DESIGN OF TWO-DEGREE-OF-FREEDOM (2DOF) PID TUNING ALGORITHMS FOR THE DIFFERENTIAL DRIVE MOBILE ROBOT USING A SINGULAR SPECIFICATION OF SETTLING-TIME

Abstract

The major problem of concern in the regulation of the output of any dynamic system is the quality of control in terms of both accuracy and stability. How best to achieve these goals simultaneously using the Proportional-Integral-Derivative (PID) control law depends on both its structural algorithmic design and tuning algorithmic design. However, there is no accepted best approach to the tuning design and implementation of the PID. Main approaches often involve the need for a prior knowledge of the plant-model dynamics, order, or use of multi-objective optimization techniques which in practice can be complex, time-consuming, and computationally expensive. In contrast, identifying the closed-loop settling-time of an input-output dynamic system under control as a sufficient and characteristic system dynamics property can help to streamline the complexity and cost of tuning. Consequently, in this research an adaptive PID tuning algorithm named the “Closed-PID Loop Model” Following Control (CPLMFC) method was designed by using the identified closed-loop settling-time of the input-output plant without prior assumption of either knowledge of the system model, or the use of numerical optimization techniques. The real-time performance of the developed algorithm was tested on a multivariable system in form of the Differential Drive Mobile Robot (DDMR) for set-point tracking and load-disturbance regulation. Satisfactory control performance of the DDMR’s two wheels at the same set-points with fast settling-times (1% settling-time typically less than the identified settling-time) and minimal overshoots (maximum overshoots were typically less than 5%) was achieved without the need for time-consuming process-model identifications experiments and numerical optimization computations. Therefore, for PID tuning-design, the use of an identified closed-loop settling-time as a characteristic system dynamics property can sufficiently ensure accurate and stable closed-loop adaptive PID control performance quality for a class of uncertain, multivariable physical dynamical systems with finite input-output settling-times.