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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 61, NO. 3, MARCH 2014

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High-Precision and Strong-Robustness Control for an MSCMG Based on Modal Separation and Rotation Motion Decoupling Strategy Yuan Ren, Member, IEEE, and Jiancheng Fang, Member, IEEE

Abstract—To resolve the common contradictions between the decoupling precision and robustness to model the errors of a magnetically suspended control moment gyro and to avoid high control effort, a high-precision and strong-robustness control strategy is presented in this paper. The described method is based on the modal separation control and rotation motion decoupling strategy. The simplified modal controller and modified feedback linearization algorithm are employed to realize the two objectives, respectively. Simultaneously, a new phase compensation approach is proposed, and its design method is presented to improve the decoupling performance and system stability. A robust servo regulator is adopted for the decoupled plants to guarantee the control performances and robustness. Comparative simulations and experiments have been developed to evaluate the effectiveness and superiority of the proposed control method. Index Terms—Decoupling control, feedback linearization, gyro effects, magnetically suspended control moment gyro (CMG) (MSCMG), modal control, robust servo regulator.

I. I NTRODUCTION

C

ONTROL MOMENT gyros (CMGs) are power-efficient attitude-control actuators that produce large torques for spacecraft [1] and robotics system, such as space robots [2], [3] and underwater robots [4]. A magnetically suspended CMG (MSCMG) is becoming a promising alternative to the traditional mechanical CMG due to its inherent superior features such as zero friction, low vibration, the ability for high rotational speeds, wide temperature ranges, adjustable bearing stiffness, and damping [5]–[9]. However, an MSCMG is a multivariable, nonlinear, and strongly coupled system with significant gyro effects and moving-gimbal effects [6], which puts a strain on its highstability and high-precision control. In particular, when the twisting motion of the magnetically suspended rotor (MSR) takes place [8], the nonlinear and coupling characteristics become stronger, presenting a more challenging issue.

Manuscript received September 3, 2012; revised February 11, 2013; accepted March 16, 2013. Date of publication April 5, 2013; date of current version August 23, 2013. This work was supported in part by the National Basic Research Program of China under Grant 2009CB72400101C and in part by the Innovation Foundation of Beihang University for Ph.D. Graduates. The authors are with the Science and Technology on Inertial Laboratory and the Fundamental Science on Novel Inertial Instrument and Navigation System Technology Laboratory, Beihang University, Beijing 100191, China (e-mail: [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIE.2013.2257147

Over the years, considerable research has been conducted to resolve the gyro effects and moving-gimbal effects. Traditionally, they are eliminated respectively by different control algorithms since the MSR system and gimbal servo system are taken as two subsystems. As for the MSR system, decentralized proportional-integral-derivative (PID) with appropriate filters is widely used due to its simplicity and robustness [10], [11], where the filters are adopted to realize phase compensation and disturbance/imbalance rejection. However, this method has some difficulty in guaranteeing the whirling mode stability of the MSR system with strong gyro effects [12]. To resolve this issue, all kinds of cross-feedback control methods [12]– [15] have been proposed, such as the speed cross-feedback control [12], filtered cross-axis gains control [14], decentralized PID plus filtered cross-feedback control [15], and so on. However, all these methods cannot achieve satisfactory control precision due to approximate linearization errors and cannot realize the complete decoupling among the four radial channels of the MSR [6]. To realize the decoupling control between the translation and rotation motions of the MSR, Dever et al. [16] propose a modal control method. However, this method cannot realize the decoupling between the 2-degree-of-freedom (DOF) rotation motions of the MSR. Therefore, it cannot completely remove the gyro effects. Yu et al. [17] propose a modal decoupling control strategy based on state feedback to stabilize the precession mode of the MSR. However, it cannot guarantee the stability of the nutation mode at high speeds due to the phase lag of the control system. The traditional way to reject the moving-gimbal effects is “gimbal angular ratecurrent feedforward control” (rate feedforward for short) due to its effectiveness and simplicity [18]. However, it is difficult to achieve satisfactory static and dynamic performances since the nonlinearity and the reaction torque disturbance from the MSR to the gimbal servo system have been neglected [6]. To resolve these issues, Fang and Ren [6] for the first time consider the MSCMG as a whole and propose a channel decoupling control strategy based on current-mode inverse system method. This can realize the exact linearization and decoupling control among the five channels, including four radial channels of the MSR and the gimbal servo channel. However, as we all know, the robustness is a common problem of the linearization and decoupling method [19]–[22]. Although this issue has been alleviated to some degree by employing the internal model controller and phase compensation filters [6], its robustness to model errors is less than satisfactory. Additionally, this algorithm is relatively complex due to the following reasons.

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First, all the five channels are required to be decoupled. Second, this method needs to perform phase compensation for all the four radial channels of the MSR to ensure the decoupling performance and nutation stability of the MSR. Third, all the five channels need to respectively resort to robust controllers to guarantee their robustness in practice. All of these inevitably cause large computational resources and seriously complicate its industrial application. In fact, a centralized control based on linearization and decoupling is exciting to realize the complete decoupling of an MSCMG since it can promote the system decoupling precision and tracking performance. Nevertheless, a modal-separation (decentralized) control is desired too since the translation and rotation motions have different characteristics and control objectives, which contributes to the system robustness and implementation simplicity. The channel decoupling approach satisfies the first requirement but does not achieve the second goal. Contrarily, the cross-feedback plus rate feedforward method cannot meet the first demand. All in all, the common issues of these methods mainly lie in the contradictions among the decoupling precision, the robustness to model errors, and the implementation simplicity. The contradictions not only influence the system performances but also complicate the parameter adjustment. To solve these contradictions, a new high-precision and strong-robustness control method is presented in this paper. The improved modal controller is employed to decouple the translation and rotation motions of the MSR, and the modified current-mode feedback linearization algorithm is adopted to achieve the exact linearization and decoupling among the 3-DOF rotation motions of the MSCMG. The main contribution of this paper lies in that the proposed control strategy can effectively resolve the common issues of the existing control methods for the MSCMG. The remainder of this paper is organized as follows. Section II reviews the system model and analyzes its coupling characteristics. Section III describes the proposed control algorithm based on the modified modal control and feedback linearization method. Section IV develops comparative simulations and experiments among different methods. Finally, Section V concludes this paper. II. M ODEL OF THE MSCMG S YSTEM AND THE C OUPLING C HARACTERISTICS A NALYSIS A. Model of the MSCMG System The schematics of the rotor forces and the coordinate systems are shown in Fig. 1, where O is the geometric center of the magnetic bearing stator; X-, Y-, and Z-axes form the generalized coordinate system of the rotor position; x and y are the linear displacements of the mass center of the rotor from point O in the X- and Y-axes, respectively; and α and β are the rotor angular displacements about the X- and Y-axes. [x, β, y, α]T form the generalized coordinates of the rotor position. fax , fay , fbx , and fby are the magnetic forces along the magnetic bearing coordinate system AX-, AY-, BX-, and BY-axes. fx and fy are the magnetic forces in the X- and Y-axes, respectively. px and py are the torques in the X- and Y-directions. G is the

Fig. 1.

