International Journal of Robotics and Automation, Vol. 27, No. 3, 2012
COMPARATIVE STUDY OF SYSTEM IDENTIFICATION APPROACHES FOR ADAPTIVE TRACKING OF MEMS GYROSCOPE Juntao Fei∗,∗∗ and Yuzheng Yang∗∗
Adaptive control is an effective approach to handle parameter variations. In the presence of model uncertainties and external disturbances, sliding mode control is necessary to be incorporated into the adaptive control to improve the robust performance of control system. Adaptive sliding mode control has the advantages of combining the robustness of variable structure methods with the tracking capability of adaptive control. In the last few years, many applications have been developed using sliding mode control and adaptive control. Utkin [1], [2] showed that variable structure control is insensitive to parameters perturbations and external disturbances. Ioannou et al. [3] derived and summarized the robust adaptive control in the Lyapunov sense. Park et al. [4]–[6] presented adaptive control to drive both axes of vibration for a MEMS gyroscope. Batur et al. [7] developed a sliding mode control for a MEMS gyroscope. Leland [8] proposed an adaptive force balanced controller for tuning the natural frequency of the drive axis of a vibratory gyroscope. Oboe et al. [9] proposed a new control scheme for the driving loop, which is particularly suitable to be implemented using switching capacitor technology. Robust adaptive controllers are proposed in [10]–[13] to control the vibration of MEMS gyroscope in the presence of external disturbance. Sun et al. [14] developed a phase-domain design approach to study the mode-matched control of MEMS vibratory gyroscope. Feng et al. [15] presented an adaptive estimator-based technique to estimate the angular motion and improve the bandwidth of MEMS gyroscope. Raman et al. [16] developed a closed-loop digitally controlled MEMS gyroscope using unconstrained sigma–delta force balanced feedback control. Saukoski et al. [17] presented a novel zero-rate output and quadrature compensation method in vibratory MEMS gyroscopes. Huang et al. [18] derived new robust adaptive algorithm for tracking control of robot manipulators. Theodoridis et al. [19] presented a new adaptive neurofuzzy controller for trajectory tracking of robot manipulators. Elibai et al. [20] introduced adaptive self-tuning control of robot manipulators with periodic disturbance estimation. Shen et al. [21] developed sliding mode control for tele-robotic neurosurgical system.
Abstract In this paper, a comparative study of adaptive vibration control approaches is presented for the system identification for microelectro-mechanical systems (MEMS) z-axis gyroscope. Two adaptive methodologies such as adaptive controller and adaptive sliding mode controller are developed and compared in the aspect of algorithm derivation and Lyapunov stability analysis. The proposed adaptive control approaches can estimate the angular velocity and the damping and stiffness coefficients including the coupling terms. Numerical simulations are investigated to verify the effectiveness of the proposed control schemes, demonstrating that the robust performance of the adaptive sliding mode control system has been improved in the presence of external disturbance compared with adaptive control.
Key Words Adaptive control, sliding mode control, stability, MEMS gyroscope
1. Introduction Micro-electro-mechanical systems (MEMS) gyroscopes have become the most growing micro-sensors for measuring angular velocity in recent years due to its compact size, low cost and high sensitivity. Most MEMS gyroscopes based on Coriolis force utilize electrostatic force driven and capacitive detection. Fabrication imperfections always result in some cross stiffness and damping effects, and the performance of the MEMS gyroscope is deteriorated by the effects of time varying parameters, quadrature errors and external disturbances. Therefore, it is necessary to utilize advanced control methods to measure the angular velocity and minimize the cross coupling terms. ∗
Jiangsu Key Laboratory of Power Transmission and Distribution Equipment Technology, Hohai University, Changzhaou, 213022, People’s Republic of China; e-mail:
[email protected] ∗∗ College of Computer and Information, Hohai University, Changzhou, 213022, People’s Republic of China; e-mail:
[email protected] Recommended by Prof. B. Shirinzadeh (DOI: 10.2316/Journal.206.2012.3.206-3693)
1
