This paper presents a method for automatic tuning of PID regulators with specifications on phase and amplitude margins. The key idea is a simple method for estimating the critical gain and the critical frequency. The procedure automatically generates the appropriate test signal. The method is not sensitive to modelling errors and disturbances. It may be used for automatic tuning of simple regulators as well as initialization of more complicated adaptive regulators. The method is based on a simple identification method which gives critical points on the Nyquist curve of the open loop transfer function. The key idea is a scheme which provides automatic excitation of the process which is nearly optimal for estimating the desired process characteristics. The methods proposed are primarily intended to tune simple regulators of the PID type. In such applications they will of course inherit the limitations of the PID algorithms. They will not work well for problems where more complicated regulators are required. The technique may, however, also be applied to more complicated regulators and the experiences obtained so far from experimentation, in laboratory and industry, indicate that the simple versions of the algorithms work very well and in addition that they are robust. The proposed algorithms may be used in several different ways. They may be incorporated in single loop controllers to provide an option for automatic tuning. They may also be used to provide a solution to the long-standing problem of safe initialization of more complicated adaptive or self-tuning schemes. When combined with a bandwidth self-tuning it is, for example, possible to obtain an adaptive regulator which may set a suitable closed loop bandwidth automatically. The methods are based on a simple identification method which gives critical points on the Nyquist curve of the open loop transfer function. The key idea is a scheme which provides automatic excitation of the process which is nearly optimal for estimating the desired process characteristics. The methods proposed are primarily intended to tune simple regulators of the PID type. In such applications they will of course inherit the limitations of the PID algorithms. They will not work well for problems where more complicated regulators are required. The technique may, however, also be applied to more complicated regulators and the experiences obtained so far from experimentation, in laboratory and industry, indicate that the simple versions of the algorithms work very well and in addition that they are robust.This paper presents a method for automatic tuning of PID regulators with specifications on phase and amplitude margins. The key idea is a simple method for estimating the critical gain and the critical frequency. The procedure automatically generates the appropriate test signal. The method is not sensitive to modelling errors and disturbances. It may be used for automatic tuning of simple regulators as well as initialization of more complicated adaptive regulators. The method is based on a simple identification method which gives critical points on the Nyquist curve of the open loop transfer function. The key idea is a scheme which provides automatic excitation of the process which is nearly optimal for estimating the desired process characteristics. The methods proposed are primarily intended to tune simple regulators of the PID type. In such applications they will of course inherit the limitations of the PID algorithms. They will not work well for problems where more complicated regulators are required. The technique may, however, also be applied to more complicated regulators and the experiences obtained so far from experimentation, in laboratory and industry, indicate that the simple versions of the algorithms work very well and in addition that they are robust. The proposed algorithms may be used in several different ways. They may be incorporated in single loop controllers to provide an option for automatic tuning. They may also be used to provide a solution to the long-standing problem of safe initialization of more complicated adaptive or self-tuning schemes. When combined with a bandwidth self-tuning it is, for example, possible to obtain an adaptive regulator which may set a suitable closed loop bandwidth automatically. The methods are based on a simple identification method which gives critical points on the Nyquist curve of the open loop transfer function. The key idea is a scheme which provides automatic excitation of the process which is nearly optimal for estimating the desired process characteristics. The methods proposed are primarily intended to tune simple regulators of the PID type. In such applications they will of course inherit the limitations of the PID algorithms. They will not work well for problems where more complicated regulators are required. The technique may, however, also be applied to more complicated regulators and the experiences obtained so far from experimentation, in laboratory and industry, indicate that the simple versions of the algorithms work very well and in addition that they are robust.