Rotor forces and the coordinate systems.

gravity force of the MSR. A and B denote the two terminals of the MSR system. Ax , Ay , Bx , and By are the four radial channels (channel Ax , Ay , Bx , and By ), and ωg is the gimbal angular rate. The 2-DOF radial rotation motions of the MSR and the gimbal rotation motion constitute the 3-DOF rotation motions of the MSCMG. Since there is no coupling between the axial hybrid magnetic bearings (HMBs) and the radial HMBs, we do not consider the translation motion in the Z-direction. According to Newton’s second law and the principle of rotor dynamics, the 5-DOF (including 2-DOF translation and 3-DOF rotation) motion equations of the MSCMG can be described as [6] ⎧ √ m¨ x = f√ 2/2mg cos θ ⎪ ax + fbx + ⎪ ⎪ ⎪ Jy (β¨ − 2/2ω˙ g ) − Jz Ω(α˙ + √w/2ωg ) ⎪ ⎪ ⎪ ⎪ = py = lm (fax√− fbx ) ⎨ (1) m¨ y = fay √ + fby + 2/2mg cos √θ ⎪ ⎪ J (¨ ˙ ⎪ α + 2/2 ω ˙ ) + J Ω( β − 2/2ω ) x g z g ⎪ ⎪ ⎪ ⎪ = px = lm (f by − fay ) ⎪ √ ⎩ Jg ω˙ g = kg ig − 2/2(px − py ) + TG cos θ − Tf where m is the mass of the MSR, θ is the gimbal angle, g is the gravity acceleration, TG is the maximum static unbalance torque of the gimbal servo system; Tf is the friction torque, and kg and ig are the torque coefficient and the coil current of the gimbal motor, respectively. Note that the major factor that impacts the accuracy of the system model is the magnetic force, while its accurate analytical expression is quite tedious or even impossible to be acquired only by mechanism modeling due to the errors of the machining, fabrication, and material. Furthermore, even if the model is built, its feedback linearization arithmetic is always quite hard and even impossible to be derived and performed. Accordingly, to acquire the relatively simple and accurate relationships among the magnetic force, current, and displacement, this paper resorts to experiments. Since the current–force factor and displacement–force factor change with current, position, and rotor speed, they are tested by using the outputting torque method [7] at different operation points. Figs. 2 and 3 show the relationships between kiλ and iλ at the center of the air gaps and the relationships between khλ and hmλ under the conditions iλ = 0, respectively. The signs “Δ,” “,” “◦,” and “” stand for the actual measured

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Fig. 2. Relationships between kiλ and iλ at the center of the air gaps (λ = ax, ay, bx, by).

Fig. 3. Relationships between khλ and kmλ under the conditions iλ = 0, respectively (λ = ax, ay, bx, by).

points of the four radial channels, and the curves are drawn through eight-order curve fitting by MATLAB software. Then, the current–force factor and the displacement–force factor at every operating point can be obtained through the table lookup method in practical applications. By this way, the expression of the magnetic force can be further developed by a variable operating-point linearization method. That is, it can be linearized as

current iλr of MBs as the current components which generate the translation and rotation motions of the MSR, respectively. Then, we have iλ = iλt + iλr , kiax iaxt = kibx ibxt , kiay iayt = kiby ibyt , kiax iaxr = −kibx ibxr , and kiay iayr = −kiby ibyr . Accordingly, (1) can be rewritten as (3), shown at the bottom of the page, where

fλ = kiλ iλ + khλ hmλ

(λ = ax, ay, bx, by)

(2)

where kiλ , khλ , hmλ , and iλ are the current–force factor, the displacement–force factor, the linear displacement of the rotor, and the winding current of channel λ, and [iax , ibx , iay , iby ]T form the magnetic bearing (MB) actuator coordinates. An assumption which is commonly made on the MSR is that it is exactly symmetrical, i.e., the magnetic center coincides exactly with the geometric center. Unfortunately, this does not happen in most practical situations due to the errors of the machining, fabrication, and material. As shown in Figs. 2 and 3, both the current–force factors and the displacement–force factors of the four radial HMBs are not quite symmetrical with respect to current and displacement, respectively, and are not equal to each other even under the same conditions. B. Analysis of Coupling Characteristics of MSCMG According to (1), it is obvious that there are strong dynamic couplings among α, β, and ωg . In this section, we will analyze the coupling characteristics between the translation and rotation motions of an MSR system. In the generated coordinate system of the rotor position, define the translation current iλt (λ = ax, ay, bx, by) and rotation

iy = ibyt = kiay iayt /kiby ix = iaxt = kibx ibxt /kiax ia = iaxr = −kibx ibxr /kiax iβ = ibyr = −kiay iayr /kiby Δkhx = khax − khbx Δkhy = khby Td = TG cos θ − Tf and [ix , iα , iy , iβ ]T constitute the modal coordinates. Then, the coordinate translation from the modal coordinates to MB actuator coordinates can be yielded ⎧i = i + i ax x α ⎪ ⎨ i = k /k (i − i ) bx iax ibx x α (4) i = k /k (i − i ) ⎪ ay iby iay y β ⎩ iby = iy + iβ . According to (3), in the generated coordinate system of the rotor position, there are no couplings between the translation and rotation motions of the MSR if and only if Δkhx = Δkhy ≡ 0, i.e., the two channels with the same translation DOF always have the same displacement–force factors. Notice that this condition does not come into existence in the practical MSCMG system as tested earlier (see Figs. 2 and 3). In fact, even for a quite symmetrical MSR system, it cannot satisfy this condition in the whole operation region since the MSR cannot be always suspended at the center of the air gaps. Then, as for the practical MSCMG system, there are strong dynamic couplings not only among the 3-DOF rotation motions of the MSCMG but also between the 2-DOF translation motions and 3-DOF rotation motions of the MSCMG. Now that the