In this paper, a novel adaptive control is derived for the state tracking control of MEMS gyroscope; moreover, for the purpose of comparison, a novel adaptive sliding mode control with integral switching surface which is different from the sliding surface [14] is designed to estimate the unknown system parameters in the presence of external disturbance. The novelty of the proposed adaptive control is that an additional controller is incorporated into the state feedback controller to give more freedom to design the adaptive controller, thus the error dynamics is determined by the reference model dynamics and additional controller. Moreover, a sliding mode control algorithm is incorporated into the proposed adaptive control and the adaptive sliding mode control with application to MEMS gyroscope in the presence of external disturbance is investigated. The main advantage of the integral sliding surface is that it can provide more design flexibility and simplify the design procedure. Using Lyapunov stability theory and Barbalat’s lemma, the convergence and stability of the closed-loop system and convergence property can be guaranteed. The contribution of this paper is that novel adaptive approaches are proposed to estimate the angular velocity and all unknown gyroscope parameters. A comparative study of adaptive control and adaptive sliding mode control for MEMS z-axis gyroscope is conducted to evaluate the performance index such as robustness of control system and convergence of tracking error, system parameter in the presence of model uncertainties and external disturbance. The control strategy proposed here has the following advantages compared to the existing ones: 1. The advantage of using adaptive control approaches is that an additional controller is incorporated into the state feedback controller to give more freedom to design the adaptive controller, thus the error dynamics is determined by the reference model dynamics and additional controller. This will provide more design flexibility and simplify the design procedure. The system parameters including angular velocity can be consistently estimated with the proposed adaptive controller. 2. A new adaptive sliding mode control is proposed to deal with system non-linearities such as model uncertainties and external disturbances to improve the trajectory tracking resolution and robustness of the control system. Meanwhile, the consistent estimation of system parameters including angular velocity can be obtained. Both of these features are the most important features of the proposed control as with existing ones.
Figure 1. Simplified model of a z-axis MEMS gyroscope.
In a z-axis gyroscope, by supposing the stiffness of spring in z-direction much larger than that in x, y directions, motion of proof mass is constrained to only along the x–y plan as shown in Fig. 1. Assuming that the measured angular velocity is almost constant over a long enough time interval, under typical assumptions Ωx ≈ Ωy ≈ 0, only the component of the angular rate Ωz causes a dynamic coupling between the x- and y-axes. Taking fabrication imperfections into account, which cause extra coupling between x and y axes, the motion equation of a gyroscope is simplified as follows: m¨ x + dxx x˙ + dxy y˙ + kxx x + kxy y = ux + 2mΩz y˙
(1)
m¨ y + dxy x˙ + dyy y˙ + kxy x + kyy y = uy − 2mΩz x˙
(2)
where x and y are the coordinates of the proof mass with respect to the gyro frame in a Cartesian coordinate system; dxx , dyy , kxx , kyy are damping and spring coefficients; dxy , kxy , called quadrature errors, are coupled damping and spring terms, respectively, mainly due to the asymmetries in suspension structure and misalignment of sensors and actuators, and ux,y are the control forces. The last two terms in (1) and (2), 2mΩz y, ˙ 2mΩz x, ˙ are the Coriolis forces and are used to reconstruct the unknown input angular rate Ωz . Dividing both sides of (1) and (2) by m, q0 , w02 , which are a reference mass, length and natural resonance frequency respectively, where m is the proof mass of a gyroscope, we get the form of the non-dimensional equation of motion as:
2. Dynamic Model of MEMS Gyroscope The dynamics of MEMS gyroscope is described in this section. A typical MEMS gyroscope configuration includes a proof mass suspended by spring beams, electrostatic actuations and sensing mechanisms for forcing an oscillatory motion and sensing the position and velocity of the proof mass as well as a rigid frame which is rotated along the rotation axis. Dynamics of a MEMS gyroscope is derived from Newton’s law in the rotating frame.
where
kxx mw02
x ¨ + dxx x˙ + dxy y˙ + wx2 x + wxy y = ux + 2Ωz y˙
(3)
y¨ + dxy x˙ + dyy y˙ + wxy x + wy2 y = uy − 2Ωz x˙
(4)
xy yy z → dxx , mw → dxy , mw → dyxy Ω w0 → Ω z , 0 0 kyy kxy → wx , mw 2 → wy , mw 2 → wxy .
