratic functional, f is a Thus, evaluating sup | f (w) − f (w)|, it is possible to decide w∈W piecewise linear continuous function [S2]. In addition, the input whether the values of w˜ 1,...,w˜ ν , chosen for the offline compu- ¯ ˜ saturation condition gives the a priori bound | f (w)|≤ψ. This tation of ψk are sufficient to achieve a desired accuracy in the information about the function f , combined with the values of estimation of f or if the value of ν must be increased. Then, the

the function at the points w˜ k ∈ W, k = 1,...,ν, implies that f MPC control can be approximately implemented online by evalu- ∗( ) is a member of the feasible function set ating the function f wtk at each sampling time so that

ψ = f ∗(w ). ¯ ˜ ˜ tk tk FFS ={f ∈ Fγ : |f (w)|≤ψ; f (wk ) = ψk , k = 1,... ,ν}, (S2) As ν increases, the approximation error decreases at the cost of increased computation time. which summarizes the available information on f . Set membership theory facilitates the derivation of an optimal estimate of f and its REFERENCES

approximation error in terms of the L p(W) norm for p ∈ [1, ∞], [S1] T. Parisini and R. Zoppoli, “A receding-horizon regulator for . 1 . || || = | ( )|p p ∈ , ∞) || || = where f p [ W f wt dw ] , p [1 , and f ∞ ess- nonlinear systems and a neural approximation,” Automatica, vol. sup | f (w)|. For given f ≈ f , the related L p approximation error is 31, no. 10, pp. 1443Ð1451, 1995. w∈W ˆ  f − f p. Since the true function f is known at only a finite number [S2] A. Bemporad, M. Morari, V. Dua, and E.N. Pistikopoulos “The of points, the error between fˆ and f is unknown. However, given explicit linear quadratic regulator for constrained systems,” Auto- the a priori information, the tightest guaranteed bound is given by matica, vol. 38, pp. 3Ð20, 2002

DECEMBER 2007 « IEEE CONTROL SYSTEMS MAGAZINE 29 fulfilled, the DVS gives the same accuracy as the theoreti- Z cal minimal variance filter. Moreover, in the presence of modeling errors and nonlinearities, the DVS guarantees stability and performs tradeoffs between optimality and X robustness, which are not achievable with EKF.

KITE GENERATOR MODELS er Θ Kite Dynamics eφ Y The model developed in [18] describes the kite dynamics. Z' W0 A fixed cartesian coordinate system (X, Y, Z) is considered eθ θ (see Figure 7), with the X axis aligned with the nominal r R wind speed vector. The wind speed vector is represented = + as Wl W0 Wt, where W0 is the nominal wind, assumed KSU to be known and expressed in (X, Y, Z) as

X' φ Y' ⎛ ⎞ Wx(Z) ⎝ ⎠ W0 = 0 ,(1) 0 FIGURE 7 Model of a single kite steering unit. A fixed cartesian coor- dinate system (X, Y, Z) is considered, with the X axis aligned with ( ) the direction of the nominal wind speed vector W0. A second carte- where Wx Z is a known function that gives the wind sian coordinate system (X , Y , Z ), centered at the KSU location, nominal speed at each altitude Z (see Figure 6). The term is considered when KSU is moving with respect to (X, Y, Z). In the Wt may have components in all directions and is assumed yo-yo configuration, since the KSU location is fixed at the ground, to be unknown, accounting for unmeasured turbulence. (X , Y , Z ) ≡ (X, Y, Z) is assumed. In the coordinate system ( , , ) (X , Y , Z ), the kite position can be expressed as a function of its A second cartesian coordinate system X Y Z , cen- distance r from the origin and of the two angles θ and φ. In the tered at the KSU location, is introduced to take into carousel configuration, the KSU rotates around the origin of account possible KSU motion with respect to (X, Y, Z); oth- ( , , ) ˙ X Y Z at distance R, with angular speed . The local coordinate erwise, (X , Y , Z ) ≡ (X, Y, Z) is assumed. In this system, system (eθ , eφ , e ) is also shown. r the kite position can be expressed as a function of its dis- tance r from the origin and the angles θ and φ, as depicted of triaxial magnetometers placed at the airfoil’s extreme in Figure 7, which also shows the basis vectors eθ , eφ , er of edges, which transmit data to the control unit by means of a local coordinate system centered at the kite location. radio signals. These data are sufficient for estimating the Applying Newton’s laws of motion to the kite in the kite position and speed. However, in order to improve esti- local coordinate system yields mation accuracy and to achieve some degree of recovery in ¨ Fθ the case of sensor failure, we plan to use a load cell to mea- θ = , (2) mr sure the length and traction force of each line as well as a ¨ Fφ vision system to determine the kite angular position. φ = , (3) mrsin θ A key issue in KiteGen operation is the detection and Fr r¨ = , (4) recovery of possible breakdowns or malfunctions of the m sensors. For example, the vision system may not operate in the presence of clouds, haze, or heavy rain. A common where m is the kite mass, and the forces Fθ , Fφ , and Fr way to treat this problem is to use estimation techniques include the contributions of the gravitational force mg, based on the system model and available measurements. apparent force Fapp, aerodynamic force Faer, and the force However, due to the kite’s nonlinear dynamics, the Fc exerted by the lines on the kite. Expressed in the local extended Kalman filter (EKF), based on approximations of coordinates, the forces are given by the nonlinearities, gives rise to numerical stability prob- lems and severe accuracy deterioration. Moreover, the EKF Fθ = (sin θ)mg + Fapp,θ + Faer,θ , (5) design is based on a model that, although quite complex Fφ = Fapp,φ + Faer,φ , (6) and nonlinear, is only an approximate description of the Fr =−(cos θ)mg + Fapp,r + Faer,r − Fc . (7) actual system. Alternatively, the direct virtual sensor (DVS) approach [16], [17] facilitates the design of an opti- mal filter based on experimental data collected in the Apparent Forces absence of sensor faults. In particular, when an accurate The components of the apparent force vector Fapp depend on model is available and the noise statistical hypotheses are the kite generator configuration. For example, for the yo-yo

