The paper proposes a new performance index, the energy resemblance index (ERI), to address the performance evaluation and design issues in the digital redesign of analogue control systems. The ERI is defined as the ratio of the integral of the square error (ISE) of the continuous-time system over the error sequence energy (ESE) of the redesigned digital system. By directly transforming the analogue controller into a digital controller as a function of sampling time, ESEs using different discretisation methods for the redesigned system can be obtained via a recursive formula. The authors prove that the ESE will approach the ISE as the sampling time approaches zero for discretisation methods which satisfy a simple condition. Performance of the redesigned digital control system using different discretisation methods at different sampling times can be evaluated based on this index. As for the design, the proper sampling time can be determined based on the user-specified ERI percentage, so that the redesigned digital system performs accordingly. It is found that performance of the redesigned digital system depends on the discretisation method used, the controlled process and the sampling time chosen. There is no particular discretisation method which outperforms the others in all cases.
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