√ ⎧ m¨ x = 2k 2/2mg cos θ ⎪ iax ix + 2khax x − Δk hx xbm + √ √ ⎪ ⎪ 2 ⎪ Jy (β¨ − 2/2ω˙ g ) − Jz Ω(α˙ + 2/2ωg ) = 2lm kiax iα + 2lm khax β + lm Δkhx xbm ⎨ √ 2/2mg cos θ m¨ y = 2k√iby iy + 2khby y − Δk√ y + hy am ⎪ 2 ⎪ ⎪ Jx (¨ α + 2/2ω˙ g√ ) + JzΩ(β˙ − 2/2Ωg ) = 2lm kiby iβ + 2lm khby α + lm Δkhy yam ⎪  ⎩ 2 Jg ω˙ g = kg ig − 2/2 2lm (kiby iβ − kiax iα ) + 2lm (khby α − khax β) + lm (Δkhy yam − Δkhx xbm ) + Td

(3)

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Fig. 4. Schematic of the simplified modal controller implementation.

rotation motion couplings among α, β, and ωg are the essential reason for the gyro effects and moving-gimbal effects, which influence both the stability and the control precision, and the couplings between the 2-DOF translation and 2-DOF rotation motions of the MSR prevent the independent control of the stiffness and damping of the MSR. Additionally, the couplings between the translation motions of the MSR and the gimbal rotation motion are relatively weak, and these can be ignored in space since there is little gravity; hence, there is no need to decouple them. Thus, the decoupling control between the translation and rotation motions of the MSR and among the 3-DOF rotation motions is reasonable and necessary. III. P ROPOSED C ONTROL S TRATEGY BASED ON M ODAL S EPARATION AND ROTATION M OTION D ECOUPLING A. Modal Separation Using Simplified Modal Control The goal of the modal control is to realize the separate control of the translation and rotation motions. To achieve this goal, the traditional method needs to cancel the negative stiffness of the HMB, which is performed in the controller by adding an equal and opposite (positive) stiffness to the MB command signal [16]. In fact, there is no need to counteract the whole negative stiffness in the actuator since there is no coupling between the translation and rotation motions of the MSR under the conditions that Δkhx = Δkhy ≡ 0. Therefore, we can only cancel the asymmetric negative stiffness, i.e., asymmetric displacement–force factors of the HMBs, instead of the whole negative stiffness. As a result, compared with the traditional modal control, the simplified one only needs to compensate for two channels, such as channels Ax and By , instead of four channels, and only the asymmetric negative stiffness needs to be canceled, which serves to simplify the decoupling control algorithm. The schematic of the simplified modal controller implementation is shown in Fig. 4, where TMC is the translation motion controller, RMC is the rotation motion controller, and ANSCC is the asymmetric negative-stiffness compensation controller. The first step is to convert the position sensor inputs into modal coordinates. Then, the separate modal controllers are applied to the sets of modal coordinates. These modal controller outputs are then converted from the modal coordinates to MB actuator coordinates and summed with the outputs of ANSCC to form the controller outputs. According to (3), the outputs of the ANSCC can be resolved as  Δkhx Δibx = kibx xbm (5) Δkhy Δiay = kiay yam .

By the asymmetric negative-stiffness compensation, the asymmetric plant becomes a symmetrical one, which can be described as √ ⎧ m¨ x = 2k 2/2mg cos θ ⎪ iax ix + 2khax x + √ √ ⎪ ⎪ ⎪ Jy (β¨ − 2/2ω˙ g ) − Jz Ω(α˙ + 2/2ωg ) ⎪ ⎪ ⎪ 2 ⎪ khax = 2lm kiax iα + 2lm ⎪ √β ⎪ ⎨ cos θ m¨ y = 2k√iby iy + 2khby y + 2/2mg √ ˙ ⎪ Jx (¨ α + 2/2ω˙ g ) + Jz Ω(β − 2/2ωg ) ⎪ ⎪ 2 ⎪ ⎪ = 2lm kiby i√ β + 2lm khby α ⎪ ⎪ ⎪ ⎪ Jg ω˙ g= kg ig − 2/2 ⎪  ⎩ 2 (khby α − khax β) + Td . × 2lm (kiby iβ − kiax iα ) + 2lm (6) That is, the rotation motions of the MSR are not coupled with the translation motions anymore. The control of the translation motions does not present any problem, and only the rotation motions exhibit speed-dependent gyroscopic effects and moving-gimbal effects. Consequently, the PID controllers are retained to realize the translation control, and the rotation motion decoupling control based on the feedback linearization method is further developed. B. Rotation Motion Decoupling Based on Improved Feedback Linearization Method According to (6), define the state variable x, input variable u, and output variable y as ˙ ωg ]T x = [x1 , x2 , x3 , x4 , x5 , x6 ]T = [α, β, θ, α, ˙ β, T T u = [u1 , u2 , u3 ] = [iα , iβ , ig ] y = [y1 , y2 , y3 ]T = [α, β, θ]T .

(7) (8) (9)

The corresponding state-variable equation of the nonlinear system (6) can be described as ⎧ 3 ⎨˙ gi (x)ui x = f (x) + i=1 ⎩ y = h(x) = [ h1 (x) h2 (x) h3 (x) ]T = [ x1 x2 x3 ]T (10) where definitions are given at the bottom of the next page. According to the differential geometry theory [24], we have Lgi hj (x) = 0 (i, j = 1, 2, 3) (11) ⎡ ⎤ Lg1 Lf h1 (x) Lg2 Lf h1 (x) Lg3 Lf h1 (x) A(x) = ⎣ Lg1 Lf h2 (x) Lg2 Lf h2 (x) Lg3 Lf h2 (x) ⎦ Lg1 Lf h3 (x) Lg2 Lf h3 (x) Lg3 Lf h3 (x) √ ⎡ ⎤ 2lm kiby l k −lm kiax + mJgiby −2J2k Jg Jx g √ ⎢ 2l k −lm kiby 2kg ⎥ lm kiax m iax ⎥ + =⎢ Jg J 2Jg ⎦ . ⎣ Jy√ √ g 2lm kiax Jg