30 IEEE CONTROL SYSTEMS MAGAZINE » DECEMBER 2007 configuration, centrifugal inertial forces have to be considered, Line Forces ˙ ˙ ˙ that is, Fapp = Fapp(θ, φ, r, θ,φ, r). For the carousel configura- Concerning the effect of the lines, the force Fc is always tion, since each KSU moves along a circular trajectory with directed along the local unit vector er and cannot be neg- constant radius R (see Figure 7), the carousel rotation angle  ative, since the kite can only pull the lines. Moreover, Fc and its derivatives must be included in the apparent force cal- is measured by a force transducer on the KSU, and, culation, so that Fapp = Fapp(θ, φ, r,,θ,˙ φ,˙ r˙, ,˙ )¨ . through control of the electric drives, it is regulated so ˙( ) ≈ ˙ ( ) ˙ ( ) that the line speed satisfies r t rref t , where rref t is Aerodynamic Forces chosen. In the case of the yo-yo configuration, ( ) = (θ, φ, , θ,˙ φ,˙ ˙, ˙ , ) The aerodynamic force Faer depends on the effective wind Fc t Fc r r rref We , while, for the carousel ( ) = (θ, φ, ,,θ,˙ φ,˙ ˙, ,˙ ˙ , ) speed We, which in the local system is computed as configuration, Fc t Fc r r rref We .

= − ,() We Wa Wl 8 Motor Dynamics In the case of the carousel configuration, the motion law for where Wa is the kite speed with respect to the ground. For the generator rotor is taken into account by the equation both the yo-yo and carousel configurations, Wa can be ¨ expressed as a function of the local coordinate system Jz = RFc(sin θ)sin φ − Tc,(14) (φ, θ, r) and the position of the KSU with respect to the fixed coordinate system (X, Y, Z). where Jz is the rotor moment of inertia and Tc is the torque Let us consider now the kite wind coordinate system, of the electric generator/motor linked to the rotor. Viscous with its origin located at the kite center of gravity, the basis terms are neglected in (14) since the rotor speed ˙ is kept vector xw aligned with the effective wind speed vector, the low as shown in the “Simulation Results” section. Tc is basis vector zw contained by the kite longitudinal plane of positive when the kite is pulling the rotor with increasing symmetry and pointing from the top surface of the kite to values of , thus generating energy, and it is negative the bottom, and the basis vector yw completing a right- when the electric generator is acting as a motor to drag the handed system. In the wind coordinate system the aerody- rotor when the kite is not able to generate a pulling force. namic force Faer,w is given by The torque Tc is set by a local controller to keep the rotor at ˙ = ˙ constant speed ref. Faer,w = FDxw + FLzw,(9) KiteGen Dynamics Description where FD is the drag force and FL is the lift force, comput- The generic system dynamics are of the form ed as x˙(t) = g(x(t), u(t), W (t), r˙ (t), ˙ (t), W (t)), (15) 1 2 x ref ref t F =− C Aρ|We| , (10) D 2 D where x(t) = [θ(t)φ(t) r(t)(t) θ(˙ t) φ(˙ t) r˙(t) (˙ t)]T are the 1 2 F =− C Aρ|We| , (11) ( ) = ψ( ) L 2 L model states and u t t is the control variable. In the  = ˙ = ˙ = case of the yo-yo configuration, ref 0. All of where ρ is the air density, A is the kite characteristic area, the model states are assumed to be measured or estimated and CL and CD are the kite lift and drag coefficients. All of for use in feedback control. Mechanical power P generated these variables are assumed to be constant. The aerody- namic force Faer can then be expressed in the local coordi- nate system as a nonlinear function of several arguments of the form F We L ⎛ ⎞ FL Faer,θ (θ, φ, r,ψ,We) = ⎝ (θ, φ, ,ψ, ) ⎠ .() Faer Faer,φ r We 12 F d D Δl Faer,r(θ, φ, r,ψ,We) ψ

