A new optimisation method of PIDC controller under constraints on robustness and sensitivity to measurement noise using amplitude optimum principle

This paper presents a new optimisation method for PID controller cascaded with a lead-lag compensator (PIDC). Parameters of the controller are obtained by solving the constrained optimisation problem. We propose two variants of the optimality criterion. The first one is defined through the max-min optimisation problem wherein objective function is the amplitude frequency response of the PIDC controller. The second one is based on an effective approximation of the minimum value of the amplitude frequency response of the PIDC controller. Consequently, we obtain a computationally less expensive problem. Both variants of optimality criterion result in efficient load disturbance and noise rejection, while robustness is ensured by constraining the value of the maximum sensitivity Ms. Good reference shaping is supported with proper constraints based on the Amplitude Optimum (AO) principle. Numerous batches of processes typically encountered in the industry are used to demonstrate the effectiveness of the proposed design method

Dominant pole placement with fractional order PID controllers: D-decomposition approach

Dominant pole placement is a useful technique designed to deal with the problem of controlling a high order or time-delay systems with low order controller such as the PID"controller. This paper tries to solve this problem by using D-decomposition method. Straightforward analytic procedure makes this method extremely powerful and easy to apply. This technique is applicable to a wide range of transfer functions: with or without time-delay, rational and non-rational ones, and those describing distributed parameter systems. In order to control as many different processes as possible, a fractional order PID controller is introduced, as a generalization of classical PID controller. As a consequence, it provides additional parameters for better adjusting system performances. The design method presented in this paper tunes the parameters of PID and fractional PID controller in order to obtain good load disturbance response with a constraint on the maximum sensitivity and sensitivity to noise measurement. Good set point response is also one of the design goals of this technique. Numerous examples taken from the process industry are given, and D-decomposition approach is compared with other PID optimization methods to show its effectiveness

Analysis of Electrical Circuits Including Fractional Order Elements

This paper deals with the analysis of electrical circuits with classical one-port elements including two novel defined one-port fractional order elements: fractional-order resistive-capacitive RC-alpha and fractional-order inductive RL-alpha element. The definitions and analytical relations between current, voltage and power of introduced fractional elements are provided. An example of fractional element realization via ladder electrical circuit composed of classical resistors, capacitors and/or inductors is presented. Several examples are analyzed to illustrate he behavior of electrical circuit with fractional order elements for different values of fractional order alpha including differentiator/integrator circuits as well as complex circuits without accumulated energy

Analysis of Electrical Circuits Including Fractional Order Elements

This paper deals with the analysis of electrical circuits with classical one-port elements including two novel defined one-port fractional order elements: fractional-order resistive-capacitive RC-alpha and fractional-order inductive RL-alpha element. The definitions and analytical relations between current, voltage and power of introduced fractional elements are provided. An example of fractional element realization via ladder electrical circuit composed of classical resistors, capacitors and/or inductors is presented. Several examples are analyzed to illustrate he behavior of electrical circuit with fractional order elements for different values of fractional order alpha including differentiator/integrator circuits as well as complex circuits without accumulated energy

On the Rational Representation of Fractional Order Lead Compensator using Pade Approximation

This paper presents simple, flexible and effective approximation method for fractional order lead-lag compensators. The proposed method relies on a Pade approximation of linear fractional order transfer functions, giving rational approximations of order N accurate enough for control applications as soon as N is greater than 2 or 3. An example of feedback loop incorporating this approximation is adopted from the well-known car suspension problem, wherein an iso-damping property of the closed loop response is achieved, with regard to a variation of the vehicle mass

On the Rational Representation of Fractional Order Lead Compensator using Pade Approximation

This paper presents simple, flexible and effective approximation method for fractional order lead-lag compensators. The proposed method relies on a Pade approximation of linear fractional order transfer functions, giving rational approximations of order N accurate enough for control applications as soon as N is greater than 2 or 3. An example of feedback loop incorporating this approximation is adopted from the well-known car suspension problem, wherein an iso-damping property of the closed loop response is achieved, with regard to a variation of the vehicle mass

On the rational representation of fractional order lead compensator using Padé approximation

This paper presents simple, flexible and effective approximation method for fractional order lead-lag compensators. The proposed method relies on a Padé approximation of linear fractional order transfer functions, giving rational approximations of order N accurate enough for control applications as soon as N is greater than 2 or 3. An example of feedback loop incorporating this approximation is adopted from the well-known car suspension problem, wherein an iso-damping property of the closed loop response is achieved, with regard to a variation of the vehicle mass