d
dxx mw0
0
d
0
Rewriting the gyroscope models (3) and (4) in state space form as: X˙ (t) = AX (t) + Bu(t) (5) 2
where
⎡
0 ⎢ ⎢ ⎢ −ωx2 A =⎢ ⎢ ⎢ 0 ⎣ −ωxy
1
0
−dxx
−ωxy
0
0
−(dxy + 2Ωz )
−ωy2
⎡ B =⎣
3. Adaptive Control Design
⎤
⎤T 0
1
0
0
0
0
0
1
⎦ ,
ux
The block diagram of adaptive control system is shown in Fig. 2. In the adaptive control design, we consider (5) as the system model and use the assumption 3.
⎥ ⎥ −(dxy − 2Ωz ) ⎥ ⎥, ⎥ ⎥ 1 ⎦ −dyy
⎤
⎡ u=⎣
0
⎦,
uy
⎡ ⎤ x ⎢ ⎥ ⎢ ⎥ ⎢ x˙ ⎥ ⎥ X =⎢ ⎢ ⎥ ⎢y⎥ ⎣ ⎦ y˙ Figure 2. Block diagram of adaptive control for MEMS gyroscope.
The reference models xm = A1 sin(ω1 t) and ym = A2 sin(ω2 t) can be written in state space form as: ⎡ ⎤ 0 1 0 0 ⎢ ⎥ ⎢ ⎥ ⎢ −ω12 0 0 0⎥ ˙ ⎢ ⎥X m ≡ Am X m Xm = ⎢ (6) ⎥ ⎢ 0 0 0 1⎥ ⎣ ⎦ 0 0 −ω22 0
The tracking error is defined as state tracking: e (t) = X (t) − X m (t) The derivative of tracking error is: e˙ (t) = Am e (t) + (A − Am )X (t) + Bu(t)
where Am is a known constant matrix. Consider the system in (5) with external disturbance as: X˙ (t) = AX (t) + Bu(t) + f (t)
(10)
(11)
The adaptive controller can be expressed:
(7)
u(t) = K T (t)X (t) + K f e (t)
where X (t) ∈ R4 , u(t) ∈ R2 and A ∈ R4×4 is unknown constant matrix, B ∈ R4×2 is known constant matrix, f (t) ∈ R4×1 is uncertain exogenous disturbances.
(12)
where K (t) is an estimate of K ∗ , the constant matrix K f satisfies that (Am + BK f ) is Hurwitz. The estimation error is defined as
Assumption 1. f(t) has matched and unmatched terms. There exists unknown matrix of appropriate dimension fm (t) such that:
˜ (t) = K (t) − K ∗ K
(13)
Substituting (13) into (5) yields,
f (t) = Bf m (t) + f u (t)
(8) ˜ T (t)X (t) + K f e(t) X˙ (t) = Am X (t) + B K
2×1
where Bfm (t) is matched disturbance, fm (t) ∈ R and fu (t) ∈ R4×1 is unmatched disturbance. Therefore, the dynamics (7) can be rewritten as X˙ (t) = AX (t) + Bu(t) + Bf m + f u
(14)
Then, we have the tracking error dynamic equation: ˜ T (t)X (t) e˙ (t) = (Am + BK f )e(t) + B K
(9)
(15)
The update law is derived based on the state X (t), and tracking error e(t), which is shown as:
Assumption 2. fm and fu are bounded such as fm (t) ≤ αm and fu (t) ≤ αu , where αm and αu are known positive constants.
˜˙ T (t) = K ˙ T (t) = −MB T Pe (t)X T (t) K
(16)
∗
Assumption 3. There exists a constant matrix K such that the following matching condition A + BK∗T = Am can be satisfied.
where M = diag{m1 m2 } is positive definite and P is positive definite and symmetric. The stability analysis of the proposed adaptive controller is summarized in Theorem 1.
The control target for MEMS gyroscope is (i) to design an adaptive controller so that the trajectory of X (t) can track the state of reference model X m (t); (ii) to estimate the angular velocity of MEMS gyroscope and all unknown gyroscope parameters.
