Generalized extended state observer based control for systems with mismatched uncertainties

The standard extended state observer based control (ESOBC) method is only applicable for a class of single-input-single-output essential-integral-chain systems with matched uncertainties. It is noticed that systems with nonintegral-chain form and mismatched uncertainties are more general and widely exist in practical engineering systems, where the standard ESOBC method is no longer available. To this end, it is imperative to explore new ESOBC approach for these systems to extend its applicability. By appropriately choosing a disturbance compensation gain, a generalized ESOBC (GESOBC) method is proposed for nonintegral-chain systems subject to mismatched uncertainties without any coordinate transformations. The proposed method is able to extend to multi-input-multi-output systems with almost no modification. Both numerical and application design examples demonstrate the feasibility and efficacy of the proposed method

Generalized Extended State Observer Based Control for Systems With Mismatched Uncertainties

This article was published in the journal IEEE Transactions on Industrial Electronics [© IEEE]. The definitive version is available at: http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=6117083. © 2012 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.The standard extended state observer based control (ESOBC) method is only applicable for a class of single-input-single-output essential-integral-chain systems with matched uncertainties. It is noticed that systems with nonintegral-chain form and mismatched uncertainties are more general and widely exist in practical engineering systems, where the standard ESOBC method is no longer available. To this end, it is imperative to explore new ESOBC approach for these systems to extend its applicability. By appropriately choosing a disturbance compensation gain, a generalized ESOBC (GESOBC) method is proposed for nonintegral-chain systems subject to mismatched uncertainties without any coordinate transformations. The proposed method is able to extend to multi-input-multi-output systems with almost no modification. Both numerical and application design examples demonstrate the feasibility and efficacy of the proposed method

High-Order Robotic Joint Sensing with Multiple Accelerometer and Gyroscope Systems

In recent years work into larger humanoid robotic systems and other highly dynamic legged robots has driven a need to increase control system performance and parameter estimation capability. This in turn has seen an increase in the use of higher order joint space derivative terms such as acceleration and jerk being introduced into the control systems and estimators. Although it is evident that the inclusion of these terms can increase the performance of the estimators and control systems, there is a distinct lack of high quality sensors or systems capable of providing this information. Instead it is apparent that those researchers aiming to employ the acceleration and jerk terms are having to resort to other poor quality methods of acquiring the information, which in turn limits the capability of the systems. The works examined suggest that in particular, access to higher quality sources of joint space acceleration measurement or estimation can lead to increases in the performance of control systems and estimators employing these terms. The aim of this work is to investigate the feasibility and capability of a new joint space sensor based on positional encoders and MEMs accelerometers that can estimate angular joint position, velocity and acceleration. The system proposed employs the accelerometer only IMU (AO-IMU) concept to estimate link angular acceleration and velocity in an inertial frame. This concept is then extended to obtain these angular components relative to the previous link. Sensor fusion techniques are then tasked with estimating the velocity states of the AO-IMU and ensuring consistency across the relative states. Two calibration schemes are proposed and demonstrated to correct for the bias, gain and cross axis effects present in the inertial sensors and to correct for the non-ideal placement of the sensors on the body frame. The performance of the system is compared to three online methods common in the literature with significant increases in performance being shown across all states, particularly in the acceleration and velocity states. The base sensor system is then augmented to explore alternate inertial sensor arrangements and structures. In this the effects of adding MEMs gyroscopes to the sensor system are studied and shown to have a small positive effect on the relative velocity state. The addition of multiple relative accelerometers are then studied to examine whether the initial system design choices could be improved upon, with this study showing greater increases in the relative acceleration and velocity states performance. Taking inspiration from the positive results of the multiple relative accelerometer study, an alternate sensor system structure is proposed whereby the robot is instrumented with AO-IMUs and the relative accelerometers omitted. This augmented structure may prove more useful in larger robotic systems. This study initially showed poor results with the low angular velocities experienced by the upper link AO-IMU introducing bias errors. This was corrected for by the inclusion of gyroscopes with the resulting system exhibiting good performance. The findings within this work show that with some modification, the AO-IMU is capable of directly measuring the relative angular acceleration and velocity of a robotic link. When combined with positional sensors this system can be extended to obtain high quality measurements of a joint’s angular position, velocity and acceleration.Thesis (MPhil) -- University of Adelaide, School of Mechanical Engineering, 201

