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033 Nonlinear control of a spatial multi-axis servo-hydraulic test facility
524
Abstracts
measurements for different relay output amplitudes. The resulting nonlinear PID controller contains stmic nonlinearities obtained by solving an inverse desoriHng function problem. Examples show the application of the methods to nonlinear planu where only the gain or both the gain and phase of the frequency response depend on the input amplitude. 032
Application of Nonlinear Control Theory to Path Tracking Control of Articulated Vehicles with Double Trailers M. Sampel, T. Kobayashl, pp 129-132
"lifts paper describes the design of a path-tracking controller for an articulated vehicle with double trailers, using time-scale transformation and exact linearization techniques, developed in nordinear control theory. The simulation shows that the proposed controller works satisfactorily, and the aRiculated vehicle with double trailers follows the desired path even when it is moving backwards. 033
Nonlinear Control of a Spatial Multi-Axis Servo. Hydraulic Test Facility H. Hahn, K.-D. Lelmimch, X. Zhang, pp 133-136
037
The paper solves a tracking problem for a class of feedback lineafizable systems in the presence of disturbances and parameter uncertainties. An internal model of the exogenous signals is augmented with the system, and a robust, observer-based, output feedback controller is designed to achieve asymptotic tracking.
038
034
A Stable Nonlinear Observer Design for Permanent. Magnet Synchronous Motors Knan-Teck Chang, Teck-Seng Low, Tong-Heng Lee, pp 137-140
The application of vector control techniques in ac drives demands accurate position and speed feedback information for the current control and servo control loops. This paper describes the design of a stable speed obse~er system suitable for use with permanentmagnet synchronous motors (PMSM) as a software transducer. The observer is developed from the dq model of the machine. A technique employing state detection and eigenvaiue confinement is used to achieve global stabih'ty and consistent convergency of the observer system.
035
New Results eat Feedback Equivalence to Passive Systems G.L. Santosuesso, PIP 141.144
This paper is concerned with the problem of rendering a nonlinear system passive via static-state feedback when there is a direct input-ootput feedthrough. It extends a solution recently proposed in the literature ff the output of the system is exclusively a function of the state, and shows that, under mild regularity assumptions, the necessary and sufficient conditions for a nonlinear system to he feedback equivalent to a passive one are: being inve~fible with relative order 1, and being weakly minirman-phase.
036
Observers with Asymptotic Gain for a Class of Linear Time-Varying Systems with Singularity J. IAvine, Guchuan Zhu, pp 145-148
This paper presents a sufficient condition for the existence of an observer with asymptotic gain, namely with a constant gain when the system is expressed in terms of its fastest time-scale. This condition crucially depends on the concept of asymptotic observability. When this property does not hold, an observer with asymptotic gain may net exist' whereas observers defined on a finite horizon may be well defined.
Semi-Global Stabilization by Dynamic Output Feedback for Minimum Phase Systems A. Ted, L. Praly, pp 153-156
The output feedback stabilization problem for systems in an "observer canonical form" is addressed. Setting a goal of semiglobal stabilization allows the removal of the previous assumption that the inverse dynamics are input-to-state stable. Further, it permits a completely linear, dynamic output feedback solution. Similar to previous results, local growth conditions are required on the vector fields of the system to guarantee convergence to the origin. 039
This paper presents a nonlinear control concept of a special multiaxis servohydraulic test facility. Based on nonlinear model equations including the servohydraufic actuator dynamics and the test table and payload mechanics, a global nonlinear diffeommphism is derived which maps the model equations into nonlinear can~mical form. Using symbolic languages, a nonlinear control law is developed and calculated, based on exact linearization techniques. The efficiency and applicability of this control concept with respect to the tracking and decoupling behaviour of the test facility are demonstrated by computer simulations.
