In this paper, we want to make a new type linear piezoelectric motor by mode shape coating or effective electrode surface coating. The mode shape is derived from the mechanical boundary conditions of the linear piezoe...In this paper, we want to make a new type linear piezoelectric motor by mode shape coating or effective electrode surface coating. The mode shape is derived from the mechanical boundary conditions of the linear piezoelectric motor. We only have access to the first three modes of formas, the effective electrode surface coating basis, as well as with the linear piezoelectric motor of normal shape do comparison. Next, we will inspect their gain or axial velocity through theoretical analysis, simulation and experiment. According to the results of the theoretical analysis, we have found that the gain or axial velocity of the linear piezoelectric motors of mode shape is much larger than the linear piezoelectric motors of normal shape. However, according to the results of simulation and experiments, we have found that the gain or axial velocity of the linear piezoelectric motors of mode shape is much greater than the linear piezoelectric motors of normal shape, which is about 1.2 to 1.4 times. The linear piezoelectric motor of mode shape 3 has the fastest axial velocity, which is about -48 mm/s and 48 mm/s under conditions of 180 Vp-p driving voltage, 21.2 kHz driving frequency (the third vibration modal), 25 gw loading and the position of loading or mass at x = 5 mm & 45 mm respectively. And its axial velocity is about 1.4 times the linear piezoelectric motor of normal shape under the same conditions. Overall, the mode shape coating helps to enhance the gain or axial velocity of the linear piezoelectric motor.展开更多
This paper presents LQR sliding surface-based Sliding Mode Controller(LQR-SMC)for balancing control of a Rotary Double Inverted Pendulum(RDIP)system.It is a challenging research topic in control engineering due to its...This paper presents LQR sliding surface-based Sliding Mode Controller(LQR-SMC)for balancing control of a Rotary Double Inverted Pendulum(RDIP)system.It is a challenging research topic in control engineering due to its nonlinearity and instability.The RDIP system uses only a motor to control two serially connected pendulums to stand at the upright position.The sliding surface is designed based on the LQR optimal gain.Nonsingular gain matrix is obtained by using the left inverse of the input matrix in the state space form of the system dynamics.The Lyapunov stability theory is used to determine the stability of the controller.To evaluate the performance of LQR-SMC,some performance indices,including the Integral Absolute Error(IAE),Integral Time Absolute Error(ITAE),and the Integrated Square Error(ISE),are used.System stability can be maintained by LQR-SMC under external disturbances as well as model and parameter uncertainties.展开更多
文摘In this paper, we want to make a new type linear piezoelectric motor by mode shape coating or effective electrode surface coating. The mode shape is derived from the mechanical boundary conditions of the linear piezoelectric motor. We only have access to the first three modes of formas, the effective electrode surface coating basis, as well as with the linear piezoelectric motor of normal shape do comparison. Next, we will inspect their gain or axial velocity through theoretical analysis, simulation and experiment. According to the results of the theoretical analysis, we have found that the gain or axial velocity of the linear piezoelectric motors of mode shape is much larger than the linear piezoelectric motors of normal shape. However, according to the results of simulation and experiments, we have found that the gain or axial velocity of the linear piezoelectric motors of mode shape is much greater than the linear piezoelectric motors of normal shape, which is about 1.2 to 1.4 times. The linear piezoelectric motor of mode shape 3 has the fastest axial velocity, which is about -48 mm/s and 48 mm/s under conditions of 180 Vp-p driving voltage, 21.2 kHz driving frequency (the third vibration modal), 25 gw loading and the position of loading or mass at x = 5 mm & 45 mm respectively. And its axial velocity is about 1.4 times the linear piezoelectric motor of normal shape under the same conditions. Overall, the mode shape coating helps to enhance the gain or axial velocity of the linear piezoelectric motor.
文摘This paper presents LQR sliding surface-based Sliding Mode Controller(LQR-SMC)for balancing control of a Rotary Double Inverted Pendulum(RDIP)system.It is a challenging research topic in control engineering due to its nonlinearity and instability.The RDIP system uses only a motor to control two serially connected pendulums to stand at the upright position.The sliding surface is designed based on the LQR optimal gain.Nonsingular gain matrix is obtained by using the left inverse of the input matrix in the state space form of the system dynamics.The Lyapunov stability theory is used to determine the stability of the controller.To evaluate the performance of LQR-SMC,some performance indices,including the Integral Absolute Error(IAE),Integral Time Absolute Error(ITAE),and the Integrated Square Error(ISE),are used.System stability can be maintained by LQR-SMC under external disturbances as well as model and parameter uncertainties.
