自适应神经元实现的直线永磁同步电机伺服系统的预见前馈补偿

介绍了高精度微进给直线永磁同步电机伺服系统的 IP位置控制 ,提出了对该系统的最优预见前馈补偿 ,以提高系统的跟踪性能。为了能适应系统参数的变化 ,采用自适应神经元来实现预见前馈补偿。自适应神经元的输入向量为预见步数 ,权值为预见前馈系数 ,权值具有明确的物理意义 ,而且权的初始值不是随机数 ,而是系统在额定情况下算出的预见前馈系数 ,从而加快了神经元的调整速度 ,提高了系统的跟踪能力。仿真实验结果证明了所提出方案的有效性

PCM控制的新型气液位置伺服系统的研究

本文提出了一种新型气液缸和气液位置伺服系统。该系统采用气液连动控制，充分发挥液压与气动各自的优点，大大提高了位置控制精度，同时克服单纯气动的特点。在气液回路上，利用两位三通阀、“ＰＣＭ”阀组及油开关阈实现分区控制和准确定位，解决了快速性和定位精度之间的矛盾，通过分析和实验研究表明，此方案是可行的。

前馈在快速高精度数字随动系统中的应用

本文给出了一种具有前馈等值的二阶无静差数字随动系统的设计方法。按照这种设计方法,只要在计算的基础上适当地调整前馈系数和开环增益,即可得到满意的系统性能指标。

多轴伺服控制器在自动化装备中的应用

在对自动化装备技术改造的过程中,需要用“电子齿轮多轴交流伺服系统”来取代使用效果欠佳的机械齿轮系统.介绍了交流伺服传动技术在某大型卷接机组中应用的总体设计方案,详细论述了该系统的工作原理,阐述了工控机、DSP、PLC及多轴伺服控制器在该装备中的综合运用.并以安川多轴伺服控制器为例,详细介绍了该装备中引入多轴伺服控制器的硬件、软件设计.实际应用表明,该设计是成功的,各项性能指标均优于原来的机械装置,能够有效降低噪音,减少能耗.

Demonstration of non-collocated vibration control of a flexible manipulator using electrical dynamic absorbers

This paper describes an experimental study into the vibration control of a servo system comprising a servo motor and a flexible manipulator. Two modes of the system are controlled by using the servo motor and an accelerometer attached to the tip of the flexible manipulator. The control system is thus non-collocated. It consists of two electrical dynamic absorbers, each of which consists of a modal filter and, in case of an out-of-phase mode, a phase inverter. The experimental results show that each absorber acts as a mechanical dynamic vibration absorber attached to each mode and significantly reduces the settling time for the system response to a step input.

Optimization of the Integrated Guidance and Control for a Dual Aerodynamic Control Missile