Fc m The kite roll angle ψ in (12) is the control variable, defined by g   l ψ = arcsin ,(13) d FIGURE 8 Forces acting on the kite. The aerodynamic lift and drag where d is the kite width and l is the length difference forces are FL and FD , respectively, the gravitational force is mg , between the two lines (see Figure 8). The roll angle ψ influ- and the pulling force F is exerted by the lines. The length difference c ences the kite motion by changing the direction of Faer. between the lines gives the roll input angle ψ.

DECEMBER 2007 « IEEE CONTROL SYSTEMS MAGAZINE 31 passive phase, respectively. Thus, different MPC con- trollers are designed to control the kite in the trac- Passive Phase tion and passive phases. Kite For the overall cycle to be productive, the total 140 Traction amount of energy pro- 120 Phase duced in the first phase 100 must be greater than the 80 energy spent in the second phase. Consequently, the Z (m) 60 KSU controller employed in the 40 traction phase must maxi- 20 40 Nominal Wind mize the produced energy, 0 20 Direction Traction Phase while the objective of the 0 0 20 Starting Conditions −20 passive phase controller is 40 60 −40 to maneuver the kite to 80 −60 100 120 −80 the traction-phase initial 140 −100 Y (m) position with minimal X (m) energy. The main reason for using MPC is that FIGURE 9 Yo-yo configuration phases. The kite steering unit acts on the kite lines in such a way that ener- input and state constraints gy is generated in the traction phase (green) and spent in the passive phase (red). Each cycle begins when the proper starting conditions (circled in blue) are satisfied. In this simulation the effects of turbu- must be imposed, for lence are neglected. example, to keep the kite sufficiently far from the with KiteGen is the sum of the power generated by ground and to account for actuator physical limitations. unrolling the lines and the power generated by the rotor Moreover, other constraints on the state variables are movement, that is, added to force the kite to follow figure-eight trajectories to prevent the lines from tangling. ˙ ˙ P(t) = r(t)Fc(t) + (t)Tc(t). (16) MPC for KiteGen Both terms in (16) can be negative when the kite lines are MPC is a model-based control technique that handles both being recovered in the yo-yo configuration or the rotor is state and input constraints. With MPC, the computation of being dragged against the wind in the carousel configuration. the control variable is performed at discrete time instants ˙ For the yo-yo configuration the term Tc is zero, and thus defined on the basis of a suitably chosen sampling period the generated mechanical energy is due only to line unrolling. t. Without wind disturbances, (15) becomes Note that (16) is related to a carousel with a single KSU. ˙( ) = ( ( ), ( ), ( ), ˙ ( ), ˙ ( )), When more kites are linked to the same carousel, the effect of x t g x t u t Wx t rref t ref t line rolling/unrolling for each kite must be included. where u(t) = ψ(t) is the control variable. At each sampling = ( ) KITEGEN CONTROL time tk k t, the measured values of the state x tk and ( ) To investigate the potential of KiteGen and to assist in the the wind speed Wx tk , together with the reference speeds ˙ ( ), ˙ ( ) ( ) design of physical prototypes, a controller is designed for rref tk ref tk are used to compute the control u t use in numerical simulations. In particular, the mathemati- through the performance index cal models of the yo-yo and carousel configurations + described in the section “Kite Generator Models” are used tk Tp ( , , ) = (˜(τ), ˜(τ), (τ), ˙ , ˙ (τ)) τ, to design nonlinear model predictive controllers. J U tk Tp L x u Wx rref ref d tk In both KiteGen configurations, energy is generated by (17) continually performing a two-phase cycle. In the first phase, the kite exploits wind power to generate mechani- where Tp = Npt, is the prediction horizon of Np steps, cal energy until a condition is reached that impairs further x˜(τ) is the state predicted inside the prediction horizon ( ) = ˜( ) = ( ) energy generation. In the second phase, the kite is recov- according to (15) using Wt t 0 and x tk x tk , and the ered to a suitable position to start another productive piecewise constant control input u˜(t) belonging to the ={˜( )}, ∈ , phase. These phases are referred to as the traction phase and sequence U u t t [tk tk+Tp ] is defined as

