Ch6 The Root Locus Method

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

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 P Control system design by RL according to performance specification.

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

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.

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.

6.6 Design example and simulation §Laser manipulator control system §The Root locus using Matlab Self-learning after class P The requirement for steady performance The requirement for stability The requirement for dynamic performance

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

Assignment §E7.17 §P7.3