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

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

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

4. 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

5. Performance

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

7. 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

8. 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 + -

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

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

11. 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

12. Control Algorithm General Form:

13. 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 */

14. 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

15. 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 10-20 times the closed loop bandwidth