Theorem 1. The adaptive controller (12) with the adaptive law (16) applied to the system (5) guarantees that all closed-loop signals are bounded, the tracking error 3
presented in the presence of both matched and mismatched external disturbances. Consider (3) and define the tracking error e (t) = X (t) − X m (t), then its derivative is:
goes to zero asymptotically and the controller parameter K converges to its true value if the condition of persistent excitation can be satisfied. Proof : Define a Lyapunov function: V =
1 T 1 ˜ T] ˜ M −1 K e Pe + tr[K 2 2
e˙ (t) = Am e (t) + (A − Am )X (t) + Bu(t) + Bf m (t) + f u (t) (20)
(17)
The proportional-integral sliding surface s = 0 is defined as:
Differentiating V with respect to time yields, ˜˙ T ] ˜ M −1 K V˙ = e T P e˙ + tr[K ˜˙ T ] ˜ M −1 K ˜ T X + tr[K = −e Qe + e PB K T
T
(18)
s (t) = λe (t) −
where P (Am + BK f ) + (Am + BK f )T P = −Q , Q is a positive definite matrix. Substituting the adaptive law (16) into (18) obtains, V˙ = −e T Qe ≤ −λmin (Q )e ≤ 0
0
t
λ(Am + BK e )e (t) dτ
(21)
where λ ∈ R2×4 satisfies that λB is non-singular, K e satisfies that (Am + BK e ) is Hurwitz. The derivative of the sliding surface becomes:
(19)
s˙ (t) = λ(A − Am )X (t) + λBu(t) + λBf m (t) + λf u (t) − λBK e e (t)
where λmin (Q) is the eigenvalue of matrix Q with minimum real part. The inequality V˙ ≤ − λmin (Q)e implies that e t is integrable as 0 e dt ≤ λmin1(Q ) [V (0) − V (t)]. Since t lim 0 e dt is bounded and e˙ is bounded, according to t→∞ Barbalat’s lemma, e will converge to zero asymptotically, lim e (t) = 0. Moreover, from the adaptive law (16), ac-
(22)
The equivalent control u eq can be obtained by setting s˙ = 0: u eq (t) = −(λB )−1 λ(A − Am )X (t) + K e e (t) − f m (t) − (λB )−1 λf u (t)
= K ∗T X (t) + K e e (t) − f m (t) − (λB )−1 λf u (t)
t→∞
cording to the persistence excitation theory [1], if X(t) is persistent excitation signal, it can be guaranteed that ˜ (t) → 0. K
(23) Then adaptive sliding mode controller can be expressed as:
Remark 1. If an external disturbance is included in the dynamical system as in (7), it is not easy to have asymptotical convergence of the error signal to zero as time goes to infinity using the proposed adaptive control as in Section 3.
u(t) = K T (t)X (t) + K e e (t) − ρ(λB )−1
s (t) s (t)
(24)
where K (t) is an estimate of K ∗ . The last component of (24) is designed to address the matched and unmatched dis us1 s turbance, which is given as u s = = −ρ(λB )−1 , s us2
4. Adaptive Sliding mode Control Design A novel adaptive sliding mode control strategy with a proportional and integral sliding surface for MEMS gyroscopes is proposed as in Fig. 3. In this section, the assumptions 1 and 2 are effective. A detailed study of the proportional-integral sliding mode control algorithm is
where ρ is a constant. Define the estimation error as: ˜ (t) = K (t) − K ∗ K
(25)
Substituting (24) and (25) into (9) gets: ˜ T (t)X (t) + BK e e (t) + Bf (t) X˙ (t) = Am X (t) + B K m −1 s (t) + f u (t) − B ρ (λB ) (26) s (t) Then, the derivative of tracking error can be obtained: T
˜ (t)X (t) + Bf (t) e˙ (t) = (Am + BK e )e (t) + B K m −1 s (t) + f u (t) − B ρ(λB ) (27) s (t)
Figure 3. Block diagram of adaptive sliding mode control for MEMS gyroscope. 4
Thus the dynamics of sliding surface s(t) can be derived
and with the special choice of λ, it can be concluded lim e(t) = 0. From the parameter updating law t→∞ ˜˙ T (t) = K ˙ T (t) = −MB T λT sX T , according to the perK
as: T
˜ (t)X (t)+λBf (t)+λfu (t)−ρ s˙ (t) = λB K m
s (t) (28) s (t)
sistence excitation theory [1], if X satisfies the persistent ˜ → 0. excitation condition, then (16) guarantees that K T It can be shown if ω1 = ω2 , XX has full rank, then excitation can be called persistent.
