Controller Design for a Second-Order Plant with Uncertain Parameters and Disturbance: Application to a DC Motor

Table 1

Simulation and experimentation parameters.

Parameter	Value
𝐸: input voltage	40 V
𝑟𝑠: internal resistance of the source and MOSFET	0.84 Ω
𝑉𝑓𝑑: diode forward voltage	1.1 V
𝐿: inductance	2.473 mH
𝑟𝐿: internal resistance of the inductor	1.695 Ω
𝐶: capacitance	46.27 𝜇F
𝑅𝑎: armature resistance	2.7289 Ω
𝐿𝑎: armature inductance	1.17 mH
𝐵: viscous friction coefficient	0.000138 N·m/rad/s
𝐽𝑒𝑞: moment of inertia	0.000115 kg·m^2
𝑘𝑡: motor torque constant	0.0663 N·m/A
𝑘𝑒: voltage constant	0.0663 V/rad/s
𝑇fric: friction torque	0.0284 N·m
𝑇𝐿: load torque	variable N·m
𝑊𝑚ref: reference speed	200 and 300 rad/s
𝐹𝑐: switching frequency	4 kHz
𝐹𝑠: sampling frequency	4 kHz
1 𝑇𝑝: unit time delay	250 𝜇s
𝑊𝑚: motor speed	28 bits resolution
𝑖𝑎: motor current	12 bits resolution
𝑑: duty cycle	10 bits resolution
Zero-order hold: fixed step discrete time	250 𝜇s
𝐼3: unity matrix of dimension 3
𝐼7: unity matrix of dimension 7
Γ1: updating gain	0.0003𝐼3
Γ2: updating gain	0.0003𝐼7
𝐶𝑏𝑒: user-defined constant	5
𝑐1 and 𝑐2: user-defined gains	1
𝑐𝑎 and 𝑐𝑐: user-defined gains	2.5
𝑢𝑎: initial control action defined by the user	30 V