Design of IIR Fractional Order Digital Integrators Using Iterative Convex Optimization Algorithm

In this paper, a new method for the design of infinite impulse response fractional order digital integrator is proposed. The maximum phase deviation from a desired linear phase is minimized under the stability and relative magnitude response error constraints. The resultant design problem is nonconvex. An iterative convex optimization algorithm based on Gauss-Newton strategy is developed by converting the non-convex constrained optimization design problem into a series of convex optimization subproblems. To approximate the desired frequency response, a pole factor is preassigned. Design examples show that the IIR fractional order digital integrators have smaller maximum phase error and maximum relative magnitude response error than the competing.