Automatic Stabilization of a Riderless Bicycle using the Active Disturbance Rejection Control Approach

[ES] Este trabajo propone una estrategia de Control por Rechazo Activo de Perturbaciones (ADRC), usando observadores extendidos de perturbación, para estabilizar una bicicleta en movimiento, sin conductor y con una velocidad de avance variable. Aunque la bicicleta tiene una dinámica inestable y no lineal alrededor de su posición vertical, que puede modelarse como un sistema Lineal de Parámetros Variantes (LPV) dependientes de la velocidad, el diseño del controlador usa un modelo simplificado de parámetros concentrados invariantes en el tiempo y una velocidad nominal constante. El esquema ADRC agrupa las discrepancias entre el modelo simplificado y la planta, junto con las perturbaciones externas en una señal aditiva unificada, que es estimada a través del observador y realimentada mediante una ley de control lineal para rechazarla. La efectividad de la estrategia es validada mediante una co-simulación entre ADAMS y MATLAB, la cual exhibe un alto desempeño y robustez sobre un modelo dinámico virtual de la bicicleta, sometida a perturbaciones externas severas y variaciones de parámetros.[EN] This work proposes an ADRC (Active Disturbance Rejection Control) strategy by disturbance extended observers to stabilize a moving riderless bicycle with a variant forward speed. Although the bicycle has an unstable and non-linear dynamics when in its upright position, which can be modeled as a LPV (Linear-Parameter-Varying) system that depends on the forward speed, a simplified time-invariant and lumped-parameter model, with an nominal constant forward speed is used in the controller design. ADRC scheme groups discrepancies between the simplified model and the plant, with external disturbances into an equivalent additive unified disturbance signal at input, which is estimated via the observer and rejected through a linear control law. The effectiveness of this strategy is validated by a co-simulation between ADAMS and MATLAB, which exhibits a high performance and robustness in a virtual dynamic model of the bicycle, submitted to severe external disturbances and parameter variations. Baquero-Suárez, M.; Cortes-Romero, J.; Arcos-Legarda, J.; Coral-Enriquez, H. (2017). Estabilización Automática de una Bicicleta sin Conductor mediante el Enfoque de Control por Rechazo Activo de Perturbaciones. Revista Iberoamericana de Automática e Informática industrial. 15(1):86-100. https://doi.org/10.4995/riai.2017.8832OJS86100151Ai-Buraiki, O., Thabit, M. B., Jun 2014. Model Predictive Control Design Approach for Autonomous Bicycle Kinematics Stabilization. In: 22nd Mediterranean Conference of Control and Automation (MED). pp. 380-383. https://doi.org/10.1109/MED.2014.6961401Bickford, D., Davison, D. E., May 2013. Systematic Multi-Loop Control for Autonomous Bicycle Path following. In: 2013 26th IEEE Canadian Conference on Electrical and Computer Engineering (CCECE). pp. 1-5. https://doi.org/10.1109/CCECE.2013.6567714Brizuela, J., Astorga, C., Zavala, A., Pattalochi, L., Canales, F., Dec 2016. State and Actuator Fault Estimation Observer Design Integrated in a Riderless Bicycle Stabilization System. fISAg Transactions 61, 199-210.Canudas