Modelling and Control Design of a V-Shaped Thermal Actuator System via Partial Derivative Equation Approach

Iterative Learning Control for V-Shaped Electrothermal Microactuator

“…A temperature response of the system is exhibited in Figure 5. It represents relatively from this simulation result that VEM is a bounded input-bounded output stable object (BIBO), which met completely with the conclusions given in [8,9,11,13], as well as with our previous work presented in [9]. Hence, the ILC approach now can be applied confidently to tracking control VEM.…”

“…Belonging to actuators in general, or VEM in particular, force and displacement are two important control variables. For thermal actuators, thermal forces depend on the displacement, and therefore, designers aim to control the displacement of the system [9].…”

“…with K 1 = 0.08 and K 2 = 0.1 will be applied. These learning parameters are chosen based on a sufficiently convergent condition for the learning process presented in [28,29,35,37], under a theoretical assumption that the VEM mathematical model given in [9] is exact. The simulation results for the displacement of the top of the beam by using the discrete time PD-type learning procedure (16) are given in Figures 8 and 9 for both cases without and with an additional output disturbance.…”

“…It is exhibited extraordinary here in the obtained results, especially in Figure 8a (without external disturbances) and Figure 9a (with an additional output disturbance), which illustrate the dependence of maximal tracking error on applied learning step number, that the tracking error does not decrease monotonously if the learning number is increased, as proven in [28][29][30][31][32][33][34][35][36][37] by using a mathematical model of VEM. A reason for it could be that an uncertain difference between the mathematical models given in [5,8,9] and the here used Simscape model of VEM has appeared. It can be deduced that these mathematical models may not be precise enough for using it to design a conventional open-loop controller for VEM.…”

“…with the chosen learning parameters K 1 = 0.08 and K 2 = K 3 = 0.1 for the two cases without and with output disturbances, respectively. These learning parameters are also chosen correspondingly to the required convergent condition presented in [28,29,35,37] and the mathematical model of VEM given in [9]. Likely by using the PD-type, as exhibited in Figures 10a and 11a for both cases without and with an additional disturbance in system output, respectively, the tracking error does not decrease monotonously by increasing the learning steps as usual.…”