Analysis of the stability control of motors used in biomechanical prostheses
We present an alternative analysis for the energy optimization and system stability in servomotors that drive biomechanical prostheses using a LQR (Linear Quadratic Regulator) controller. The model is designed in the state space, and we use the Lyapunov F
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Universidad Nacional del Nordeste (UNNE). Corrientes, Argentina
Abstract— We present an alternative analysis for the energy optimization and system stability in servomotors that drive biomechanical prostheses using a LQR (Linear Quadratic Regulator) controller. The model is designed in the state space, and we use the Lyapunov Function as a parameter of the system stability. From the observation of the dynamical response and transition of the system variables, angular position, angular velocity and armature current of the model, we found that the use of LQR with its respective controlling action generates in the system a convergence to an equilibrium point xe in less than 3 seconds, ensuring stability with a shorter trajectory. Keywords—Prosthesis, Servomotor, Stability, LQR. I. INTRODUCTION
The design of artificial limbs requires full knowledge not only of the mechanics of the mechanisms, but also a clear understanding of electromechanical devices, among which driving motors play a key role in the area of prostheses. The maximal speed, force and stability of the anatomical limb are still unparalleled by the artificial prosthesis. These limitations are due to physical restraints of current technology to achieve the properties which the natural limb exhibits. Matching muscle speed and force with technological actuator is not an easy task, mainly when choosing a driving motor with the appropriate speed-torque relationship [1]. Instability of driving motors adds to the complexity of proper prosthesis design. It is known that many theories in physical sciences are based or expressed in terms of optimality. In the field of motor control, optimality also plays a key role. The optimization processes give rise to a specific motor system under investigation (adaptation, development, evolution, recovery). These processes cause the system to perform better and better. In the area of theoretical investigations, it is natural to search for limits of optimal performance of motor control [2]. Several methods are used to control speed of DC mo-tors [3]. Neenu [4] reports that Proportional-Integral-Derivative (PID) controllers have been widely used for speed position control. Selecting PID parameters using genetic algorithms has lead to a more efficient controller [5]. Other authors like
Boumediene [6], used a Particle Swarm Optimization (PSO) instead of GA. They presented a PID controller based on PSO. They found that PID-PSO controller gives good performance and minimal rise time. Sharaf [7] presented a novel PID dual loop controller for a solar photovoltaic (PV) powered industrial permanent mag-net DC motor drive. However, in spite of the robustness and apparently simple structure of PID control strategy, optimiz-ing the gains of PID controller is still a difficult task [8]. An alternative method is the Linear Quadratic Regulator (LQR). Its performance index is found by using a mathematical algorithm that minimizes a cost function. This function is often defined as a sum of the deviations of key measurements from their desired
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