− 2lm kiby Jg

kg Jg

(12) Accordingly, det A(x) = −

2 4lm kiax kiby kg = 0. Jx Jy Jg

(13)

REN AND FANG: HIGH-PRECISION AND STRONG-ROBUSTNESS CONTROL FOR AN MSCMG

It can be drawn that the system (10) is of vector relative degree {2, 2, 2}, and 6 = 2 + 2 + 2 is equal to the system dimension, i.e., the system can be full state feedback linearized [25]–[27]. By using a coordinate transformation ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ h1 (x) x1 z1 ⎢ z2 ⎥ ⎢ Lf h1 (x) ⎥ ⎢ x4 ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ z3 ⎥ ⎢ h2 (x) ⎥ ⎢ x2 ⎥ (14) ⎢ ⎥=⎢ ⎥=⎢ ⎥ ⎢ z4 ⎥ ⎢ Lf h2 (x) ⎥ ⎢ x5 ⎥ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ z5 x3 h3 (x) z6 x6 Lf h3 (x) and by the nonlinear feedback control law u = −A−1 (x)(v − ϕ)

(15)

where v = [v1 , v2 , v3 ]T is the new control variable and √ ⎡ 2l2 (k x −k x )−√2T ⎤ 2 2lm khby x1 −H(x5 − 2/2x6 hby 1 hax 2 d m + 2Jg Jx √ ⎢ 2l2 (k x −k x )+√2T ⎥ 2 hax 2 hby 1 d 4 − 2/2x6 ⎥ m ϕ=⎢ + 2lm khax x2 +H(x ⎣ ⎦ 2Jg Jy √ Td 2 2 Jg lm (khax x2 − khby x1 ) + Jg (16) the system (10) can be decoupled into three two-order pseudolinear subsystems. Then, the nonlinear feedback control arithmetic u can be derived by substituting (12) and (16) into (15). Since the differential operation (such as the resolutions of x4 , x5 , and x6 ) practically results in noise and random errors, which inevitably affects the decoupling and tracking performances. To address this issue, the incomplete derivation is substituted for the pure derivation in this paper. Then, the modified feedback control arithmetic can be described as    √ 2 1 v3 Jy v 2 − u ˆ1 = 2lm kiax 2    √ 2 2 −H x ˜4 + x ˜6 − 2lm khax x2 (17a) 2

⎡

x4 x5 x6 √ 2 2lm (khby x1 −khax x2 )− 2Td + 2Jg

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   √ 2 1 v3 Jx v 1 − u ˆ2 = 2lm kiby 2    √ 2 2 x ˜6 − 2lm khby x1 (17b) +H x ˜5 − 2  √  2 1 Jx + Jy Jx y1 Jg + u ˆ3 = v3 + kg 2 2  √ √ 2 2 Jy y2 + H(˜ x4 + x − ˜ 5 ) − Td (17c) 2 2 where x ˜4 , x ˜5 , and x ˜6 are respectively the incomplete derivaˆ1 , u ˆ2 , and u ˆ3 are the modified tions of x1 , x2 , and x3 and u values of u1 , u2 , and u3 , respectively, after employing the incomplete derivation. C. Realization of the Proposed Control Strategy The decoupled plants are often combined with robust controllers since the remaining coupling and nonlinearity always exist in practice [28], [29]. A robust servo regulator is employed in this paper due to its excellent tracking and robust performances [30], [31], which consists of servo compensator T (s) and stabilizing compensator K(s). As for the 3-DOF rotation motions, their pseudolinear subsystems can be described as Gp (s) = 1/s2 . According to the design method of the robust servo regulator, let T (s) = (a0 + a1 s)/s and K(s) = k0 + k1 s. Then, the closed-loop transfer function of the pseudolinear subsystem can be described as φ(s) =

a0 + a 1 s . (18) s3 + (2ξωn + δ)s2 + (ωn2 + 2ξωn δ) s + δωn2

To simplify the selection of the controller parameters, we can design the system which has a pair of complex number dominant poles and the other poles far away from the imaginary axis, i.e., Δ

φ(s) =

ωn2 (s + δ) . (s + δ) (s2 + 2ξωn s + ωn2 )

⎤

⎥ ⎢ ⎥ ⎢ ⎥ ⎢ √ ⎥ ⎢ 2 2lm khby x1 −H(x5 − 2/2x6 ) ⎥ f (x) = ⎢ ⎥ ⎢ Jx √ ⎥ ⎢ 2l2 (k x −k x )+√2T 2 2lm khax x2 +H(x4 + 2/2x6 ) ⎥ d ⎢ m hax 2 hby 1 + ⎦ ⎣ 2Jg Jy √ Td 2 2 l k(k x − k x ) + hax 2 hby 1 Jg m Jg ⎤ ⎤ ⎡ ⎡ ⎡ 0 0 0 0 ⎥ ⎥ ⎢ ⎢ ⎢ 0 0 ⎥ ⎥ ⎢ ⎢ ⎢ 0 ⎥ ⎥ ⎢ ⎢ ⎢ √0 0 ⎥ ⎥ ⎢ ⎢ ⎢ − 2kg 2lm kiby lm kiby −lm kiax g1 (x) = ⎢ g g (x) = (x) = + ⎥ ⎥ ⎢ ⎢ 2Jg 2 3 Jg Jg ⎥ ⎥ ⎢ ⎢ Jx ⎢ √ −lm kiby ⎥ ⎢ 2lm kiax + lm kiax ⎥ ⎢ ⎢ 2kg ⎦ ⎦ ⎣ Jy√ ⎣ ⎣ 2Jg Jg J √ g kg 2 − 2 Jg lm kaix Jg lm kiby J g

⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦

(19)

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Fig. 5. Schematic of the proposed decoupling controller based on improved modal control and feedback linearization.

