Ch6 The Root Locus Method

1. Ch6 The Root Locus Method

2. 6.3 Generalized root locus • Parameter root locus • Zero-degree root locus Equivalent unity feedback transform An example (refer to Script 4-12) System contains inner positive-feedback- loop

3. 6.4 Parameter design by RL • Root locus is a single-parameter method • An example: Welding head control How to design two or more parameter by RL? Refer to P354-356 Control system design by RL according to performance specification.

4. 6.5 PID controllers • Three-term or PID controller (P366) • Transfer function in frequency domain • Controller in the time domain

5. Mechanism of PID • PID controller provides a proportional term, an integration term and a derivative term. It is widely applied to many industrial process. Its popularity can be attributed partly to its good control performance and to the simplicity of design manner. • PID controller introduces a TF with one pole at the origin and two zeros that can be located arbitrarily in the LH s-plane.

6. PID explanation by RL The TF of PID controller If a high dynamic performance is desired, then designers can select zeros of to lie further left in the LHP and set K to drive the roots near the complex zeros.

7. 6.6 Design example and simulation • Laser manipulator control system • The Root locus using Matlab • The requirement for steady performance • The requirement for stability • The requirement for dynamic performance Self-learning after class P373-380

8. Summary • The relationship between performance and roots location • The concept of Root Locus • The RL procedure • The generalized RL and parameter RL • A powerful tool for the analysis and design of modern control system

9. Assignment • E7.17 • P7.3