Magnitude (dB) 60 40 Magnitude of Downstream Impedance Estimation Network Analyzer iin Vg 20 0 102 Zsource 103 + Vin - 104 Phase (°) 100 50 + Test Signal Estimation Network Analyzer -50 102 103 Control User Constraints Adaptation Figure 15. A comparison of (a) an identified Zload (LRC) and Magnitude (dB) (b) a network analyzer measurement. + Vref Fitted Model 104 System Identification Frequency (Hz) (b) Figure 17. A generalized schematic of a switching converter, its embedded digital controller, and the proposed adaptive control structure. Magnitude of Downstream Impedance 30 Test Sequence (PRBS) 20 Estimation Analytic 10 0 102 103 104 (a) Phase of Downstream Impedance Phase (°) Digital Controller Embedded Controller - Control Gains 0 40 + Zload Vout - PWM (a) Phase of Downstream Impedance + i out Switching Power Converter 300 200 Estimation Analytic 100 0 102 103 Frequency (Hz) (b) Converter Perturbation Responses: v(t ), i(t ) FFT Analysis Desired Model Order Number of Poles/ Number of Zeros User Constraints Complex G ( jw ) Model Fitting Numerator (s) Denominator (s) Adaptive Control Synthesis Control Gains 104 Digital Controller Update Figure 16. A comparison of (a) an identified Zload (CPL) and Figure 18. A flowchart for adaptive control design using digital (b) an analytic model. network analyzer techniques. identifying key plant transfer functions and impedances at its terminals and of self-commissioning accordingly to meet user specified constraints. This functionality can be implemented in state-of-the-art digital controller platforms. As an example, in this section, an adaptively controlled power converter is briefly described. The power converter with its embedded digital controller is shown in Figure 17. The controller uses the WSI techniques introduced earlier to implement an adaptive strategy as described in the flowchart of Figure 18. As shown, the control platform perturbs the converter by injecting the PRBS sequence. The plant responses are collected, and the nonparametric frequency-domain response is extracted through FFT-based analysis. A parametric model with a specified number of poles and zeros is then constructed using a model fitting algorithm. The fitted model along with user-specified performance constraints is fed to the adaptive control synthesis unit, which in this example is based on the internal model control method. The control adaptation process is completed by updating the digital controller with the computed gains. The routine repeats itself on a regular basis by actively perturbing the converter and keeping the controller updated with respect to the most recent system IEEE Elec trific ation Magazine / S EP T EM BE R 2 0 1 7 65