32 IEEE CONTROL SYSTEMS MAGAZINE » DECEMBER 2007 ˜( ) = u t Yo-Yo Configuration Controller ¯ , ∈ , , = ,... , + − , ui for all t [ti ti+1] i k k Tc 1 The traction phase begins when the kite is flying in a ¯ , ∈ , , = + ,... , + − , uk+Tc−1 for all t [ti ti+1] i k Tc k Tp 1 prescribed zone downwind of the KSU, at a suitable (18) altitude ZI with a given line length r0 (see Figure 9). where Tc = Nct, and Nc ≤ Np is the control horizon. The function L(·) in (17) is defined to maxi- Θ X mize the energy generated in the = 0 traction phase and minimize the Θ Θ energy spent in the passive = 0 Traction Phase with phase. Moreover, to account for Left Wind physical limitations on both the kite behavior and the control Passive Phase Left Wind input ψ, constraints of the form and Right Wind Θ Change Change x˜(t) ∈ X, u˜(t) ∈ U can be includ- ed. In particular, to keep the kite Y sufficiently far from the ground, Θ Θ the state constraint = 1

θ( ) ≤ θ Traction Phase with t Θ Θ = 2 Right Wind

Nominal is considered with θ<π/2. Actua- Θ = Θ W0 Wind Direction tor physical limitations are taken 3 into account by the constraints (a)

|ψ(t)|≤ψ, |ψ(˙ t)|≤ψ.˙ Passive Phase Tables 2 and 4 provide details 400 Traction Phase on the values of ψ and ψ˙ for the 300 yo-yo and carousel configura- Kite tions, respectively. Additional 200 constraints are added to force Z (m) KSU Trajectory 100 the kite to follow figure-eight Nominal 600 trajectories rather than circular 0 Wind Rotor ones to prevent the tangling of Direction Center 400 300 200 the lines. Such constraints force 100 φ 0 the angle to oscillate at half −100 X (m) −200 the frequency of the angle θ , Y (m) −300 −400 thus generating the desired kite trajectory. (b) The predictive control law, FIGURE 10 (a) Carousel configuration phases. The same rotor arm is depicted with three subse- which is computed using a quent angular values. The passive phase starts when the rotor arm reaches the angular position receding horizon strategy, is a 0, and lasts until the rotation angle 3 is reached. To maneuver the kite to a suitable position to nonlinear static function of the begin the traction phase (highlighted in blue), the passive phase is divided into 3 subphases (gray, system state x, the nominal orange, and green) delimited by rotation angles 1 and 2. (b) Kite trajectory with carousel config- uration. The kite follows figure-eight orbits, which maximize its speed during the traction phase measured wind speed Wx, and (green), while during the passive phase (red) the airfoil speed is very low to reduce drag forces. the reference speeds r˙ , ˙ of ref ref The kite steering unit follows a circular trajectory at ground height, with radius R. the form

When the traction phase starts, the kite flies as line ψ( ) = ( ( ), ( ), ˙ ( ), ˙ ( )). ( ) ˙ tk f x tk Wx tk rref tk ref tk 19 length r increases due to a positive value rref of the line

DECEMBER 2007 « IEEE CONTROL SYSTEMS MAGAZINE 33 and high line winding speed. Basically, the stronger the ˙ wind, the higher the value of rref that can be set while 300 Passive Phase obtaining high force values. The control system objective in the traction phase is to maximize the energy generated 250 , + during the prediction interval [tk tk TP]. Since the 200 instantaneous generated mechanical power is Traction P(t) = r˙(t)F (t), MPC minimizes the cost function 150 Phase c