Las futuras misiones para misiles aire-aire operando dentro de la atmósfera requieren la interceptación de blancos a mayores velocidades y más maniobrables, incluyendo los esperados vehículos aéreos de combate no tripulados. La intercepción tiene que lograrse desde cualquier ángulo de lanzamiento. Una de las principales discusiones en la tecnología de misiles en la actualidad es cómo satisfacer estos nuevos requisitos incrementando la capacidad de maniobra del misil y en paralelo, a través de mejoras en los métodos de guiado y control modernos. Esta Tesis aborda estos dos objetivos simultáneamente, al proponer un diseño integrando el guiado y el control de vuelo (autopiloto) y aplicarlo a misiles con control aerodinámico simultáneo en canard y cola. Un primer avance de los resultados obtenidos ha sido publicado recientemente en el Journal of Aerospace Engineering, en Abril de 2015, [Ibarrondo y Sanz-Aranguez, 2015]. El valor del diseño integrado obtenido es que permite al misil cumplir con los requisitos operacionales mencionados empleando únicamente control aerodinámico. El diseño propuesto se compara favorablemente con esquemas más tradicionales, consiguiendo menores distancias de paso al blanco y necesitando de menores esfuerzos de control incluso en presencia de ruidos. En esta Tesis se demostrará cómo la introducción del doble mando, donde tanto el canard como las aletas de cola son móviles, puede mejorar las actuaciones de un misil existente. Comparado con un misil con control en cola, el doble control requiere sólo introducir dos servos adicionales para accionar los canards también en guiñada y cabeceo. La sección de cola será responsable de controlar el misil en balanceo mediante deflexiones diferenciales de los controles. En el caso del doble mando, la complicación añadida es que los vórtices desprendidos de los canards se propagan corriente abajo y pueden incidir sobre las superficies de cola, alterando sus características de control. Como un primer aporte, se ha desarrollado un modelo analítico completo para la aerodinámica no lineal de un misil con doble control, incluyendo la caracterización de este efecto de acoplamiento aerodinámico. Hay dos modos de funcionamiento en picado y guiñada para un misil de doble mando: ”desviación” y ”opuesto”. En modo ”desviación”, los controles actúan en la misma dirección, generando un cambio inmediato en la sustentación y produciendo un movimiento de translación en el misil. La respuesta es rápida, pero en el modo ”desviación” los misiles con doble control pueden tener dificultades para alcanzar grandes ángulos de ataque y altas aceleraciones laterales. Cuando los controles actúan en direcciones opuestas, el misil rota y el ángulo de ataque del fuselaje se incrementa para generar mayores aceleraciones en estado estacionario, aunque el tiempo de respuesta es mayor. Con el modelo aerodinámico completo, es posible obtener una parametrización dependiente de los estados de la dinámica de corto periodo del misil. Debido al efecto de acoplamiento entre los controles, la respuesta en bucle abierto no depende linealmente de los controles. El autopiloto se optimiza para obtener la maniobra requerida por la ley de guiado sin exceder ninguno de los límites aerodinámicos o mecánicos del misil. Una segunda contribución de la tesis es el desarrollo de un autopiloto con múltiples entradas de control y que integra la aerodinámica no lineal, controlando los tres canales de picado, guiñada y cabeceo de forma simultánea. Las ganancias del autopiloto dependen de los estados del misil y se calculan a cada paso de integración mediante la resolución de una ecuación de Riccati de orden 21x21. Las ganancias obtenidas son sub-óptimas, debido a que una solución completa de la ecuación de Hamilton-Jacobi-Bellman no puede obtenerse de manera práctica, y se asumen ciertas simplificaciones. Se incorpora asimismo un mecanismo que permite acelerar la respuesta en caso necesario. Como parte del autopiloto, se define una estrategia para repartir el esfuerzo de control entre el canard y la cola. Esto se consigue mediante un controlador aumentado situado antes del bucle de optimización, que minimiza el esfuerzo total de control para maniobrar. Esta ley de alimentación directa mantiene al misil cerca de sus condiciones de equilibrio, garantizando una respuesta transitoria adecuada. El controlador no lineal elimina la respuesta de fase no-mínima característica de la cola. En esta Tesis se consideran dos diseños para el guiado y control, el control en Doble-Lazo y el control Integrado. En la aproximación de Doble-Lazo, el autopiloto se sitúa dentro de un bucle interior y se diseña independientemente del guiado, que conforma el bucle más exterior del control. Esta estructura asume que existe separación espectral entre los dos, esto es, que los tiempos de respuesta del autopiloto son mucho mayores que los tiempos característicos del guiado. En el estudio se combina el autopiloto desarrollado con una ley de guiado óptimo. Los resultados obtenidos demuestran que se consiguen aumentos muy importantes en las actuaciones frente a misiles con control canard o control en cola, y que la interceptación, cuando se lanza cerca del curso de colisión, se consigue desde cualquier ángulo alrededor del blanco. Para el misil de doble mando, la estrategia óptima resulta en utilizar el modo de control opuesto en la aproximación al blanco y utilizar el modo de desviación justo antes del impacto. Sin embargo la lógica de doble bucle no consigue el impacto cuando hay desviaciones importantes con respecto al curso de colisión. Una de las razones es que parte de la demanda de guiado se pierde, ya que el misil solo es capaz de modificar su aceleración lateral, y no tiene control sobre su aceleración axial, a no ser que incorpore un motor de empuje regulable. La hipótesis de separación mencionada, y que constituye la base del Doble-Bucle, puede no ser aplicable cuando la dinámica del misil es muy alta en las proximidades del blanco. Si se combinan el guiado y el autopiloto en un único bucle, la información de los estados del misil está disponible para el cálculo de la ley de guiado, y puede calcularse la estrategia optima de guiado considerando las capacidades y la actitud del misil. Una tercera contribución de la Tesis es la resolución de este segundo diseño, la integración no lineal del guiado y del autopiloto (IGA) para el misil de doble control. Aproximaciones anteriores en la literatura han planteado este sistema en ejes cuerpo, resultando en un sistema muy inestable debido al bajo amortiguamiento del misil en cabeceo y guiñada. Las simplificaciones que se tomaron también causan que el misil se deslice alrededor del blanco y no consiga la intercepción. En nuestra aproximación el problema se plantea en ejes inerciales y se recurre a la dinámica de los