Robust Fractional Adaptive Control Based on the Strictly Positive Realness Condition: This paper presents a new approach to robust adaptive control, using fractional order systems as parallel feedforward in the adaptation loop. The problem is that adaptive control systems may diverge when confronted with finite sensor and actuator dynamics, or with parasitic disturbances. One of the classical robust adaptive control solutions to these problems makes use of parallel feedforward and simplified adaptive controllers based on the concept of positive realness. The proposed control scheme is based on the Almost Strictly Positive Realness (ASPR) property of the plant. We show that this condition implies also robust stability in the case of fractional order controllers. An application to Model Reference Adaptive Control (MRAC) with a fractional order adaptation rule is provided with an implementable algorithm. A simulation example of a SISO robust adaptive control system illustrates the advantages of the proposed method in the presence of disturbances and noise.

Controllers based on fractional order calculus are gaining more and more interests from the control community. This type of controllers may involve fractional integration, fractional differentiation and/or fractional systems in their structure or implementation. They have been introduced in the control applications in a continuous effort to enhance the system control quality performances and robustness. In this study, a new scheme of fractional order adaptive controller via high‐gain output feedback for a class of linear, time‐invariant, minimum phase and single input‐single output systems of relative degree one is proposed. The basic idea of the new design is a further modification in the adaptive proportional control law by the introduction of a fractional integration besides of the regular one of the squared output of the system in the adaptation gain of the control strategy. An analytical stability proof of the feedback control system is presented. The control quality enhancement of the proposed control scheme compared with the classical one has been presented through the simulation results of an illustrative example.

The design method of polynomial control laws by mean of pole placement are actually smart solutions to many industrial applications. This category of controllers is very popular in the industry; however most of their applications concern only problems with constant reference signals. In this paper, we propose an indirect adaptive controller by fractional order pole placement. The proposed control strategy is based on the self-tuning control structure and on-line estimation of the plant model parameters using the Recursive Least Squares (RLS) algorithm. To show the effectiveness of the proposed control scheme two simulation examples are presented. The first example is the control of a DC motor angular speed and the second one is the control of an air-lubricated capstan drive for precision positioning. Improvement in the system control dynamical behavior compared to classical control scheme has been shown for the two illustrative examples