Z (m) + 100 tk Tp ( ) =− ˙(τ) (τ) τ. ( ) J tk r Fc d 20 50 KSU tk 100 0 50 − −50 0 50 0 50 100 150 − The traction phase ends when the length of the lines reach- 200 250 300 100 Y (m) X (m) es a given value r and the passive phase begins. The passive phase is divided into three subphases. In ˙( ) FIGURE 11 Simulation results for the yo-yo configuration. Kite trajec- the first subphase, the line speed r t is controlled to tories are reported during the traction (green) and passive (red) smoothly decrease toward zero. The control objective is to phases of a complete yo-yo configuration cycle in the presence of move the kite into a zone with low values of θ and high wind turbulence. Note that the behavior is similar to Figure 9 despite values of |φ| (see Figure 7), where the effective wind speed the turbulence. We and force Fc are low and the kite can be recovered with low energy expense. Then, in the second subphase, r˙(t) is controlled to smoothly decrease from zero to a negative 60 value, which provides a compromise between high rewinding speed and low force F . During this passive 50 c Traction Phase subphase, the control objective is to minimize the energy 40 spent to rewind the lines. This second subphase ends 30 when the line length r reaches the desired minimum value. In the third passive subphase, r˙(t) is controlled to smooth- 20 Mean Generated Power ly increase toward zero from the previous negative set-

Power (kW) 10 point. The control objective is to move the kite in the Passive Phase traction phase starting zone. The passive phase ends when 0 the starting conditions for the traction phase are reached. −10

−20 Carousel Configuration Controller 0 50 100 150 200 In the carousel configuration (see figures 4 and 10), the

Time (s) torque Tc given by the carousel motor/generator is such

FIGURE 12 Simulated power obtained with the yo-yo configuration. A complete cycle is considered in the presence of wind turbulence. 0.6 The instantaneous course of the generated power during the trac- tion phase (green) is reported together with the power spent for the 0.4 kite recovery in the passive phase (red). The mean value of the 0.2 power generated during the cycle, which is represented by a dashed line, is 11.8 kW. The corresponding generated energy is 0 2613 kJ per cycle. −0.2

−0.4 speed reference provided by the local motor controller. − Since a traction force Fc is created on the kite lines, the 0.6 system generates mechanical power. The predictive −0.8 control law computes the line angle ψ (see Figure 8) in Reference Line Winding Speed (m/s) −1 order to vary Fc and thus optimize the aerodynamic 0 50 100 150 200 250 300 350 behavior of the kite for energy generation. The line Carousel Angle Θ (°) angle ψ is obtained by varying l according to (13) by FIGURE 13 Line speed reference imposed during a complete imposing a setpoint on the desired line length achieved carousel cycle. The commanded line speed r˙(t) is chosen on the by the local motor controller. basis of simulation data to increase the mean generated power and ˙ The value of the reference line speed rref is chosen as a to ensure that the lengths of the lines at the beginning of each cycle compromise between obtaining high traction force action are the same.

34 IEEE CONTROL SYSTEMS MAGAZINE » DECEMBER 2007 450 400 350 Kite Trajectory 300 Passive Phase 250 Z (m) 200 150 100 50 0 450 KSU Trajectory 300 150 Traction Phase 0 −150 Y (m) −300 −450 −450 −300 −150 0 150 300 450 600 750 X (m)

FIGURE 14 Simulation results for the carousel configuration. Kite and kite steering unit trajectories are reported during traction (green) and passive (red) phases related to two complete cycles in the presence of turbulence. Note that, despite the turbulence, the trajectories show good repeatability.

2,500 Traction Phase Traction Phase 2,000

190 1,500 180 170 Mean 160 1,000 Generated 150 Power Z (m) 140 300 Power (kW) 500 130 120 250 0 −240− 200 260−280 Passive Phase −300− X (m) Passive Phase 320−340 150 −360 −500 Y (m) 0 100 200 300 400 500 600 700 FIGURE 15 Figure-eight kite orbits during the traction phase for the Carousel Angle Θ (°) carousel configuration. Such orbits are imposed by means of suit- FIGURE 16 Power generated with the carousel configuration. Two com- able constraints on the angles θ and φ to avoid line wrapping. plete cycles are considered in the presence of wind turbulence. The instantaneous course of the generated power during the traction phas- es (green) is reported together with the power required for the kite recovery in the passive phases (red). Note the nearly null values of that the rotor moves at the constant reference angular energy usage during the passive phases. The mean value of the power ˙ generated during the two cycles is 621 kW and is represented by a speed ref , which is chosen to optimize the net energy dashed line. The corresponding generated energy is 234 MJ per cycle. generated in the cycle. Since the angular speed is constant, each kite can be controlled independently, provided that tk+Tp the lines never collide. Thus, a single kite is considered in ( ) =− ˙(τ) (τ) + (τ)˙ (τ) τ. ( ) J tk r Fc Tgen d 21 the following. The traction phase begins at the rotor angu- tk = lar position 3, where the nominal wind direction is such that the kite can pull the rotor arm [see Figure 10(a)]. When the rotor arm reaches the angle 0, the kite can A suitable trajectory for the line speed r˙ during the traction no longer pull the carousel, and the traction phase ends. phase is set to further increase generated power. Recalling Then, the passive phase starts, and the electric generator that mechanical power obtained at each instant is the sum linked to the rotor acts as a motor to drag the carousel of the effects given by line unrolling and rotor movement, between angles 0 and 3. Meanwhile, the kite is moved MPC minimizes the cost function to a suitable position for initiating the next traction phase.

