Embedded Control Systems Dr. Bonnie Heck School of ECE Georgia Tech

Introduction Goal: Meet design specifications on performance even under varying operating conditions Examples: car cruise control, temperature control, flight controls, motor control, robotic manipulator

Feedback Control System to be controlled Output Actuator Sensor Controller + - Reference Measurement Disturbance

Embedded Control Components Sensors: transducers that convert physical quantities to voltage Controller: Analog or digital implementation of the control –Digital controller: DSP board, microcontroller, or PC with ADC and DAC Actuators: physical device that converts controller outputs to system inputs Drive Electronics: power, power amplifier, analog filters

Performance

Closed Loop Frequency Response Frequency (Hz or rad/sec) Magnitude DC Value 0 Bandwidth

Design Metrics Speed of Response –Speed at which transient decays (bandwidth) Accuracy –Smallness of error (DC value) Relative Stability –Amount of error tolerated in model before system goes unstable

Design Procedure System to be controlled Output Actuator Sensor Controller + - Reference Measurement ADC DAC Control D(z) Error, E(z) Command, U(z) From sensor To actuatorReference + -

Common Controllers Proportional Proportional + Derivative (PD) Proportional + Integral (PI) Proportional + Integral + Derivative (PID)

Desired Responses Frequency (Hz or rad/sec) Magnitude DC Value 0 Bandwidth Time Response Frequency Response

Design Strategy Speed of Response –Bandwidth increases as K increases Accuracy –DC value approaches 1 as K increases Relative Stability –Often relative stability goes down as K increases

Control Algorithm General Form:

Pseudo-code //Initialize u_1 = 0; u_2 = 0; e_1 = 0; e_2 = 0; while(1){y = readsensor(); e=r-y; u = -a1*u_1-a2*u_2+e+b1*e_1+b2*e_2; output(u); //pass to actuator driver u_2=u_1; u_1 = u; e_2 = e_1; e_1 = e; wait(sample_time); } /* a better way is to use a hardware timer to trigger an event, the event handler runs this code */

Sampling Period Nyquist: sample at twice the highest frequency –But, the signal being sampled is not bandlimited Rule of thumb: sample at 10 to 20 times the bandwidth of the closed loop system, slower reduces performance and may destabilize the system

Summary Feedback control adds robustness (good performance even with varying conditions) Embedded controls implemented with DSP boards, microcontrollers, PCs, FPGA boards Larger gain, K: faster response, better accuracy, possibly lower stability Sample at times the closed loop bandwidth