cuaterniones, eliminado estos inconvenientes. No se limita a la dinámica de corto periodo del misil, porque se construye incluyendo de modo explícito la velocidad dentro del bucle de optimización. La formulación resultante en el IGA es independiente de la maniobra del blanco, que sin embargo se ha de incluir en el cálculo del modelo en Doble-bucle. Un típico inconveniente de los sistemas integrados con controlador proporcional, es el problema de las escalas. Los errores de guiado dominan sobre los errores de posición del misil y saturan el controlador, provocando la pérdida del misil. Este problema se ha tratado aquí con un controlador aumentado previo al bucle de optimización, que define un estado de equilibrio local para el sistema integrado, que pasa a actuar como un regulador. Los criterios de actuaciones para el IGA son los mismos que para el sistema de Doble-Bucle. Sin embargo el problema matemático resultante es muy complejo. El problema óptimo para tiempo finito resulta en una ecuación diferencial de Riccati con condiciones terminales, que no puede resolverse. Mediante un cambio de variable y la introducción de una matriz de transición, este problema se transforma en una ecuación diferencial de Lyapunov que puede resolverse mediante métodos numéricos. La solución resultante solo es aplicable en un entorno cercano del blanco. Cuando la distancia entre misil y blanco es mayor, se desarrolla una solución aproximada basada en la solución de una ecuación algebraica de Riccati para cada paso de integración. Los resultados que se han obtenido demuestran, a través de análisis numéricos en distintos escenarios, que la solución integrada es mejor que el sistema de Doble-Bucle. Las trayectorias resultantes son muy distintas. El IGA preserva el guiado del misil y consigue maximizar el uso de la propulsión, consiguiendo la interceptación del blanco en menores tiempos de vuelo. El sistema es capaz de lograr el impacto donde el Doble-Bucle falla, y además requiere un orden menos de magnitud en la cantidad de cálculos necesarios. El efecto de los ruidos radar, datos discretos y errores del radomo se investigan. El IGA es más robusto, resultando menos afectado por perturbaciones que el Doble- Bucle, especialmente porque el núcleo de optimización en el IGA es independiente de la maniobra del blanco. La estimación de la maniobra del blanco es siempre imprecisa y contaminada por ruido, y degrada la precisión de la solución de Doble-Bucle. Finalmente, como una cuarta contribución, se demuestra que el misil con guiado IGA es capaz de realizar una maniobra de defensa contra un blanco que ataque por su cola, sólo con control aerodinámico. Las trayectorias estudiadas consideran una fase pre-programada de alta velocidad de giro, manteniendo siempre el misil dentro de su envuelta de vuelo. Este procedimiento no necesita recurrir a soluciones técnicamente más complejas como el control vectorial del empuje o control por chorro para ejecutar esta maniobra. En todas las demostraciones matemáticas se utiliza el producto de Kronecker como una herramienta practica para manejar las parametrizaciones dependientes de variables, que resultan en matrices de grandes dimensiones. ABSTRACT Future missions for air to air endo-atmospheric missiles require the interception of targets with higher speeds and more maneuverable, including forthcoming unmanned supersonic combat vehicles. The interception will need to be achieved from any angle and off-boresight launch conditions. One of the most significant discussions in missile technology today is how to satisfy these new operational requirements by increasing missile maneuvering capabilities and in parallel, through the development of more advanced guidance and control methods. This Thesis addresses these two objectives by proposing a novel optimal integrated guidance and autopilot design scheme, applicable to more maneuverable missiles with forward and rearward aerodynamic controls. A first insight of these results have been recently published in the Journal of Aerospace Engineering in April 2015, [Ibarrondo and Sanz-Aránguez, 2015]. The value of this integrated solution is that it allows the missile to comply with the aforementioned requirements only by applying aerodynamic control. The proposed design is compared against more traditional guidance and control approaches with positive results, achieving reduced control efforts and lower miss distances with the integrated logic even in the presence of noises. In this Thesis it will be demonstrated how the dual control missile, where canard and tail fins are both movable, can enhance the capabilities of an existing missile airframe. Compared to a tail missile, dual control only requires two additional servos to actuate the canards in pitch and yaw. The tail section will be responsible to maintain the missile stabilized in roll, like in a classic tail missile. The additional complexity is that the vortices shed from the canard propagate downstream where they interact with the tail surfaces, altering the tail expected control characteristics. These aerodynamic phenomena must be properly described, as a preliminary step, with high enough precision for advanced guidance and control studies. As a first contribution we have developed a full analytical model of the nonlinear aerodynamics of a missile with dual control, including the characterization of this cross-control coupling effect. This development has been produced from a theoretical model validated with reliable practical data obtained from wind tunnel experiments available in the scientific literature, complement with computer fluid dynamics and semi-experimental methods. There are two modes of operating a missile with forward and rear controls, ”divert” and ”opposite” modes. In divert mode, controls are deflected in the same direction, generating an increment in direct lift and missile translation. Response is fast, but in this mode, dual control missiles may have difficulties in achieving large angles of attack and high level of lateral accelerations. When controls are deflected in opposite directions (opposite mode) the missile airframe rotates and the body angle of attack is increased to generate greater accelerations in steady-state, although the response time is larger. With the aero-model, a state dependent parametrization of the dual control missile short term dynamics can be obtained. Due to the cross-coupling effect, the open loop dynamics for the dual control missile is not linearly dependent of the fin positions. The short term missile dynamics are blended with the servo system to obtain an extended autopilot model, where the response is linear with the control fins turning rates, that will be the control variables. The flight control loop is optimized to achieve the maneuver required by the guidance law without exceeding