ELG 4152 Modern Control Professor Riadh Habash Team

ELG 4152 Modern Control Professor: Riadh Habash Team Member: Min Shi, 3150752 Yuxiang Chen, 3481495 Yichen Fan, 3588950 Peng Liang, 3520871

Introduction Hybrid Control over induction servo motor. Application: manipulators. • • Automobile industry Ship building industry Aerospace industry Other fields needs heavy lifting by any manipulators. Induction Servo Motor Characteristics: • • • Heavy duty, good torque Fast acceleration Accurate positioning Low armature inductance, low electrical time constant Often seen with brushed Commutation required Regular maintenance Highly non-linear, controller needed Higher cost

Reference R. J. Wai, C. -M. Lin and C. -F. Hsu “Hybrid Control for Induction Servo Motor” (IEEE Proc. Control Theory Appl, Vol 149, No. 6, pp. 555 -561 November 2002) Rong-Jong Wai “Robust Control for Induction Servo Motor Drive” (Department of Electrical Engineering Yuan Ze University, 2001) F. -J. Lin, R. -J. Wai “Hybrid controller using a neural network for a PM synchronous servo motor drive” (IEEE Proc. Control Theory Appl, Vol 145, No. 3, pp. 223 -229, May 1998) Rong-Jong Wai, Kuo-Min Lin, and Chung-You Lin “Total Sliding-Mode Speed Control of Field-Oriented Induction Motor Servo Drive” (Department of Electrical Engineering, Yuan Ze University, Chung-Shan Institute of Science and Technology) R. Firoozian, T. J. Lim “COMPARISON OF PID AND ACTIVE CONTROL TECHNIQUES FOR ELECTRO-HYDRAULIC SERVO MOTORS” (Department of Mechanical & Process Engineering, Univemity of Sheffield) Rong-Jong Wai “Development of Intelligent Position Control System Using Optimal Design Technique” (IEEE TRANS INDUSTRIAL ELECTRONICS, VOL. 50, pp. 219231, FEBRUARY 2003) http: //www. hansen-motor. com/servo-motors. htm

Induction Servo Motor • The induction servomotor we used in our project is a 3 phase Y-connected four-pole 800 W 60 Hz 120 V/5. 4 A type motor. • The mechanical equation of the induction servomotor drive can be represented as: • Where θ is the motor position; U(t) is the control effort. An, Bn are given: An=-B/J= -1. 1172 (s*rad)-1; Bn=Kt/J=101. 4854 (A*s 2)-1; B, J, Kt are constant for servo motor Kt=0. 4851 Nm/A; J=0. 00478 Nms 2; B=0. 00534 Nms/rad

Objective • Our objective is to control a induction servo motor position with 2 different hybrid controls from ‘Robust Control’, ‘Computed Torque’ and ‘Sliding Surface’ controlling methods. • Figures and graphics will be shown for each controlling methods and also for Hybrid methods for comparison.

Solution(1)---PID • PID controller, the most conventional method. • However, the performance of PID controller can be significantly compromised when the controlled system is highly nonlinear (as servo motors), and has large uncertainty (i. e. external torque).

Solution (2)---other methods • The following methods are the most common ones for induction servo motors controlling: – Robust – Computed torque – Sliding mode

Advanced Control • Besides the methods we mentioned above, there are two advanced control methods that are commonly adopted by the industry. – Fuzzy logic feed back control system – Neural network control system • But due to their complexity for testing and implementation, we are not going to use these two methods in our control system. Hybrid Control • Hybrid 1: Adding ‘Sliding surface’ before error goes into ‘Robust Control’ • Hybrid 2: Adding ‘Computed Torque’ into ‘Robust Control’

Robust Mode • Advantages: – The error caused by uncertainties will be compensated. – Insensitive to the uncertainties variation. • Disadvantages: – More sensitive to the external force compare to ‘Sliding Surface’ method. – Large control effort (expenditure) compare to ‘Computed Torque’ method. – More complex electric circuit.

Robust • Simulink Diagram:

Robust • Robust Control Law: • The equation for • Xp is defined as: Xp=[θ ω]T θ: rotor position ω: rotor speed • The equation for K • Ec is defined as: Ec= e is equivalent to θe • The equation for • is the pseudo inverse of =[1. 25] • R is the desired input

Graphic results with no uncertainties (external torque) • Simulink results rotor position vs reference model (Dash line for reference model) – Rotor position follows the reference model quite well – Control effort is larger than computed torque but smaller than sliding mode. – Error is from -0. 3 to 0. 3. Control Effort Error

Results with external load disturbance of 0. 5 Nm occurring at 5 s rotor position vs reference model • Simulink results (Dash line for reference model) – Rotor position still quite follows the reference model, but is worse than sliding mode. – Control effort jumped to 1 at 5 s. – An Error change at 6 s. Control Effort END CYX Error

