The dynamics of discrete-time fractional order control systems depends on the method used for implementing the fractional derivatives and integrals. A reliable numerical approach adopts the generalized mean of the continuous to discrete conversion. The extra freedom provided by the proposed method must be carefully optimized by the user. This paper investigates the use of multidimensional scaling for evaluating and visualizing the performance of generalized mean discrete-time fractional controllers. Two alternative performance indices are adopted for comparing the time and frequency responses of the controlled system when adopting different combinations of the parameters. Numerical experiments with a fractional PID and two linear plants demonstrate the feasibility of the method for comparing and visualizing multiple test cases.

离散时间分数阶控制系统的动力学取决于用于实现分数导数和积分的方法。可靠的数值方法采用连续到离散转换的广义均值。用户必须仔细优化所提出的方法提供的额外自由度。本文研究了使用多维标度来评估和可视化广义平均离散时间分数控制器的性能。当采用参数的不同组合时，采用两个替代的性能指标来比较受控系统的时间和频率响应。用分数PID和两个线性工厂进行的数值实验证明了该方法用于比较和可视化多个测试用例的可行性。