DECEMBER 2007 « IEEE CONTROL SYSTEMS MAGAZINE 35 TABLE 1 Model and control parameters of the simulated TABLE 4 Objectives and starting conditions for the cycle yo-yo configuration. Note, in particular, the small phases and state and input constraints for the carousel characteristic area and low aerodynamic efficiency. configuration. In the passive phase, the controller is designed to drive θ to θI during the first subphase, φ to φI θ θ Symbol Numeric Value Description and Units during the second subphase, and to II during the third subphase. These values are chosen to minimize the energy m 2.5 Kite mass (kg) used to return the kite to its position at the beginning of the A 5 Characteristic area (m2) traction phase. In particular, small values of θ and φ ρ 1.2 Air density (kg/m3) correspond to zones with low values of the effective wind C 1.2 Lift coefficient L speed and the tangential component of the pulling force F C 0.15 Drag coefficient c D [see (14)]. State and input constraints are imposed E = CL 8 Aerodynamic efficiency CD throughout the cycle. r˙ 1.5 Traction phase reference for r˙ (m/s) r˙ −2.5 Passive phase reference for Constraint Definition Constraint Description r˙ (m/s) ◦ 0 = 35 Passive phase starting condition Tc 0.1 Sample time (s) ◦ θI = 20 First passive subphase objective Nc 1 Control horizon ◦ 1 = 135 Second passive subphase starting condition Np 25 Prediction horizon ◦ φI = 140 Third passive subphase objective ◦ 2 = 150 Third passive subphase starting condition ◦ θII = 50 Third passive subphase objective ◦ 3 = 165 Traction phase starting condition TABLE 2 State and input constraints and cycle starting and |θ(t)|≤85◦ State constraint ending conditions for the simulated yo-yo configuration. |ψ(t)|≤3◦ Input constraints θ ≥ θ |φ − φ¯ |≤ ◦ |ψ(˙ )|≤ ◦/ The traction phase starts when I , I 5 , and t 20 s r < r I . The passive phase starts when r > r¯. State and input constraints are imposed throughout the cycle. ing the passive phase. In the first subphase, the control Constraint Definition Constraint Description objective is to move each kite to a zone with a low value θ θ = ◦ of [see figures 7 and 10(b)], where the effective wind I 40 Traction phase starting conditions φ = 0◦ speed We and pulling force component tangential to the I θ φ = r I = 105 m carousel Fc sin sin are much lower. At 1, the sec- r = 290 m Maximum line length ond passive subphase begins, where the objective is to |θ(t)|≤85◦ State constraint change the kite angular position φ toward φI to begin the |ψ(t)|≤4◦ Input constraints ◦ traction phase. At = , the third passive subphase |ψ(˙ t)|≤20 /s 2 begins, where the control objective is to increase the kite angle θ toward θII to prepare the generator for the sub- squent traction phase. For details, see [7]. TABLE 3 Model and control parameters for the carousel configuration. Despite the low aerodynamic efficiency, this SIMULATION RESULTS structure can generate a significant amount of energy as shown by the results reported in Figure 16. Simulations of the KiteGen system were performed using the wind speed model Symbol Numeric Value Description and Units m 50 Kite mass (kg) 0.04Z + 8 m/s, if Z ≤ 100 m, 2 ( ) = A 100 Characteristic area (m ) Wx Z . ( − ) + , > . 8 0 0171 Z 100 12 m/s if Z 100 m Jz 910 Rotor moment of inertia (kg-m2) (22) R 300 Rotor radius (m) ρ 1.2 Air density (kg/m3) The nominal wind speed is 8 m/s at 0 m altitude, while CL 1.2 Lift coefficient CD 0.15 Drag coefficient the wind speed grows linearly to 12 m/s at 100 m altitude = CL E C 8 Aerodynamic efficiency and up to 17.2 m/s at 300 m altitude. Moreover, wind ˙ D ˙ ref 0.16 Reference (rev/min) turbulence Wt is introduced, with uniformly distributed Tc 0.2 Sample time (s) random components along the inertial axes (X, Y, Z). The Nc 1 Control horizon (steps) absolute value of each component of Wt ranges from 0 Np 5 Prediction horizon (steps) m/s to 3 m/s, which corresponds to 36% of the nominal wind speed at 100 m altitude. The passive phase is divided into three subphases. Transitions between subphases are marked by suitable Yo-Yo Configuration values 1 and 2 of the rotor angle [see Figure 10(a)], For simulation, we consider a yo-yo configuration similar which are chosen to minimize the total energy spent dur- to the physical prototype. The numerical values of the kite