any of the missile aerodynamic or mechanical limitations. The specific aero-limitations and relevant performance indicators for the dual control are set as part of the analysis. A second contribution of this Thesis is the development of a step-tracking multi-input autopilot that integrates non-linear aerodynamics. The designed dual control missile autopilot is a full three dimensional autopilot, where roll, pitch and yaw are integrated, calculating command inputs simultaneously. The autopilot control gains are state dependent, and calculated at each integration step solving a matrix Riccati equation of order 21x21. The resulting gains are sub-optimal as a full solution for the Hamilton-Jacobi-Bellman equation cannot be resolved in practical terms and some simplifications are taken. Acceleration mechanisms with an λ-shift is incorporated in the design. As part of the autopilot, a strategy is defined for proper allocation of control effort between canard and tail channels. This is achieved with an augmented feed forward controller that minimizes the total control effort of the missile to maneuver. The feedforward law also maintains the missile near trim conditions, obtaining a well manner response of the missile. The nonlinear controller proves to eliminate the non-minimum phase effect of the tail. Two guidance and control designs have been considered in this Thesis: the Two- Loop and the Integrated approaches. In the Two-Loop approach, the autopilot is placed in an inner loop and designed separately from an outer guidance loop. This structure assumes that spectral separation holds, meaning that the autopilot response times are much higher than the guidance command updates. The developed nonlinear autopilot is linked in the study to an optimal guidance law. Simulations are carried on launching close to collision course against supersonic and highly maneuver targets. Results demonstrate a large boost in performance provided by the dual control versus more traditional canard and tail missiles, where interception with the dual control close to collision course is achieved form 365deg all around the target. It is shown that for the dual control missile the optimal flight strategy results in using opposite control in its approach to target and quick corrections with divert just before impact. However the Two-Loop logic fails to achieve target interception when there are large deviations initially from collision course. One of the reasons is that part of the guidance command is not followed, because the missile is not able to control its axial acceleration without a throttleable engine. Also the separation hypothesis may not be applicable for a high dynamic vehicle like a dual control missile approaching a maneuvering target. If the guidance and autopilot are combined into a single loop, the guidance law will have information of the missile states and could calculate the most optimal approach to the target considering the actual capabilities and attitude of the missile. A third contribution of this Thesis is the resolution of the mentioned second design, the non-linear integrated guidance and autopilot (IGA) problem for the dual control missile. Previous approaches in the literature have posed the problem in body axes, resulting in high unstable behavior due to the low damping of the missile, and have also caused the missile to slide around the target and not actually hitting it. The IGA system is posed here in inertial axes and quaternion dynamics, eliminating these inconveniences. It is not restricted to the missile short term dynamic, and we have explicitly included the missile speed as a state variable. The IGA formulation is also independent of the target maneuver model that is explicitly included in the Two-loop optimal guidance law model. A typical problem of the integrated systems with a proportional control law is the problem of scales. The guidance errors are larger than missile state errors during most of the flight and result in high gains, control saturation and loss of control. It has been addressed here with an integrated feedforward controller that defines a local equilibrium state at each flight point and the controller acts as a regulator to minimize the IGA states excursions versus the defined feedforward state. The performance criteria for the IGA are the same as in the Two-Loop case. However the resulting optimization problem is mathematically very complex. The optimal problem in a finite-time horizon results in an irresoluble state dependent differential Riccati equation with terminal conditions. With a change of variable and the introduction of a transition matrix, the equation is transformed into a time differential Lyapunov equation that can be solved with known numerical methods in real time. This solution results range limited, and applicable when the missile is in a close neighborhood of the target. For larger ranges, an approximate solution is used, obtained from solution of an algebraic matrix Riccati equation at each integration step. The results obtained show, by mean of several comparative numerical tests in diverse homing scenarios, than the integrated approach is a better solution that the Two- Loop scheme. Trajectories obtained are very different in the two cases. The IGA fully preserves the guidance command and it is able to maximize the utilization of the missile propulsion system, achieving interception with lower miss distances and in lower flight times. The IGA can achieve interception against off-boresight targets where the Two- Loop was not able to success. As an additional advantage, the IGA also requires one order of magnitude less calculations than the Two-Loop solution. The effects of radar noises, discrete radar data and radome errors are investigated. IGA solution is robust, and less affected by radar than the Two-Loop, especially because the target maneuvers are not part of the IGA core optimization loop. Estimation of target acceleration is always imprecise and noisy and degrade the performance of the two-Loop solution. The IGA trajectories are such that minimize the impact of radome errors in the guidance loop. Finally, as a fourth contribution, it is demonstrated that the missile with IGA guidance is capable of performing a defense against attacks from its rear hemisphere, as a tail attack, only with aerodynamic control. The studied trajectories have a preprogrammed high rate turn maneuver, maintaining the missile within its controllable envelope. This solution does not recur to more complex features in service today, like vector control of the missile thrust or side thrusters. In all the mathematical treatments and demonstrations, the Kronecker product has been introduced as a practical tool to handle the state dependent parametrizations that have resulted in very high order matrix equations.