deWit, C., Tsiotras, P., 1999. Dynamic Tire Friction Models for Vehicle Traction Control. In: Proceedings of the 38th IEEE Conference on Decision and Control. Vol. 4. pp. 3746-3751. https://doi.org/10.1109/CDC.1999.827937Cerone, V., Andreo, D., Larsson, M., Regruto, D., Oct 2010. Stabilization of a Riderless Bicycle, A Linear-Parameter-Varying Approach [applications of control]. Control Systems, IEEE 30 (5), 23-32. https://doi.org/10.1109/MCS.2010.937745Cortés Romero, J., Luviano Juárez, A., Álvarez Salas, R., Sira Ramírez, H., Aug 2010. Fast Identification and Control of an Uncertain Brushless DC Motor Using Algebraic Methods. In: 12th International Power Electronics Congress (CIEP). pp. 9-14. https://doi.org/10.1109/CIEP.2010.5598844Cortés Romero, J., Ramos, G., Coral Enriquez, H., Aug 2014. Generalized Proportional Integral Control for Periodic Signals under Active Disturbance Rejection Approach. ISA Transactions 53 (6), 1901-1909. https://doi.org/10.1016/j.isatra.2014.07.001Emaru, T., Tsuchiya, T., Dec 2005. Research on Estimating Smoothed Value and Differential Value by using Sliding Mode System. IEEE Transactions on Robotics and Automation 21 (6), 391-402.Gao, B., Junpeng Shao, Xiaodong Yang, Nov 2014. A Compound Control Strategy Combining Velocity Compensation with ADRC of Electroydraulic Position Servo Control System. ISA Transactions 53 (6), 1910-1918. https://doi.org/10.1016/j.isatra.2014.06.011Goldstein, H., 1953. Classical Mechanics, 3rd Edition. Addison-Wesley, Ch. 5, pp. 184-188.Gordon Wilson, D., Jim Papadopoulos, 2004. Bicycling Science, 3rd Edition. The MIT Press, Ch. 8, pp. 263-310.Hwang, C.-L., Hsiu-Ming Wu, Shih, C.-L., May 2009. Fuzzy Sliding Mode Underactuated Control for Autonomous Dynamic Balance of an Electrical Bicycle. IEEE Transactions on Control Systems Technology 17 (3), 658-670. https://doi.org/10.1109/TCST.2008.2004349Jin, H., Yang, D., Liu, Z., Zang, X., Li, G., Zhu, Y., Dec 2015. A Gyroscope-Based Inverted Pendulum with Application to Posture Stabilization of Bicycle Vehicle. In: 2015 IEEE International Conference on Robotics and Biomimetics (ROBIO). pp. 2103-2108. https://doi.org/10.1109/ROBIO.2015.7419084Kooijman, J. D. G., Meijaard, J. P., Papadopoulos, J. M., Ruina, A., Schwab, A. L., 2011. A Bicycle can be Self-Stable without Gyroscopic or Caster Effects. Science 332 (6027), 339-342. https://doi.org/10.1126/science.1201959Kooijman, J. D. G., Schwab, A. L., Meijaard, J. P., May 2008. Experimental Validation of a Model for the Motion of an Uncontrolled Bicycle. Multibody System Dynamics 19 (1), 115-132. https://doi.org/10.1007/s11044-007-9050-xLam, P. Y., Sep 2011. Gyroscopic Stabilization of a Kid-Size Bicycle. In: 2011 IEEE 5th International Conference on Cybernetics and Intelligent Systems (CIS). pp. 247-252. https://doi.org/10.1109/ICCIS.2011.6070336Lewis, F. L., Popa, L. X. D., 2008. Optimal and Robust Estimation, with an Introduction to Stochastic Control Theory, 2nd Edition. CRC Press, Ch. 3, pp. 151-204.Limebeer, D. J. N., Sharp, R. S., Oct 2006. Bicycles, Motorcycles, and Models. IEEE Control Systems 26 (5), 34-61. https://doi.org/10.1109/MCS.2006.1700044Meijaard, J., Papadopoulos, J. M., Ruina, A., Schwab, A., 2007. Linearized Dynamics Equations for the Balance and Steer of a Bicycle: a Benchmark and Review. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 463 (2084), 1955-1982. https://doi.org/10.1098/rspa.2007.1857Michini, B., Sean Torrez, 2007. Autonomous Stability Control of a Moving Bicycle. Tech. rep., Massachusetts Institute of Technology, USA, 77 Massachusetts Ave, Rm 33-336 - Cambridge MA 02139.Neimark, J. I., N. A. Fufaev, 2004. Translations of Mathematical Monographs. In: Dynamics of Nonholonomic Systems. Vol. 33. American Mathematical Society, Ch. 6, pp. 330-373.Nenner, U., Linker, R., Gutman, P.-O., 2010. Robust Feedback Stabilization of an Unmanned Motorcycle. Control Engineering Practice 18 (8), 970-978. https://doi.org/10.1016/j.conengprac.2010.04.003Papadopoulos, J. M., 1987. Bicycle Steering Dynamics and Self-stability: A Summary Report on Work in Progress. Cornell bicycle research project, Cornell University, Ithaca, NY.Schwab, A., Meijaard, J., Papadopoulos, J., 2005a. Benchmark Results on the Linearized Equations of Motion of an Uncontrolled Bicycle. Journal of Mechanical Science and Technology 19 (1), 292-304. https://doi.org/10.1007/BF02916147Schwab, A. L., J. P. Meijaard, Papadopoulos, J. M., Aug 2005b. A Multibody Dynamics Benchmark on the Equations of Motion of an Uncontrolled Bicycle. In: Proceedings of the Fifth EUROMECH Nonlinear Dynamics Conference. pp. 511-521.Schwab, A. L., Meijaard, J. P., May 2013. A Review on Bicycle Dynamics and Rider Control. Vehicle System Dynamics 51 (7), 1059-1090. https://doi.org/10.1080/00423114.2013.793365Schwab, A. L., Meijaard, J. P., Kooijman, J. D. G., Aug 2012. Lateral Dynamics of a Bicycle with a Passive Rider Model: Stability and Controllability. Vehicle System Dynamics 50 (8), 1209-1224. https://doi.org/10.1080/00423114.2011.610898Srivastava, S., Pandit, V., 2016. A PI/PID Controller for Time Delay Systems with Desired Closed Loop Time Response and Guaranteed Gain and Phase Margins. Journal of Process Control 37, 70-77. https://doi.org/10.1016/j.jprocont.2015.11.001Åström, K. J., Hägglund, T., 1995. PID Controllers: Theory, Design, and Tuning, 2nd Edition. ISA, Ch. 3, pp. 80-92.Åström, K. J., Klein, R. E., Lennartsson, A., Aug 2005. Bicycle Dynamics and Control: Adapted Bicycles for Education and Research. IEEE Control Systems 25 (4), 26-47. https://doi.org/10.1109/MCS.2005.1499389Su, Y. X., Zheng, C. H., Dong Sun, Duan, B. Y., Aug 2005. A Simple Nonlinear Velocity Estimator for High-Performance Motion Control. IEEE Transactions on Industrial Electronics 52 (4), 1161-1169. https://doi.org/10.1109/TIE.2005.851598Sun, B., Zhiqiang Gao, Oct 2005. A DSP-based Active Disturbance Rejection Control Design for a 1-Kw H-bridge DC-DC Power Converter. IEEE Transactions on Industrial Electronics 52 (5), 1271-1277. https://doi.org/10.1109/TIE.2005.855679Tanelli, M., Schiavo, F., Savaresi, S. M., Ferretti, G., Oct 2006. Object-Oriented Multibody Motorcycle Modelling for Control Systems Prototyping. In: IEEE International Conference on Control Applications. pp. 2695-2700.Whipple, F., 1899. The Stability of the Motion of a Bicycle. Quart. J. Pure Appl. Math. 30 (120), 312-348.Yuanyuan, F., Runjia, D., Yuping, X., 2017. Steering Angle Balance Control Method for Rider-Less Bicycle Based on ADAMS. Springer Singapore, Singapore, Ch. 1, pp. 15-31