To improve the system response speed, this paper chooses δ = 5, ωn = 400 rad/s, and ξ = 0.707. Then, combining (18) and (19) yields the controller parameters ⎧ a = δωn2 = 800000 ⎪ ⎨ 0 a1 = ωn2 = 160000 (20) ⎪ k ⎩ 0 = 2ξωn δ = 2828 k1 = δ + 2ξωn = 570.7. The schematic of the proposed decoupling controller based on the modified modal control and feedback linearization method is shown in Fig. 5. Gt (s) denotes the PID controller for the translation motions of the MSR, and Gc (s) is the compensation filter for its rotation motions, whose design method will be described in the next section. Then, the controller outputs, i.e., the reference currents of the MSCMG, can be yielded ⎧ ∗ iax = ix + u ˆ1 Gc (s) ⎪ ⎪ ⎪ ∗ ⎪ = k /k ˆ1 Gc (s)) + Δibx i ⎨ bx iax ibx (ix − u i∗ay = kiby /kiay (iy − u ˆ2 Gc (s)) + Δiay (21) ⎪ ⎪ ˆ2 Gc (s) ⎪ i∗by = iy + u ⎪ ⎩ i∗ = u ˆ3 . g Compared with the channel decoupling method, the proposed method contributes to improving the system robustness against the model errors because the translation controller does not depend heavily on the precise model anymore. That is, the robustness of the translation motions can be greatly improved by the proposed strategy. Compared to the traditional crossfeedback plus rate feedforward control method, this strategy can realize higher control precision since it realizes the exact linearization and decoupling among the 3-DOF rotation motions. D. Dynamic Compensation Filter Design To suppress the influence of the unmodeled dynamics on the system decoupling performance and nutation stability of the MSR, dynamic compensation filters are necessary for the decoupled pseudolinear subsystems [6]. Different from the existing compensation strategies [6], [32], the presented method need not to compensate for every radial channel of the MSR. We only compensate for the two rotation motions of the MSR, not including two translation motions.

Fig. 6. Positive frequency phase response curves of the control channel before and after phase compensation.

That is, there are only two compensation filters instead of four. Therefore, compared to the existing methods, computational resources and noise amplification introduced by phase compensation can be greatly reduced. When analyzing the nutation stability of the MSR, the gimbal servo system can be ignored since its operating bandwidth is far lower than that of the nutation frequency in practice, i.e., it has little effect on the nutation stability of the MSR. Then, the feedback linearization algorithm of the MSR can be simplified as   1 2 Jy v 2 − H x ˜4 − 2lm khax x2 2lm kiax   1 2 Jx v 1 − H x u ˆ2 = ˜5 − 2lm khby x1 . 2lm kiby

u ˆ1 =

(22a) (22b)

According to the stability criterion of the nutation mode [15], the complex-coefficient transfer function of the control channel for the MSR rotation motions can be described as   1 s 2 G(s) = khax + jH Jr (T (s)+K(s))+2lm 2lm kiby 1 + ks ×Ga (s)Gf (s)

(23)

where k is the incomplete derivative coefficient, k = 0.0001, j is the imaginary unit, j 2 = −1, and Ga (s) and Gf (s) are the transfer functions of the power amplifier system for the MBs and the antialias filter of the displacement signals. Then, its positive frequency phase response curve can be produced as shown in the thin line in Fig. 6. As a result, the phase margin of the nutation mode at the rated nutation frequency (about 280 Hz) can be yielded, which is about 5◦ . Supposing that the desired phase margin of the nutation mode is 45◦ , one can obtain that the phase needed to be compensated at the rated nutation frequency is about 40◦ . Based on these, considering the simplicity of realization and noise rejection, a second-order filter can be designed, whose transfer function is given by Gc (s) =

5.3s2 + 8600s + 1.2 × 107 . 2.5s + 5200s + 1.2 × 107

(24)

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TABLE I S YSTEM PARAMETERS OF THE MSCMG

Fig. 7.

Photograph of the fabricated laboratory setup.

The thick line in Fig. 6 shows the positive frequency phase response curve of the control channel after phase compensation. From Fig. 6, the phase margin of the nutation mode of the MSR at 280 Hz has increased from about 5◦ to about 45◦ . This demonstrates that the relative stability of the MSR can be greatly increased by employing the dynamic compensation filter.

TABLE II M AIN PARAMETERS OF THE C ONTROLLERS

IV. S IMULATION AND E XPERIMENTAL S TUDY Comparative simulations and experiments among the traditional method (decentralized PID plus cross-feedback and rate feedforward control), the channel decoupling method, and the proposed one have been carried out in this section to evaluate the performances of the proposed method. A. Experimental Setup Extensive experiments have been performed on the setup shown in Fig. 7, where the HMBs are driven by five H-bridge unipolar switching power amplifiers independently. As for the hardware implementation, a TMS320C31 digital signal processor is adopted, and analog-to-digital converter (ADC) 1674 is employed. Both the sampling and servo periods are set to 150 μs, and the switching period is set to 50 μs. Eddy-current displacement sensors are adopted to test the MSR displacements. The generalized coordinates of the rotor position can be achieved by coordinate translation since the radial sensors and actuators are located at different positions along the shaft and their positions are known. For a fair comparison of the decoupling, tracking, and computer run time of different methods, both the proposed method and the channel decoupling approach employ the same robust servo regulator and dynamic compensation filter described as (20) and (24), respectively. The main system parameters and the controller coefficients used in simulations and experiments are listed in Tables I and II. In Table I, xb is the protective air gap of the radial HMBs; ls refers to the distance between the central point of the radial displacement sensor and O. R and L are the coil resistance and inductance of the radial HMBs; Rg and Lg are the circuit resistance and inductance of the gimbal servo motor. In Table II, kam and ic are the proportional and feedback coefficients of the current-loop controller for the MSR system; kp ,

TABLE III COMPUTER RUN TIME OF DIFFERENT CONTROL METHODS

ki , and kd are the proportional, integral, and differential coefficients of the decentralized PID plus cross-feedback controller [14]; khc and klc are the cross-coefficients of the high-pass and low-pass filters, respectively; kc is the total cross-coefficient; fh and fl are the cutoff frequencies of the two-order highpass and low-pass filters; krp , kri , and krd are the proportional, integral, and differential coefficients of the angular rate loop of the gimbal servo system; and kcp is the proportional coefficient of the current loop of the gimbal servo system. All of these are the main parameters for the traditional controller. Additionally, the three methods have the same current-loop controller for the MSR. In addition, the current–force factor and displacement– force factor at every operating point have been tested in Section II, and thus, they can be obtained using the table lookup method. The computer run times, i.e., the computation delays, of the three methods are compared, and the test results are given in Table III. From Table III, the proposed method has a much

