A Guide to Design Disturbance Observer-based Motion Control Systems in Discrete-time Domain

Abstract

This paper analyses and synthesises the Disturbance Observer (DOb) based motion control systems in the discretetime domain. By employing Bode Integral Theorem, it is shown that continuous-time analysis methods fall-short in explaining the dynamic behaviours of the DOb-based robust motion controllers implemented by computers and microcontrollers. For example, continuous-time analysis methods cannot explain why the robust stability and performance of the digital motion controller deteriorate as the bandwidth of the DOb increases. Therefore, unexpected dynamic responses (e.g., poor stability and performance, and high-sensitivity to disturbances and noise) may be observed when the parameters of the digital robust motion controller are tuned by using continuous-time synthesis methods in practice. This paper also analytically derives the robust stability and performance constraints of the DOb-based motion controllers in the discrete-time domain. The proposed design constraints allow one to systematically synthesise a high-performance digital robust motion controller. The validity of the proposed analysis and synthesis methods are verified by simulations.

Design Constraints of Disturbance Observer-based Motion Control Systems are Stricter in the Discrete-Time Domain

“…Figure 1 illustrates the block diagram of the DOb in the continues-time and discrete-time domains [16,27] To estimate the internal and external disturbances of a motion control system, a DOb is synthesised using the identified (i.e., nominal) system model, a low-pass-filter, and the velocity measurement of a servo system as illustrated in Fig. 1.…”

“…Therefore, we need to put more effort to find the upper and lower bounds on the nominal plant model and the bandwidth of the DOb. Reader is referred to [27] for an example of analytical design constraints of the DOb in the discrete-time domain.…”

“…To conduct high-performance motion control applications via DOb, the control parameters (viz. the bandwidth of the observer, nominal plant parameters, and the outer-loop performance controller) of the robust motion control systems should be properly tuned [23,26,27]. When the design constraints of the DOb are violated, the robust stability and performance of the motion controller may notably deteriorate [27].…”

“…the bandwidth of the observer, nominal plant parameters, and the outer-loop performance controller) of the robust motion control systems should be properly tuned [23,26,27]. When the design constraints of the DOb are violated, the robust stability and performance of the motion controller may notably deteriorate [27]. Therefore, it is essential to determine the upper and lower bounds on the bandwidth of the DOb, nominal plant parameters, and outer-loop performance controller.…”

“…The achievable bandwidth is also limited by the fundamental constraint of feedback control systems. Moreover, this also puts an upper bound on the plant model mismatch, which limits the achievable phase-lead effect in the inner-loop [27].…”