Experimental characterization and modelling of a servo-pneumatic system for a knee loading apparatus

The new knee test rig developed in University of Bologna used pneumatic cylinder as actuator system. Specific characterization and modelling about the pneumatic cylinder and the related devices are needed in better controlling the test rig. In this thesis, an experimental environment for the related device is set up with data acquisition system using Real-time Windows Target, Simulink, MatLab. Based on the experimental data, a fitted model for the pneumatic cylinder friction is found.

Adaptive depth estimation in image based visual servo control of dynamic systems

This paper considers the question of designing a fully image based visual servo control for a dynamic system. The work is motivated by the ongoing development of image based visual servo control of small aerial robotic vehicles. The observed targets considered are coloured blobs on a flat surface to which the normal direction is known. The theoretical framework is directly applicable to the case of markings on a horizontal floor or landing field. The image features used are a first order spherical moment for position and an image flow measurement for velocity. A fully non-linear adaptive control design is provided that ensures global stability of the closed-loop system. © 2005 IEEE.

Spherical image-based visual servo and structure estimation

This paper presents a formulation of image-based visual servoing (IBVS) for a spherical camera where coordinates are parameterized in terms of colatitude and longitude: IBVSSph. The image Jacobian is derived and simulation results are presented for canonical rotational, translational as well as general motion. Problems with large rotations that affect the planar perspective form of IBVS are not present on the sphere, whereas the desirable robustness properties of IBVS are shown to be retained. We also describe a structure from motion (SfM) system based on camera-centric spherical coordinates and show how a recursive estimator can be used to recover structure. The spherical formulations for IBVS and SfM are particularly suitable for platforms, such as aerial and underwater robots, that move in SE(3).