Robust Servomechanism Output Feedback Controllers for a Clam of Feedback Linearizable Systems H.K. Khalil, pp 149-152
An Approximate Frobenlus Theorem J. Hauser, Zhigang Xu, pp 157-160
In this paper, the authors consider the approximate integrability of a smooth nonsingular distribution around a manifold. They give suffident conditions for the distribution to be order p-1 integrable around a manifold. If the distribution is transverse to the manifold, then the sufficient conditions are also necessary. Except for the error terms, the result is similar to the Frobenius Theorem. An example is used to show the application of the approximate Frobunins Theorem to the approximate feedback linearization of a nonlinear control system about the equilibrimn manifold. O4O Feedback Implementability of Sliding Modes in Nonlinear Control Systems G. Bartolini, V. Utkin, T. Zolez~, pp 161-163 The paper considers general multivariable control systems, described by nonlinear ordinary differential equations. Given any sliding manifold in the state space and any ideal sfiding motion on it, an explicit control algorithm is found, which allows the same dynamic behaviour of the ideal motion to be obtained, up to any fixed tolerance, by using the trajectories of a new control system. This system is all'me in the control variables, and is obtained by transforming the original one via a suitable switching logic. The affine dependence on the control variables guarantees the fulfilment of the approximability property, thereby extending the scope of the theory.
041
Exponential Stabilization of Uncertain Nonlinear Systems by a Reducod-Order Compensator Engin Yaz, Asad Azemi, pp 165-168
This paper first introduces an exponentially convergent reducedorder observer for state reconstruction of uncertain nonfinear systems. Then, the state estimates obtained are used in a dynamic scheme for exponential stai~zafion of the controlled system. The nonlinear gains utilized in the obse~er and controller are similar to those of the variable-structure designs but are continuous in nature, and result in simpler convergence analysis.
042
An Algorithm for Optimal Control of Nonlinear Systems with Model-Reality Differences P.D. Roberts, pp 169-174
An iterative procedure, known as Dynamic ]ntograted System Optimization and Parameter Estimation (DISOPE), is described for solving nonlinear optimal control problems where the model employed to compute the optimal solution is different from reality. An algorithm (implemented in MATLAB on the basis of a tinear model and quadratic performance, but where it is not required that
Abstracts
measurements for different relay output amplitudes. The resulting nonlinear PID controller contains stmic nonlinearities obtained by solving an inverse desoriHng function problem. Examples show the application of the methods to nonlinear planu where only the gain or both the gain and phase of the frequency response depend on the input amplitude. 032
Application of Nonlinear Control Theory to Path Tracking Control of Articulated Vehicles with Double Trailers M. Sampel, T. Kobayashl, pp 129-132
"lifts paper describes the design of a path-tracking controller for an articulated vehicle with double trailers, using time-scale transformation and exact linearization techniques, developed in nordinear control theory. The simulation shows that the proposed controller works satisfactorily, and the aRiculated vehicle with double trailers follows the desired path even when it is moving backwards. 033
Nonlinear Control of a Spatial Multi-Axis Servo. Hydraulic Test Facility H. Hahn, K.-D. Lelmimch, X. Zhang, pp 133-136
037
The paper solves a tracking problem for a class of feedback lineafizable systems in the presence of disturbances and parameter uncertainties. An internal model of the exogenous signals is augmented with the system, and a robust, observer-based, output feedback controller is designed to achieve asymptotic tracking.
038
034
A Stable Nonlinear Observer Design for Permanent. Magnet Synchronous Motors Knan-Teck Chang, Teck-Seng Low, Tong-Heng Lee, pp 137-140
The application of vector control techniques in ac drives demands accurate position and speed feedback information for the current control and servo control loops. This paper describes the design of a stable speed obse~er system suitable for use with permanentmagnet synchronous motors (PMSM) as a software transducer. The observer is developed from the dq model of the machine. A technique employing state detection and eigenvaiue confinement is used to achieve global stabih'ty and consistent convergency of the observer system.
