Experimental determination of motor model parameters ETEC6419

Step input response Take a step input response to the motor A decision then needs to be made concerning a first or second order model of the motor system First we will consider a first order approximation based on experimental measurements

First order approximation Enter a step input to the motor system (apply a fixed voltage input) Wait until the motor reaches steady state Measure the motor shaft RPM at steady state Determine the ratio of the output shaft speed to the input voltage which provides the system gain (K). Repeat this experiment for different step input voltages. Determine the average gain value (K).

Time constant Enter a step input voltage and determine the steady state value. Determine the time taken to reach 63% of the steady state value. The time taken represents the time constant. Repeat this experiment for different step input voltages. Take the average of the different time constants measured as the time constant of the system.

First order system equation

Second order approximations Second order approximations work best when there is overshoot in the system. The following method assumes a system is present with overshoot present in the system.

Second order gain Enter a step input to the motor system (apply a fixed voltage input) Wait until the motor reaches steady state Measure the motor shaft RPM at steady state Determine the ratio of the output shaft speed to the input voltage which provides the system gain (K). Repeat this experiment for different step input voltages. Determine the average gain value (K).

Percentage Peak overshoot Enter a step input voltage to the motor. Measure the motor speed at steady state Determine the motor speed at peak overshoot using an instrumented motor system Using the equation below, determine the value ζ for the system

Repeat this experiment for different step input voltages. Using all the values calculated for ζ, determine the average ζ value for the system

Peak time Enter a step input voltage to the motor. Measure the motor speed at steady state Determine the time at peak overshoot using an instrumented motor system Using the equation below and the value ζ previously calculated for the system, determine the value ω n for the system

Repeat this experiment for different step input voltages. Using all the values calculated for ω n, determine the average ω n value for the system

Second order system equation Using the values calculated for ζ and ω n The second order model is given by