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Fig. 8. Comparative simulation and experimental results of the rotor translation displacements, the twisting angles, and the gimbal angular rate between the traditional method and the proposed method. (a) Comparative simulation results. (b) Experimental results of the proposed method with ωn = 400 rad/s. (c) Experimental results of the traditional method with kp = 2.5. (d) Experimental results of the traditional method with kp = 3.5.

shorter computer run time than that of the channel decoupling method and takes the similar time as the traditional method. This verifies that the proposed control strategy can largely simplify the industrial realization compared with the channel decoupling method, which is consistent with the analysis in Section I. According to the literature [33], the digital control delay can be obtained by Td = Tad + Tcal + Tawa + 0.5Tc , where Tad , Tcal , Tawa , and Tc express the ADC delay, computation delay, pulsewidth modulation awaiting delay, and servo period. The ADC delay time is about 100 μs since the conversion time of one sampling channel is 10 μs and there are ten sampling channels. Therefore, the total digital control delays of the pro-

posed control method, the traditional method, and the channel decoupling method are 275, 275, and 325 μs, respectively. B. Performances of Tracking, Decoupling, and Stability At first, we verify the tracking, decoupling, and stability performances. Under the conditions that Ω = 12 000 r/min and ωgr = 0◦ /s, at t = 0.2 s, the reference translation displacement yr steps from 0 to 20 μm, and at t = 0.4 s, the reference gimbal angle θr tracks the cosine signal 0.3183 cos(5πt + π)◦ , i.e., the given gimbal angular rate ωgr is 5 sin(5πt)◦ /s. Figs. 8 and 9 show their comparative simulation and experimental results among different methods. For the sake of convenience, the

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Fig. 9. Comparative simulation and experimental results of the rotor translation displacements, the twisting angles, and the gimbal angular rate between the channel decoupling method and the proposed method. (a) Comparative simulation results between the two methods. (b) Comparative simulation results of the proposed method with different ωn . (c) Comparative simulation results of the two methods with the same time delay. (d) Experimental results of the proposed method with ωn = 600 rad/s. (e) Experimental results of the channel decoupling method with ωn = 400 rad/s. (f) Experimental results of the channel decoupling method with ωn = 600 rad/s.

signs “T,” “C,” and “P” in the simulation results of this paper demonstrate the traditional method, the channel decoupling method, and the proposed one, respectively.

As shown in Figs. 8(a) and 9(a), when encountering the step of translation y, both the channel decoupling method and the proposed one do not bring any disturbance to x, α, β,

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and ωg . Simultaneously, when encountering the sine fluctuation of the gimbal angular rate, both the two methods do not result in any impact on x and y. On the contrary, as for the traditional method, there are about 0.6-μm disturbances on x and y during the gimbal angular rate fluctuation. This indicates that, as for the channel decoupling approach, the proposed method can also decouple the translation and rotation motions of the MSR. Moreover, the modal separation of the MSR can well reject the disturbance from the gimbal angular rate fluctuation, which is in accordance with the analysis in Section II. According to Fig. 8(a), as for the traditional method with kp = 2.5, there are about 20-μm overshoot on y and 2.5-Hz sinusoidal disturbances with the amplitude of 1.5 × 10−4 (corresponding to 17.0 μm) on α and β when tracking the step signal of y and the sine signal of the gimbal angular rate, respectively. In contrast, the above values are reduced to about 0 μm and 3.2 × 10−5 (corresponding to 3. 6 μm) when using the proposed method, although the disturbance can be alleviated from 1.5 × 10−4 to 1.0 × 10−4 by increasing the kp of the traditional method from 2.5 to 3.5, which inevitably increases the overshoot on y (from 20 μm to 30 μm). Most importantly, too large kp is unfavorable to the nutation stability of the MSR according to the nutation stability criterion [15] for the MSR with significant gyro effects. Fig. 9(a) and (b) shows the comparative simulation results between the two decoupling methods with different ωn ’s. As for ωn = 400 rad/s, the channel decoupling method has much longer settling time than that of the proposed one when tracking the step command. Although this has been solved by increasing ωn from 400 to 600 rad/s, it introduces about 8-μm overshoot on y simultaneously. Also, too large ωn degrades the nutation stability. Contrarily, there is no such issue when employing the proposed method. As shown in Fig. 9(b), the increase of ωn (from 400 to 600 rad/s) does not increase any overshoot on y. Note that, even with the same ωn , both α and β suffer larger disturbance with the channel decoupling method than that with the proposed one. This is caused by the excessive computation delay of the channel decoupling method. To verify this conclusion, suppose that the two methods have the same digital control delay, i.e., 325 μs, which is performed by adding an extra time-delay unit of 50 μs to the proposed controller, and then, the above simulation is repeated. The results are shown in Fig. 9(c). From Fig. 9(c), the two methods now have the same impact on α and β during the angular rate fluctuation, which effectively testifies the conclusion above. As for the proposed method, the adjusting time of translation y does not change with the computation delay. This further demonstrates that the proposed method can realize the modal separation of the MSR, achieving the independent control of stiffness and damping. To further validate the effectiveness of the dynamic compensation filters in the proposed controller, the above experiments have also been carried out before and after employing these filters. Fig. 10(a) shows the comparative simulation results, and Fig. 10(b) gives the experimental results before employing the two dynamic compensation filters (Fig. 8(b) shows the results after employing the filters).

Fig. 10. Simulation and experimental results of the proposed method before and after employing the phase compensation filters. (a) Comparative simulation results before and after employing the phase compensation filters. (b) Experimental results before employing the phase compensation filters.

From Fig. 10(a), when the compensation filters are not adopted, both α and β suffer larger overshoots and oscillations than the case with the compensation filters, which shows that both the decoupling characteristics and stability are seriously degraded without the compensation filters. This agrees well with the analysis in Section III. Although there are some differences between the experimental results [see Figs. 8(b)–(d), 9(d)–(f), and 10(b)] and the simulation ones due to noise, static, and dynamic imbalances, they agree with each other on the whole. All of these prove that the proposed method has the better decoupling, tracking, and stability performances than that of both the channel decoupling method and the traditional one.

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Fig. 11. Comparative simulation and experimental results among the three different methods. (a) Comparative simulation results. (b) Experimental results of the traditional method with kp = 2.5. (c) Experimental results of the channel decoupling method with ωn = 400 rad/s. (d) Experimental results of the proposed method with ωn = 400 rad/s.