The update law for the estimated parameters is chosen as follows: ˜˙ T (t) = K ˙ T (t) = −MB T λT sX T (t) K
Remark 2. Both the tracking errors are state tracking in the proposed adaptive control (Section 3) and proposed adaptive sliding mode control (Section 4), but their derivatives are different because only the external disturbances are considered in the adaptive sliding mode control design. Therefore (15) and (20) of the error dynamics are completely different between these two control methodologies.
(29)
where it is based on the state X (t) and sliding surface s (t). The stability analysis of the proposed adaptive sliding mode control can be summarized in Theorem 2. Theorem 2. The adaptive controller (24) with the adaptive law (29) applied to the system (9) guarantees that all closed-loop signals are bounded with the choice of ρ ≥ λBαm + λαu + η, the tracking error and sliding surface go to zero asymptotically, and the controller parameter K converges to its true value if the condition of persistent excitation can be satisfied.
Remark 3. To eliminate the chattering, a smooth sliding mode component is proposed as u(t) = K T (t)X (t) + K e e − (λB )−1 ρ
Proof : Define a Lyapunov function candidate: V =
1 T 1 ˜ T] ˜ M −1 K s s + tr[K 2 2
(33)
where ε > 0 is small constant. 5. Simulation Example
(30)
The proposed adaptive control and adaptive sliding mode control is evaluated on the MEMS gyroscope model [2], [4]. For the purpose of model uncertainties, there are ±10% parameter variations for the spring and damping coefficients with respect to their nominal values and ±10% magnitude changes in the coupling terms, i.e., dxy and ωxy , again with respect to their nominal values. Random variable signal with zero mean and unity variance is considered as external disturbance. The parameters of the MEMS gyroscope are as follows:
Differentiating V with respect to time yields: ˜˙ T ] ˜ M −1 K V˙ = s T s˙ + tr[K
˜ T (t)X (t) + λBf + λf − ρ s = s T λB K m u s ˜˙ T ] ˜ M −1 K + tr[K
s ˜ T(t)X (t) + s T λBf m + s T λf u + s T λB K s ˜ M −1 K ˜˙ T ] + tr[K (31)
= −s Tρ
m = 0.57e−8 kg, −6
dxy = 0.0429e
Substituting the adaptive law (29) into (31) yields:
dxx = 0.429e−6 N s/m,
w0 = 1 kHz,
+ s λB f m + s λf u
dyy = 0.687e−6 N s/m,
N s/m,
kxx = 80.98 N/m,
V˙ = −ρs + s T λBf m + s T λf u ≤ −ρs
kxy = 5 N/m,
q0 = 10
−6
kyy = 71.62 N/m,
m.
The unknown angular velocity is assumed Ωz = 5.0 rad/s and the initial condition on K matrix is The desired motion trajectories are K (0) = 0.95K ∗ . xm = sin(w1 t) and ym = 1.2 sin(w2 t), where w1 = 6.71 kHz and w2 =5.11 kHz. The adaptive gain of (16) is
≤ −ρs + s λB αm + s λαu = −s [ρ − λB αm + λαu ]
s s + ε
(32)
with the choice of ρ ≥ λB αm + λαu + η, where η is a positive constant, V˙ becomes negative semi-definite, i.e., V˙ ≤ −ηs . This implies that the trajectory reaches the sliding surface in finite time and remains on the sliding surface. The fact that V˙ is negative semi˜ are all bounded. The definite ensures that V , s and K inequality V˙ ≤ −ηs implies that s is integrable as t t s dt ≤ η1 [V (0) − V (t)]. and lim 0 s dt is bounded. 0 t→∞ t Since lim 0 s dt and s˙ are bounded, Barbalat lemma
M = diag 20 20 . The Kf in (15) is chosen as ⎡ ⎤ −10000 −10000 1000 20000 ⎦. The Ke Kf = ⎣ −1000 −1000 −1000 −1000 and sliding mode matrix λ in (21) are ⎡ ⎤ chosen as Ke = ⎣
−10000
−10000
1000
20000
−1000
−1000
−1000
−1000
⎡
t→∞
guarantees that lim s (t) = 0, then from the definition t→∞ t of sliding surface s (t) = λe (t) − 0 λ(Am + BK e )e (t)dτ
⎣ 5
0
10
0
0
0
0
0
10
⎤
⎦, respectively.
