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 Energy 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 renewable energy [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 wind power 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 electric generator. 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 wind farm 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 wind turbine’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 (e θ , e φ , 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 .