Experimental Assessment of Fractional-Order PDD1/2 Control of a Brushless DC Motor with Inertial Load

Abstract

The application of Fractional Calculus to control mechatronic devices is a promising research area. The most common approach to Fractional-Order (FO) control design is the PIλDµ scheme, which adopts integrals and derivatives of non-integer order λ and µ. A different possible approach is to add FO terms to the PID control, instead of replacing integer order terms; for example, in the PDD1/2 scheme, the half-derivative term is added to the classical PD. In the present paper, by mainly focusing on the transitory behaviour, a comparison among PD, PDµ, and PDD1/2 control schemes is carried out, with reference to a real-world mechatronic implementation: a position-controlled rotor actuated by a DC brushless motor. While using a general non-dimensional approach, the three control schemes are first compared by continuous-time simulations, and tuning criteria are outlined. Afterwards, the effects of the discrete-time digital implementation of the controllers are investigated by both simulation and experimental tests. The results show how PDD1/2 is an effective and almost cost-free solution for improving the trajectory-tracking performance in position control of mechatronic devices, with limited computational burden and, consequently, easily implementable on most commercial motion control drives.

Fractional-Order PII1/2DD1/2 Control: Theoretical Aspects and Application to a Mechatronic Axis

“…In [38] the PD, PD µ and PDD 1/2 controls of a purely inertial system are compared by simulation, and the results indicate that the two FO schemes have similar performance, but the PDD 1/2 is characterized by a slightly better readiness and a slightly higher overshoot. In [39] the comparison among PD, PD µ and PDD 1/2 is validated by experimental tests, highlighting the benefits of the proposed control approach in real working conditions, not limited to the classical step response.…”

“…In the case of fractional order systems, the amount of damping cannot be quantified by only one dimensionless damping ratio, as for complex poles of integer-order systems; for example, in the implementation of the PII 1/2 DD 1/2 control scheme, damping is associated both to the derivative term (damping of integer order 1) and to the half-derivative term (damping of order 1/2). The two dimensionless damping ratios related to these damping terms and their effects are discussed in [36,39].…”

“…The main limitation of this study is the lack of generality due to the fact that the performance improvement obtained by means of the PII 1/2 DD 1/2 scheme with respect to PID was evaluated only for a case study with specific system parameters and starting from an arbitrary initial set of PID gains. In the work that follows, the comparison among the PID, PII 1/2 DD 1/2 and PI λ D µ controllers will be performed using a non-dimensional approach, as already done in [39] for the PD, PDD 1/2 and PD µ controllers, without integral actions. This will provide more general results and indications on possible tuning criteria for the control of second-order linear systems, a category which may include with good approximation of many automation devices.…”

Comparing Methods of DC Motor Control for UUVs

“…Pappalardo also proposed developments to system identification [42] that could prove useful. Bruzzone recently introduced motor control based on fractional-calculus [43], and it seems that expression of self-awareness statements in deterministic artificial intelligence could be amplified.…”

Fractional Order Control of Power Electronic Converters in Industrial Drives and Renewable Energy Systems: A Review

“…A half derivative term was added to the PD controller in [88] to design a PDD 1 2 controller which was used in the position control of a BLDC for improving the tracking performance. This was found to be an easy and cost-effective solution and could be easily implemented in commercial drives.…”