C. Robustness to Model Errors To further demonstrate the robustness of the proposed control strategy, comparative simulations and experiments among the three different methods have been developed too. At t = 0.1 s, assume that the current–force factors of the four radial HMBs decrease by 40%. After 0.3 s, the reference displacement yr steps from 0 to 20 μm, and at t = 0.6 s, the reference gimbal angular rate ωgr begins to track the sine trajectory with the frequency of 2.5 Hz and amplitude of 5◦ /s. The comparative simulation and experimental results are shown in Fig. 11. From Fig. 11(a), as for the traditional method and the proposed method, the parameter variations do not introduce obvious disturbances into x and y. On the contrary, they result in about 25-μm disturbances on x and y with the chan-

nel decoupling method. This shows that, compared with the channel decoupling method, the robustness of the translation motions has been largely improved by the proposed method. Simultaneously, there are respectively about 45-μm and 15-μm overshoots on y during its step response with the traditional method and the channel decoupling method. Compared to the case without model errors [see Figs. 8(a) and 9(a)], these overshoots are much larger. Contrarily, there is little or no overshoot on y with the proposed method when encountering the parameter variations. Additionally, the amplitudes of the sine disturbances on α and β are about 3.0 × 10−4 , 2.7 × 10−4 , and 2.5 × 10−4 with the traditional method, the channel decoupling method, and the proposed one, respectively. Although the decoupling performance of the proposed method degrades too

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compared with the case where there are no model errors, it is still the best one among the three methods under the same conditions. The experimental results as shown in Fig. 11(b)–(d) further verify the correctness of the simulation. All of these demonstrate that the proposed method greatly enhances the robustness to model errors compared with the existing methods, overcoming their common issues. V. C ONCLUSION To resolve the common contradictions of the existing control methods for an MSCMG, a new control strategy based on simplified modal control and modified feedback linearization method is presented. Comparative simulation and experimental results show that, compared with the traditional method and the existing channel decoupling method, the proposed method has the following characteristics. 1) It has superior decoupling and tracking performances as well as stronger robustness. 2) It is quite simple to implement and convenient to debug and tune. 3) It can realize separate control of the stiffness and damping of the MSR. In a word, the proposed control strategy can effectively realize the high-precision and strong-robustness control of the MSCMG without high control effort. R EFERENCES [1] S. P. Bhat and P. K. Tiwari, “Controllability of spacecraft attitude using control moment gyroscopes,” IEEE Trans. Autom. Control, vol. 54, no. 3, pp. 585–590, Mar. 2009. [2] M. D. Carpenter and M. A. Peck, “Dynamics of a high-agility, lowpower imaging payload,” IEEE Trans. Robot., vol. 24, no. 3, pp. 666–675, Jun. 2008. [3] B. Thornton, T. Ura, Y. Nose, and S. Turnock, “Zero-G class underwater robots: Unrestricted attitude control using control moment gyros,” IEEE J. Ocean. Eng., vol. 32, no. 3, pp. 565–583, Jul. 2007. [4] M. D. Carpenter and M. A. Peck, “Reducing base reactions with gyroscopic actuation of space-robotic systems,” IEEE Trans. Robot., vol. 25, no. 6, pp. 1262–1270, Dec. 2009. [5] T. Schuhmann, W. Hofmann, and R. Werner, “Improving operational performance of active magnetic bearings using Kalman filter and state feedback control,” IEEE Trans. Ind. Electron., vol. 59, no. 2, pp. 821– 829, Feb. 2012. [6] J. Fang and Y. Ren, “High-precision control for a single-gimbal magnetically suspended control moment gyro based on inverse system method,” IEEE Trans. Ind. Electron., vol. 58, no. 9, pp. 4331–4342, Sep. 2011. [7] J. Fang and Y. Ren, “Decoupling control of a magnetically suspended rotor in a control moment gyro based on inverse system method,” IEEE/ASME Trans. Mechatronics, vol. 17, no. 6, pp. 1133–1144, Dec. 2012. [8] Y. Ren and J. Fang, “High-stability and fast-response twisting motion control for the magnetically suspended rotor system in a control moment gyro,” IEEE/ASME Trans. Mechatronics, vol. 18, no. 5, pp. 1625–1634, Oct. 2013. [9] J. Fang, J. Sun, H. Liu, and J. Tang, “A novel 3-DOF axial hybrid magnetic bearing,” IEEE Trans. Magn., vol. 46, no. 12, pp. 4034–4045, Dec. 2010. [10] S. Lei and A. Palazzolo, “Control of flexible rotor systems with active magnetic bearings,” J. Sound Vib., vol. 314, no. 1/2, pp. 19–38, Jul. 2008. [11] J. Park and A. Palazzolo, “Magnetically suspended VSCMGs for simultaneous attitude control and power transfer IPAC service,” Trans. ASME,

[12] [13] [14]

[15]

[16]

[17] [18] [19] [20]

[21] [22] [23] [24] [25] [26]

[27] [28] [29] [30] [31]

[32]

[33]