36 IEEE CONTROL SYSTEMS MAGAZINE » DECEMBER 2007 model and control parameters are 400 reported in Table 1, while Table 2 Traction Phase Traction Phase contains the state values for the 350 start and end conditions of each phase as well as the values of the 300 state and input constraints. Figure 11 shows the trajectory of 250 the kite, while the power generated during the cycle is reported in Fig- 200 ure 12. The mean power is 11.8 kW, which corresponds to energy gener- 150 ation of 2613 kJ per cycle. 100 Carousel Configuration

A carousel with a single KSU is Effective Wind Speed Magnitude (km/h) 50 considered. The model and con- Passive Phase Passive Phase trol parameters employed are 0 0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 reported in Table 3, while Table 4 Time (s) contains the start and end condi- tions for each phase, as well as the FIGURE 17 Simulated effective wind speed for the carousel configuration. The course of |We| values of the state and input con- during the traction subphases (green) and the passive subphases (red) is related to two com- straints. The line speed during the plete carousel cycles. The average values are 250 km/h during the traction phase and 85 km/h during the passive phase. cycle is reported in Figure 13. This reference trajectory is chosen on the basis of the previous simula- tion to maximize the mean generated power and to REFERENCES ensure that the length of the lines at the beginning of [1] “Renewables 2005: Global status report” Renewable Energy Policy Net- work, Worldwatch Institute, Wash. D.C., 2005 [Online]. Available: each cycle is the same. http://www.REN21.net Figure 14 shows the trajectories of the kite and the [2] M. Ippolito, “Smart control system exploiting the characteristics of gener- control unit during two full cycles in the presence of ran- ic kites or airfoils to convert energy,” European patent 02840646, Dec. 2004. dom wind disturbances. Figure 15 depicts some orbits [3] M. Milanese and M. Ippolito “Automatic control system and process for the flight of kites,” International Patent PCT/IT2007/00325, May 2007. traced by the kite during the traction phase, while the [4] M. Canale, L. Fagiano, M. Ippolito, and M. Milanese, “Control of tethered power generated during the two cycles is reported in airfoils for a new class of wind energy generator,” in Proc. 45th IEEE Conf. Figure 16. The mean power is 621 kW, and the generated Decision and Control, San Diego, CA, pp. 2006, 4020–4026. [5] B. Houska and M. Diehl, “Optimal control for power gnerating kites,” in energy is 234 MJ per cycle. Figure 17 depicts the course Proc. 9th European Control Conf., Kos, Greece, 2007, pp. 3560–3567. of the effective wind speed |We| (see the section “Kite [6] A.R. Podgaets and W.J. Ockels, “Flight control of the high altitude wind Generator Models” for details). It can be noted that dur- power system,” in Proc. 7th Conf. Sustainable Applications Tropical Island States, Cape Canaveral, FL, 2007, pp. 125–130. ing the traction phase the mean effective wind speed is [7] M. Canale, L. Fagiano, M. Milanese, and M. Ippolito, “KiteGen project: about 14 times greater than the tangential speed of the Control as key technology for a quantum leap in wind energy generators,” rotor connected to the generator, which is 18 km/h. in Proc. 26th American Control Conf., New York, 2007, pp. 3522–3528. ( , , ) [8] A. Betz, Introduction to the Theory of Flow Machines. New York: Pergamon, 1966. Since the fixed coordinate system X Y Z is defined on [9] M.L. Loyd, “,” J. Energy, vol. 4, no. 3, pp. 106–111, the basis of the nominal wind direction, a measurable 1980. change of the latter can be overcome by rotating the [10] Danish Association of Wind Industry Web site [Online]. Available: ( , , ) www.windpower.org whole coordinate system X Y Z , thus obtaining the [11] D.Q. Mayne, J.B. Rawlings, C.V. Rao, and P.O.M. Scokaert, “Con- same performance without changing either the control strained model predictive control: Stability and optimality,” Automatica, system parameters or the starting conditions of the vari- vol. 36, pp. 789–814, 2000. [12] M. Canale and M. Milanese, “FMPC: A fast implementation of model ous phases. predictive control,” in Proc. 16th IFAC World Congress, Prague, Czech Repub- lic, July 2005. ACKNOWLEDGMENTS [13] M. Canale, L. Fagiano, and M. Milanese, “Fast implementation of pre- dictive controllers using SM methodologies,” in Proc. 46th IEEE Conf. Deci- KiteGen project is partially supported by Regione sion and Control, New Orleans, LA, 2007. Piemonte under the Project “Controllo di aquiloni di [14] M. Milanese and C. Novara, “Set membership identification of nonlinear potenza per la generazione eolica di energia” and by Min- systems,” Automatica, vol. 40, pp. 957–975, 2004. [15] M. Milanese and C. Novara, “Structured set membership identification of istero dell’Università e della Ricerca of Italy under the nonlinear systems with application to vehicles with controlled suspensions,” National Project “Advanced control and identification Control Eng. Practice, vol. 15, pp. 1–16, 2007. techniques for innovative applications.” [16] K. Hsu, M. Milanese, C. Novara, and K. Poolla, “Nonlinear virtual