⎦
and
λ=
With the choice of
Figure 7. Adaptation of angular velocity using adaptive sliding mode control.
Figure 4. The tracking error using adaptive control.
Figure 5. The tracking error using adaptive sliding mode control.
Figure 8. Adaptation of control parameters using adaptive control.
Figure 6. Adaptation of angular velocity using adaptive control. 6
Figure 10. Convergence of the sliding surface s(t).
Figure 9. Adaptation of control parameters using adaptive sliding mode control. ⎡ λ= ⎣
Figure 11. The smooth sliding mode control input.
⎤ 0
10
0
0
⎦, from the convergence of s(t) 0 0 0 10 to zero, it can be easily concluded that e(t) convergences to zero. The switching gain in (24) is chosen as ρ = diag{ 10000 M = diag{ 20
10000 }.
angular velocity using adaptive sliding mode control has larger overshoot at the beginning but much smaller rise time than that using adaptive control. Figure 10 demonstrates that the sliding surfaces converge to zero asymptotically. It is observed in Fig. 11 that the chattering has been diminished using the smooth sliding mode controller. The robust performance of adaptive sliding mode control in the presence of model uncertainties and external disturbances is better than that of the adaptive control because the system non-linearities such as model uncertainties and external disturbances cannot be compensated in the adaptive controller but can be incorporated into the adaptive sliding mode control.
The adaptive gain in (29) is
20 }, ε = 0.01 in (33).
Figures 4 and 5 compare the tracking errors, where e1 = x − xm denotes tracking error in x-axle, e3 = y − ym denotes tracking error in y-axle. It is observed that the tracking errors all converge to zero asymptotically and the tracking error of adaptive sliding mode control has better transient performance than that of adaptive control. Figures 6–9 compare the adaptation of the angular velocity and controller, parameters using these two different controllers, respectively. It can be observed from these figures that the former achieves better parameter identification performance than the latter. The estimate of
6. Conclusion The designs of adaptive control and adaptive sliding mode control for MEMS gyroscope are investigated and 7
compared in this paper. Novel adaptive approaches are proposed and Lyapunov stability conditions are established. The difference between these two adaptive approaches is that model uncertainties and external disturbances can be incorporated into the adaptive sliding mode algorithm to improve the robustness of the control system. Numerical simulations shown that if the persistent excitation can be satisfied, all unknown gyroscope parameters, including the angular velocity, converge to their true values, and tracking error is going to zero asymptotically. In the presence of model uncertainties and external disturbance, adaptive sliding mode control has better robustness compared with adaptive control.
[16] J. Raman, E. Cretu, P. Rombouts, and L. Weyten, A closedloop digitally controlled MEMS gyroscope with unconstrained sigma-delta force-feedback, IEEE Sensors Journal, 9 (3), 2009, 297–305. [17] M. Saukoski, L. Aaltonen, and K. Halonen, Zero-rate output and quadrature compensation in vibratory MEMS gyroscopes, IEEE Sensors Journal, 7 (12), 2007, 1639–1652. [18] C.Q. Huang, X.F. Peng, X.G. Wang, and S.J. Shi, New robustadaptive algorithm for tracking control of robot manipulators, International Journal of Robotics and Automation, 23 (2), 2008, 67–78. [19] D.C. Theodoridis, Y.S. Boutalis, and M.A. Christodoulou, A new adaptive neuro-fuzzy controller for trajectory tracking of robot manipulators, International Journal of Robotics and Automation, 26 (1), 2011, 64–75. [20] A. Delibai, E. Zergeroglu, I.B. Kukdemiral, and G. Cansever, Adaptive self-tuning control of robot manipulators with periodic disturbance estimation, International Journal of Robotics and Automation, 24 (1), 2010, 48–56. [21] Y. Shen, W. Shen, and J. Gu, Sliding-mode control for telerobotic neurosurgical system, International Journal of Robotics and Automation, 22(1), 2007, 19–31.