Sliding Mode • Advantages: – Improve performance based on computed torque – Insensitive to the uncertainties variation • Disadvantages: – Very large control effort

Sliding Mode • Simulink diagram:

Sliding Mode • Sliding mode law: • Control law for Ueq: • Control law for Uvs: • Where s(t) is the output of sliding surface, which is defined as follow:

Results with no uncertainties • Simulink results rotor position vs reference model (Dash line for reference model) – Rotor position follows the reference model quite well – Control effort is larger than computed torque – Error is from -0. 1 to 0. 1 Control Effort Error

Results with external load disturbance of 0. 5 Nm occurring at 5 s rotor position vs reference model • Simulink results (Dash line for reference model) – Rotor position still quite follows the reference model with uncertainties – Control effort very large but still around zeros. – Error is from -0. 1 to -. 02, but keep steady Control Effort Error

Computed Torque • Advantages: – Conventional – Relatively Lowest control effort – High performance if no uncertainties • Disadvantages: – The stability will be destroyed when uncertainties occur

Computed Torque • Simulink Diagram:

Computed Torque • Computed torque law: - θe is the tracking error, defined as: θe = θ- θd -K 1, and K 2 should match with the Hunuitz polynomial equation, that is the roots of the following eqution lie open left-half of complex plane. Here, we choose K 1=16, K 2=64

Results with no uncertainties • Simulink results rotor position vs reference model (Dash line for reference model) – Rotor position follows the reference model quite well – Control effort is relatively low – Error is from -0. 15 to 0. 15 Control Effort Error

Results with external load disturbance of 0. 5 Nm occurring at 5 s rotor position vs reference model • Simulink results (Dash line for reference model) – System stability of rotor position control failed – Control effort jumped to 1 at 5 s – Error jumped to -1. 5 at 5 s without changing the P-P value Control Effort Error

Midstage Summary Controller Error Computati on effort Application Robust Control plants with a bit more expensive but better behavior over external conditions Computed Torque Fields where motor will not experience any obvious external torque With a strong budget, this controlling method gives best error resistance Sliding Mode Best Medium Worst 2 different Hybrid Control System will be presented in the coming part

Improvement • All the three methods has significant drawbacks. • The tracking error still too large for all these methods. • The performance and control effort can be further improved by using hybrid control system.

Hybrid 1: Robust+Sliding surfance • Advantages: – The best performance for both with and without uncertainties. – Less insensitive to the variation of parameters. • Disadvantages: – Control effort is relatively large.

Hybrid 1 • Simulink Diagram:

Hybrid 1 • Control law: – The sliding surface is added before the tracking error θe goes into the Robust control. Sliding surface:

Results with no uncertainties • Simulink results rotor position vs reference model (Dash line for reference model) – Rotor position almost the same as the reference model – Control effort is relatively large. – Error is from -0. 022 to 0. 028. Control Effort Error

Results with external load disturbance of 0. 5 Nm occurring at 5 s rotor position vs reference model • Simulink results (Dash line for reference model) – Rotor position still very close to the reference model – Control effort jumped to 1 at 5 s. – An Error change at 6 s, but the error is still very small. Control Effort Error

Hybrid 2: Robust+Computed Torque • Advantages: – The better performance without uncertainties. – Very small control effort for both with and without uncertainties. • Disadvantages: – Performance gets bad with uncertainties, but will compensate later on.

Hybrid 2 • Simulink Diagram:

Hybrid 2 • Control law: – The control effort is defined as: U(t)=Ua(t)+Ub(b) Ua(t) is the control effort from the robust. Ub(t) is the control effort from the computed torque.

Results with no uncertainties • Simulink results rotor position vs reference model (Dash line for reference model) – Rotor position almost the same as the reference model – Control effort is very small. – Error is from -0. 033 to 0. 04. Control Effort Error

Results with external load disturbance of 0. 5 Nm occurring at 5 s rotor position vs reference model • Simulink results (Dash line for reference model) – Rotor position affect by the uncertainty, but compensates later on. – Control effort has no change. – An Error change at 6 s, but is getting smaller gradually. Control Effort Error

Comparison • Common improvement: – Both hybrid control systems improve the performance significantly. • Trade-off: – Hybrid control 1 has better performance and less sensitive to external torque, but with a larger control effort. – Hybrid control 2 has less control effort, but with a larger tracking error, especially with external torque.

Final Conclusion • Our new hybrid control systems decreases the tracking error at both conditions. • But Our new methods has a trade-off in error tracking and control effort. • Although we did not optimize every part, our two new methods are the better choice, and one of the hybrid control may be recommend to meet the specification requirement.

Thank you very much! 谢谢! merci beaucoup! Any Questions?