DECEMBER 2007 « IEEE CONTROL SYSTEMS MAGAZINE 37 sensors design from data,” in Proc. IFAC Symp. System Identification (SYSID), Lorenzo Fagiano received the master’s degree in auto- Newcastle, Australia, pp. 576–581, 2006. motive engineering in 2004 from Politecnico di Torino, [17] K. Hsu, M. Milanese, C. Novara, and K. Poolla, “Filter design from data: Direct vs. two-step approaches,” in Proc. 25th American Control Conf., Min- Italy. In 2005 he worked at Centro Ricerche Fiat, Italy, in neapolis, MN, 2006, pp. 1606–1611. the active vehicle systems area. Since January 2006 he has [18] M. Diehl, “Real-time optimization for large scale nonlinear processes,” been a Ph.D. student at Politecnico di Torino. His main Ph.D. dissertation, University of Heidelberg, Germany, 2001 [Online]. Avail- able: http://www.iwr.uni-heidelberg.de/~Moritz.Diehl/DISSERTATION/ research interests include constrained robust and nonlinear diehl_diss.pdf control and set membership theory for control purposes, applied to vehicle stability control and the KiteGen project. AUTHOR INFORMATION Mario Milanese ([email protected]) graduat- Massimo Canale received the Laurea degree in electronic ed in electronic engineering from the Politecnico di Torino, engineering (1992) and the Ph.D. in systems engineering Torino, Italy, in 1967. Since 1980, he has been a full profes- (1997), both from the Politecnico di Torino, Italy. From sor of system theory at Politecnico di Torino. From 1982 to 1997 to 1998, he worked as a software engineer in the R&D 1987, he was head of the Dipartimento di Automatica e department of Comau Robotics, Italy. Since 1998, he has Informatica at the Politecnico di Torino. His research inter- been an assistant professor in the Dipartimento di Auto- ests include identification, prediction, and control of matica e Informatica of the Politecnico di Torino. His uncertain systems with applications to biomedical, auto- research interests include robust control, model predictive motive, aerospace, financial, environmental, and energy control, set membership approximation, and application to problems. He is the author of more than 200 papers in automotive and aerospace problems. international journals and conference proceedings.

To conclude the column, I would and Faryar Jabbari, the Student member activities. Claire is not only like to mention that being the VPMA Activities Chair. Their precious an excellent scientist, as the huge of this society for two years has been advice, together with their energy number of awards she has already a wonderful experience, which and their wonderful temperament, received despite her young age testi- allowed me to interact with persons I has made my job not only easier but fies, but also an energetic and reliable initially knew just by name and often very pleasant and enjoyable! person. So, I wish her good luck, hav- whom I now regard as real friends. In Finally, I find the chance to men- ing no doubts that she will do a great particular, I would like to mention tion that in January 2008, I will step job as VPMA. Rick Middleton, the vice president for down, and Claire Tomlin will be tak- Maria Elena Valcher conference activities and past VPMA, ing over the role of vice president for

38 IEEE CONTROL SYSTEMS MAGAZINE » DECEMBER 2007