Dynamic Image-based visual servo control using centroid and optic flow features

This paper considers the question of designing a fully image-based visual servo control for a class of dynamic systems. The work is motivated by the ongoing development of image-based visual servo control of small aerial robotic vehicles. The kinematics and dynamics of a rigid-body dynamical system (such as a vehicle airframe) maneuvering over a flat target plane with observable features are expressed in terms of an unnormalized spherical centroid and an optic flow measurement. The image-plane dynamics with respect to force input are dependent on the height of the camera above the target plane. This dependence is compensated by introducing virtual height dynamics and adaptive estimation in the proposed control. A fully nonlinear adaptive control design is provided that ensures asymptotic stability of the closed-loop system for all feasible initial conditions. The choice of control gains is based on an analysis of the asymptotic dynamics of the system. Results from a realistic simulation are presented that demonstrate the performance of the closed-loop system. To the author's knowledge, this paper documents the first time that an image-based visual servo control has been proposed for a dynamic system using vision measurement for both position and velocity.

Performance tests for visual servo control systems, with application to partitioned approaches to visual servo control

Visual servoing has been a viable method of robot manipulator control for more than a decade. Initial developments involved positionbased visual servoing (PBVS), in which the control signal exists in Cartesian space. The younger method, image-based visual servoing (IBVS), has seen considerable development in recent years. PBVS and IBVS offer tradeoffs in performance, and neither can solve all tasks that may confront a robot. In response to these issues, several methods have been devised that partition the control scheme, allowing some motions to be performed in the manner of a PBVS system, while the remaining motions are performed using an IBVS approach. To date, there has been little research that explores the relative strengths and weaknesses of these methods. In this paper we present such an evaluation. We have chosen three recent visual servo approaches for evaluation in addition to the traditional PBVS and IBVS approaches. We posit a set of performance metrics that measure quantitatively the performance of a visual servo controller for a specific task. We then evaluate each of the candidate visual servo methods for four canonical tasks with simulations and with experiments in a robotic work cell.

Development of an autonomous unmanned aerial system to collect time-stamped samples from the atmosphere and localize potential pathogen sources

This paper presents the hardware development and testing of a new concept for air sampling via the integration of a prototype spore trap onboard an unmanned aerial system (UAS).We propose the integration of a prototype spore trap onboard a UAS to allow multiple capture of spores of pathogens in single remote locations at high or low altitude, otherwise not possible with stationary sampling devices.We also demonstrate the capability of this system for the capture of multiple time-stamped samples during a single mission.Wind tunnel testing was followed by simulation, and flight testing was conducted to measure and quantify the spread during simulated airborne air sampling operations. During autonomous operations, the onboard autopilot commands the servo to rotate the sampling device to a new indexed location once the UAS vehicle reaches the predefined waypoint or set of waypoints (which represents the region of interest). Time-stamped UAS data are continuously logged during the flight to assist with analysis of the particles collected. Testing and validation of the autopilot and spore trap integration, functionality, and performance is described. These tools may enhance the ability to detect new incursions of spores

De Vcme amigo, servo, venerador...:letras e civilidade nas Gerais do setecentos

O presente trabalho procura discutir a sociedade formada em Minas Gerais entre fins do século XVIII e início do XIX. Pelas particularidades que envolveram sua criação e ocupação, a colônia portuguesa na América foi palco de configurações identitárias específicas que conviveram durante o período da crise do Antigo Sistema Colonial, alternando as formas de relacionamento e autoimagem dos colonos. Em Minas Gerais, as sociabilidades foram influenciadas também pelas práticas de educação, de leitura e pela posse de livros. Para analisar a questão, procuramos utilizar parte da intensa produção epistolar produzida no período com base, principalmente, no acervo da Coleção Casa dos Contos.

Participative modelling and big issues: defining features of system dynamics?

In this article the author discusses participative modelling in system dynamics and issues underlying it. It states that in the heart of system dynamics is the servo-mechanism theory. It argues that it is wrong to see an optimal solution being applied by the empowered parties just because it exhibits self-evident truth and an analysis is not enough to encourage people to do things in different way. It mentions other models including the simulation models used for developing strategy discussions.

Lumped Element Modeling of a Flexible Manipulator System

This paper is concerned with a modeling method that can be used for an experimental identification of a dynamic system. More specifically, an equivalent lumped element system is presented to represent in a unique and exact manner a complete proportional-derivative (PD) controlled servo positioning system having a flexible manipulator. The impedance and mobility approach is used to transform the P and D control gains to an electrical spring and an electrical damper, respectively. The impedance model method is used to transform the flexible manipulator to a coupled system between a single contact mass at the driving position and a series of noncontact masses each of which is connected to the contact mass via a resilient member. This method is applicable whenever the driving point response of such a manipulator is available. Experimental work is presented to support the theory developed.