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PID Create a PID controller in parallel form. Construction: SYS = PID(Kp,Ki,Kd,Tf) creates a continuous-time PID controller in parallel form with a first-order derivative filter: Ki Kd*s Kp + ---- + -------- s Tf*s+1 The scalars Kp, Ki, Kd, and Tf specify the proportional gain, integral gain, derivative gain, and filter time constant. The Tf value must be nonnegative for stability. The default values are Kp=1, Ki=0, Kd=0, and Tf=0. If a parameter is omitted, its default value is used. For example, PID(Kp,Ki,Kd) creates a PID controller with pure derivative term. The resulting SYS is of type PID if Kp,Ki,Kd,Tf are all real, and of type GENSS if one of the gains is tunable (see REALP and GENMAT). SYS = PID(Kp,Ki,Kd,Tf,Ts) creates a discrete-time PID controller with sample time Ts>0. The discrete-time PID formula is Kd Kp + Ki * IF(z) + -------------- Tf + DF(z) where IF(z) and DF(z) are the discrete integrator formulas for the integral and derivative terms. Use the "IFormula" and "DFormula" properties to specify these formulas. Available formulas include: 'ForwardEuler' Ts/(z-1) 'BackwardEuler' Ts*z/(z-1) 'Trapezoidal' (Ts/2)*(z+1)/(z-1) The default formula is ForwardEuler. The 'IFormula' and 'DFormula' settings are ignored for continuous-time PIDs. The following settings are disallowed because they generate unstable PIDs: (1) (Kd > 0, Tf = 0) and DFormula='Trapezoidal' (2) (Kd > 0, Tf > 0) and DFormula='ForwardEuler' and Ts>=2*Tf You can set additional properties by using name/value pairs. For example, sys = pid(1,2,3,0.5,0.1,'IFormula','T','TimeUnit','min') also specifies the integral-term formula and the time units. Type "properties(pid)" for a complete list of PID properties, and type help pid.<PropertyName> for help on a particular property. You can create arrays of PID objects by specifying arrays of values for Kp,Ki,Kd,Tf. For example, if Kp and Ki are 3-by-4 arrays, PID(Kp,Ki) creates a 3-by-4 array of PID controllers. Conversion: PIDSYS = PID(SYS) converts the dynamic system SYS to a PID object. An error is thrown when SYS cannot be expressed as a PID controller in parallel form. PIDSYS = PID(SYS,'IFormula',Value1,'DFormula',Value2) returns an equivalent PID controller with different formulas for the integral and derivative terms. See also PIDSTD, PID2, PIDSTD2, tunablePID, tunablePID2, TF. Documentation for pid doc pid Other uses of pid DynamicSystem/pid StaticModel/pid