035
New Results eat Feedback Equivalence to Passive Systems G.L. Santosuesso, PIP 141.144
This paper is concerned with the problem of rendering a nonlinear system passive via static-state feedback when there is a direct input-ootput feedthrough. It extends a solution recently proposed in the literature ff the output of the system is exclusively a function of the state, and shows that, under mild regularity assumptions, the necessary and sufficient conditions for a nonlinear system to he feedback equivalent to a passive one are: being inve~fible with relative order 1, and being weakly minirman-phase.
036
Observers with Asymptotic Gain for a Class of Linear Time-Varying Systems with Singularity J. IAvine, Guchuan Zhu, pp 145-148
This paper presents a sufficient condition for the existence of an observer with asymptotic gain, namely with a constant gain when the system is expressed in terms of its fastest time-scale. This condition crucially depends on the concept of asymptotic observability. When this property does not hold, an observer with asymptotic gain may net exist' whereas observers defined on a finite horizon may be well defined.
Semi-Global Stabilization by Dynamic Output Feedback for Minimum Phase Systems A. Ted, L. Praly, pp 153-156
The output feedback stabilization problem for systems in an "observer canonical form" is addressed. Setting a goal of semiglobal stabilization allows the removal of the previous assumption that the inverse dynamics are input-to-state stable. Further, it permits a completely linear, dynamic output feedback solution. Similar to previous results, local growth conditions are required on the vector fields of the system to guarantee convergence to the origin. 039
This paper presents a nonlinear control concept of a special multiaxis servohydraulic test facility. Based on nonlinear model equations including the servohydraufic actuator dynamics and the test table and payload mechanics, a global nonlinear diffeommphism is derived which maps the model equations into nonlinear can~mical form. Using symbolic languages, a nonlinear control law is developed and calculated, based on exact linearization techniques. The efficiency and applicability of this control concept with respect to the tracking and decoupling behaviour of the test facility are demonstrated by computer simulations.
Robust Servomechanism Output Feedback Controllers for a Clam of Feedback Linearizable Systems H.K. Khalil, pp 149-152
An Approximate Frobenlus Theorem J. Hauser, Zhigang Xu, pp 157-160
In this paper, the authors consider the approximate integrability of a smooth nonsingular distribution around a manifold. They give suffident conditions for the distribution to be order p-1 integrable around a manifold. If the distribution is transverse to the manifold, then the sufficient conditions are also necessary. Except for the error terms, the result is similar to the Frobenius Theorem. An example is used to show the application of the approximate Frobunins Theorem to the approximate feedback linearization of a nonlinear control system about the equilibrimn manifold. O4O Feedback Implementability of Sliding Modes in Nonlinear Control Systems G. Bartolini, V. Utkin, T. Zolez~, pp 161-163 The paper considers general multivariable control systems, described by nonlinear ordinary differential equations. Given any sliding manifold in the state space and any ideal sfiding motion on it, an explicit control algorithm is found, which allows the same dynamic behaviour of the ideal motion to be obtained, up to any fixed tolerance, by using the trajectories of a new control system. This system is all'me in the control variables, and is obtained by transforming the original one via a suitable switching logic. The affine dependence on the control variables guarantees the fulfilment of the approximability property, thereby extending the scope of the theory.
041
Exponential Stabilization of Uncertain Nonlinear Systems by a Reducod-Order Compensator Engin Yaz, Asad Azemi, pp 165-168
This paper first introduces an exponentially convergent reducedorder observer for state reconstruction of uncertain nonfinear systems. Then, the state estimates obtained are used in a dynamic scheme for exponential stai~zafion of the controlled system. The nonlinear gains utilized in the obse~er and controller are similar to those of the variable-structure designs but are continuous in nature, and result in simpler convergence analysis.
042
An Algorithm for Optimal Control of Nonlinear Systems with Model-Reality Differences P.D. Roberts, pp 169-174
An iterative procedure, known as Dynamic ]ntograted System Optimization and Parameter Estimation (DISOPE), is described for solving nonlinear optimal control problems where the model employed to compute the optimal solution is different from reality. An algorithm (implemented in MATLAB on the basis of a tinear model and quadratic performance, but where it is not required that