Acknowledgements The authors thank the anonymous reviewers for useful comments that improved the quality of the manuscript. This work is supported by National Science Foundation of China under Grant No. 61074056, The Natural Science Foundation of Jiangsu Province under Grant No. BK2010201, Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry.
Biographies Juntao Fei received the B.S. degree in Electrical Engineering from Hefei University of Technology, China, in 1991, the M.S. degree in Electrical Engineering from University of Science and Technology of China in 1998, and the M.S. and Ph.D. degrees in Mechanical Engineering from The University of Akron, OH, USA, in 2003 and 2007, respectively. He was a Visiting Scholar at University of Virginia, VA, USA, from 2002 to 2003. He was a Postdoctoral Research Fellow at University of Louisiana, LA, USA, from 2007 to 2009. He is currently a Professor at Hohai University, China. He has authored and/or coauthored more than 70 referred technical papers and 3 books. His research interests include adaptive control, robotics and control, intelligent control, dynamics and control of MEMS, and smart materials and structures.
References [1] V.I. Utkin, Variable structure systems with sliding modes, IEEE Transactions on Automatic Control, 22, 1977, 212–222. [2] V.I. Utkin, Sliding modes in control and optimization (SpringerVerlag, 1992). [3] P. Ioannou and J. Sun, Robust adaptive control (Prentice-Hall, 1996). [4] S. Park and R. Horowitz, Adaptive control for z-axis MEMS gyroscope, Proc. American Control Conf., 2001, 1223–1228. [5] S. Park and R. Horowitz, New adaptive mode of operation for MEMS gyroscopes, ASME Transaction Dynamic Systems, Measurement and Control, 126, 2004, 800–810. [6] S. Park, R. Horowitz, H. Sung, and Y. Nam, Trajectoryswitching algorithm for a MEMS gyroscope, IEEE Transactions on Instrumentation and Measurement, 56 (6), 2007, 2561–2569. [7] C. Batur and T. Sreeramreddy, Sliding mode control of a simulated MEMS gyroscope, ISA Transactions, 45 (1), 2006, 99–108. [8] R. Leland, Adaptive control of a MEMS gyroscope using Lyapunov methods, IEEE Transactions on Control Systems Technology, 14 (2), 2006, 278–283. [9] R. Oboe, R. Antonello, E. Lasalandra, G.S. Durante, and L. Prandi, Control of a Z-axis MEMS vibrational gyroscope, IEEE Transactions on Mechatronics, 10 (2), 2005, 364–370. [10] J. Fei and C. Batur, Robust adaptive control for a MEMS vibratory gyroscope, International Journal of Advanced Manufacturing Technology, 42 (3), 2009, 293–300. [11] J. Fei and C. Batur, A novel adaptive sliding mode control with application to MEMS gyroscope, ISA Transactions, 48 (1), 2009, 73–78. [12] J. Fei, X. Fan, and W. Dai, Robust tracking control of triaxial angular velocity sensors using adaptive sliding mode approach, International Journal of Advanced Manufacturing Technology, 52, 2011, 627–636. [13] J. Fei, Robust adaptive vibration tracking control for a MEMS vibratory gyroscope with bound estimation, IET Control Theory and Application, 4 (6), 2010, 1019–1026. [14] S. Sung and W. Sung, On the mode-matched control of MEMS vibratory gyroscope via phase-domain analysis and design, IEEE/ASME Transactions on Mechatronics, 14 (4), 2009, 446–455. [15] Z. Feng and M. Fan, Adaptive input estimation methods for improving the bandwidth of microgyroscopes, IEEE Sensors Journal, 7 (4), 2007, 562–567.
Yuzheng Yang received his B.S. degree in Electrical Engineering from Hohai University in 2011. He is currently working towards the M.S. degree in Control Science and Engineering at Hohai University. His research interests are adaptive control, neural network control, modelling and control of MEMS.
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