J. Dyn. Syst., Meas. Control, vol. 132, no. 5, pp. 051001-1–051001-15, Aug. 2010. M. Ahrens, L. Kucera, and R. Larsonneur, “Performance of a magnetically suspended flywheel energy storage device,” IEEE Trans. Control Syst. Technol., vol. 4, no. 5, pp. 494–502, Sep. 1996. V. Tamisier, “Optimal control of the gyroscopic effects,” in Proc. IEEE Int. Symp. Ind. Electron., Montreal, QC, Canada, Jul. 2006, pp. 2556–2561. G. V. Brown, A. Kascak, R. H. Jansen, T. P. Dever, and K. P. Duffy, “Stabilizing gyroscopic modes in magnetic-bearing-supported flywheels by using cross-axis proportional gains,” in Proc. AIAA Guid., Navigat., Control Conf. Exhib., San Francisco, CA, USA, Aug. 2005, pp. 2005–5955. Y. Fan and J. Fang, “Experimental research on the nutational stability of magnetically suspended momentum flywheel in control moment gyroscope (CMG),” in Proc. 9th Int. Symp. Magn. Bearings, Lexington, KY, USA, Aug. 2004, pp. 116–121. T. P. Dever, G. V. Brown, K. P. Duffy, and R. H. Jansen, “Modeling and development of a magnetic bearing controller for a high speed flywheel system,” in Proc. 2nd Int. Energy Convers. Eng. Conf., Providence, RI, USA, Aug. 2004, pp. 2004–5626. W. Yu, S. Luan, and J. Fang, “Model and control law of CMG active magnetic bearing rotor,” J. Astronaut., vol. 24, no. 6, pp. 541–545, Nov. 2003. T. Wei and J. Fang, “Moving-gimbal effect and angular rate feedforward control in magnetically suspended rotor system of CMG,” J. Astronaut., vol. 26, no. 1, pp. 19–23, Jan. 2005. M. Chen and C. R. Knospe, “Feedback linearization of active magnetic bearings: Current-mode implementation,” IEEE/ASME Trans. Mechatronics, vol. 10, no. 6, pp. 632–639, Dec. 2005. R. Morales, V. Feliu, and H. Sira-Ramirez, “Nonlinear control for magnetic levitation systems based on fast online algebraic identification of the input gain,” IEEE Trans. Control Syst. Technol., vol. 19, no. 4, pp. 757– 771, Jul. 2011. Z. Sun and S. S. Ge, “Nonregular feedback linearization: A nonsmooth approach,” IEEE Trans. Autom. Control, vol. 48, no. 10, pp. 1772–1776, Oct. 2003. S. -L. Chen and C. -C. Weng, “Robust control of a voltage-controlled three-pole active magnetic bearing system,” IEEE/ASME Trans. Mechatronics, vol. 15, no. 3, pp. 381–388, Jun. 2010. J. D. Lindlau and C. R. Knospe, “Feedback linearization of an active magnetic bearing with voltage control,” IEEE Trans. Control Syst. Technol., vol. 10, no. 1, pp. 21–31, Jan. 2002. F. Wu, X. -P. Zhang, P. Ju, and M. J. H. Sterling, “Decentralized nonlinear control of wind turbine with doubly fed induction generator,” IEEE Trans. Power Syst., vol. 23, no. 2, pp. 613–621, May 2008. Z. Zhong and J. Wang, “Looper-tension almost disturbance decoupling control for hot strip finishing mill based on feedback linearization,” IEEE Trans. Ind. Electron., vol. 58, no. 8, pp. 3668–3679, Aug. 2011. B. Bahrani, S. Kenzelmann, and A. Rufer, “Multivariable-PI-based dq current control of voltage source converters with superior axis decoupling capability,” IEEE Trans. Ind. Electron., vol. 58, no. 7, pp. 3016–3026, Jul. 2011. I. A. Smadi, H. Omori, and Y. Fujimoto, “Development, analysis, and experimental realization of a direct-drive helical motor,” IEEE Trans. Ind. Electron., vol. 59, no. 5, pp. 2208–2216, May 2012. K.-H. Kim, Y.-C. Jeung, D.-C. Lee, and H.-G. Kim, “LVRT scheme of PMSG wind power systems based on feedback linearization,” IEEE Trans. Power Electron., vol. 27, no. 5, pp. 2376–2384, May 2012. T.-S. Lee and J.-H. Liu, “Modeling and control of a three-phase fourswitch PWM voltage-source rectifier in d-q synchronous frame,” IEEE Trans. Power Electron., vol. 26, no. 9, pp. 2476–2489, Sep. 2011. E. J. Davison, “The robust control of a servomechanism problem for linear time-invariant multivariable systems,” IEEE Trans. Autom. Control, vol. AC-21, no. 1, pp. 25–34, Feb. 1976. H. Karimi, E. J. Davison, and R. Iravani, “Multivariable servomechanism controller for autonomous operation of a distributed generation unit: Design and performance evaluation,” IEEE Trans. Power Syst., vol. 25, no. 2, pp. 853–865, May 2010. J. Fang and Y. Ren, “Self-adaptive phase-lead compensation based on unsymmetrical current sampling resistance network for magnetic bearing switching power amplifiers,” IEEE Trans. Ind. Electron., vol. 59, no. 2, pp. 1218–1227, Feb. 2012. Y. Ren and J. Fang, “Current-sensing resistor design to include current derivative in PWM H-bridge unipolar switching power amplifiers for magnetic bearings,” IEEE Trans. Ind. Electron., vol. 59, no. 12, pp. 4590– 4600, Dec. 2012.

REN AND FANG: HIGH-PRECISION AND STRONG-ROBUSTNESS CONTROL FOR AN MSCMG

Yuan Ren (S’11–M’12) was born in Sichuan, China, in 1982. He received the B.S. degree from Ordnance Engineering College, Shijiazhuang, China, in 2003, the M.S. degree in control theory and control engineering from Jiangsu University, Zhenjiang, China, in 2008, and the Ph.D. degree from Beihang University, Beijing, China, in 2012. He studied and conducted research at Tsinghua University, Beijing, from 2006 to 2007. He is currently a Lecturer with the Science and Technology on Inertial Laboratory and the Fundamental Science on Novel Inertial Instrument and Navigation System Technology Laboratory, Beihang Universtiy, Beijing. His main research interests include the attitude control system technology of spacecraft and novel inertial instrument and equipment technology.

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Jiancheng Fang (M’12) was born in September 1965. He received the B.S. degree from Shandong University of Technology (now Shandong University), Jinan, China, in 1983, the M.S. degree from Xi’an Jiaotong University, Xi’an, China, in 1988, and the Ph.D. degree from Southeast University, Nanjing, China, in 1996. He is the Dean of the School of Instrumentation Science and Optoelectronics Engineering, Beihang University, Beijing, China. He has authored or coauthored over 200 papers and four books. He has been granted 35 Chinese invention patents as the first inventor. His current research mainly focuses on the attitude control system technology of spacecraft, novel inertial instrument and equipment technology, inertial navigation, and integrated navigation technologies of aerial vehicles. Prof. Fang has the special appointment professorship with the title of “Cheung Kong Scholar,” which has been jointly established by the Ministry of Education of China and the Li Ka Shing Foundation. He is in the first group of Principal Scientists of the National Laboratory for Aeronautics and Astronautics of China. He received the first-class National Science and Technology Progress Award of China as the third contributor in 2006, the first-class National Invention Award of China as the first inventor, and the second-class National Science and Technology Progress Award of China as the first contributor in 2007.