IPDT Model-Based Ziegler-Nichols Tuning Generalized to Controllers with Higher-Order Derivatives.

The paper extends the earlier work entitled "Making the PI and PID Controller Tuning Inspired by Ziegler and Nichols Precise and Reliable", to higher-order controllers and a broader range of experiments. The original series PI and PID controllers, based on automatic reset calculated by filtered controller outputs, are now augmented by higher-order output derivatives. This increases the number of degrees of freedom that can be used to modify the resulting dynamics, accelerates transient responses, and increases robustness to unmodeled dynamics and uncertainties. The fourth order noise attenuation filter used in the original work allows for the addition of an acceleration feedback signal, thus resulting in a series PIDA controller or even a jerk feedback that leads to a PIDAJ series controller. Such a design can further use the original process and filter approximation of the step responses through the integral-plus-dead-time (IPDT) model, while allowing experimentation with disturbance and setpoint step responses of the series PI, PID, PIDA and PIDAJ controllers, and thus, evaluating the role of output derivatives and noise attenuation from a broader perspective. All controllers considered are tuned using the Multiple Real Dominant Pole (MRDP) method, which is complemented by a factorization of the controller transfer functions to achieve the smallest possible time constant for automatic reset. The smallest time constant is chosen to improve the constrained transient response of the considered controller types. The obtained excellent performance and robustness allow the proposed controllers to be applied to a wider range of systems with dominant first-order dynamics. The proposed design is illustrated on a real-time speed control of a stable direct-current (DC) motor, which is approximated (together with a noise attenuation filter) by an IPDT model. The transient responses obtained are nearly time-optimal, with control signal limitations active for most setpoint step responses. Four controllers with different degrees of derivative with generalized automatic reset were used for comparison. It was found that controllers with higher-order derivatives may significantly improve the disturbance performance and virtually eliminate overshoots in the setpoint step responses in constrained velocity control.

Measurement System for Piezoelectric Resonance Impedance Spectroscopy Under Combined AC and High-Voltage DC Loading.

Piezoelectric resonance impedance spectroscopy is a standardized measurement technique for determining the electromechanical, elastic, and dielectric parameters of piezoceramics. However, commercial measurement setups are designed for small-signal measurements and encounter difficulties when constant driving voltages/currents are required at resonances, higher fields, or combined AC and DC loading. The latter is particularly important to evaluate the DC bias-hardening effect of piezoelectrics. Here, we propose a novel measurement system for piezoelectric resonance impedance spectroscopy under combined AC and high-voltage DC loading that complies with established standards. The system is based on two separate output amplifier stages and includes voltage/current probes, a laser vibrometer, custom protection components, and control software with optimization algorithm. In its current form, the measurement setup allows the application of AC frequencies up to 500 kHz and DC signals up to ±10 kV on samples with impedance between 10-1 and 106 Ω . The operation of the proposed setup was benchmarked against commercial impedance analyzers in the small-signal range and reference equivalent circuits. Test measurements under combined AC and DC loading were performed on a soft Pb(Zr,Ti)O3 piezoceramic. The results revealed that a DC bias voltage applied along the polarization direction ferroelectrically hardens the material, while the material softens and eventually depolarizes when the DC bias voltage is applied in the opposite direction. The results confirm the suitability of the designed measurement system and open new exciting possibilities for tuning the piezoelectric properties by DC bias fields.

Performance Portrait Method: An Intelligent PID Controller Design Based on a Database of Relevant Systems Behaviors.

The article deals with a computer-supported design of optimal and robust proportional-integral-derivative controllers with two degrees of freedom (2DoF PID) for a double integrator plus dead-time (DIPDT) process model. The particular design steps are discussed in terms of intelligent use of all available information extracted from a database of control tracking and disturbance rejection step responses, assessed by means of speed and shape-related performance measures of the process input and output signals, and denoted as a performance portrait (PP). In the first step, the performance portrait method (PPM) is used as a verifier, for whether the pilot analytical design of the parallel 2DoF PID controller did not omit practically interesting settings and shows that the optimality analysis can easily be extended to the series 2DoF PID controller. This is important as an explicit observer of equivalent input disturbances based on steady-state input values of ultra-local DIPDT models, while the parallel PID controller, allowing faster transient responses, needs an additional low-pass filter when reconstructed equivalent disturbances are required. Next, the design efficiency and conciseness in analyzing the effects of different loop parameters on changing the optimal processes are illustrated by an iterative use of PPM, enabled by the visualization of the dependence between the closed-loop performance and the shapes of the control signals. The main contributions of the paper are the introduction of PPM as an intelligent method for controller tuning that mimics an expert with sufficient experience to select the most appropriate solution based on a database of known solutions. In doing so, the analysis in this paper reveals new, previously undiscovered dimensions of PID control design.

Making the PI and PID Controller Tuning Inspired by Ziegler and Nichols Precise and Reliable.

This paper deals with the design of a DC motor speed control implemented by an embedded controller. The design is simple and brings some important changes to the traditional Ziegler-Nichols tuning. The design also includes a novel anti-windup implementation of the controller and an integrated noise-reduction filter design. The proposed tuning method considers all important aspects of the control, such as pre-processing of the measured signals and filtering (to attenuate the measurement noise), time delays of the process, modeling and identification of the process, and constraints on the control signal. Three important aspects of designing PI and PID controllers for processes with noisy output on Arduino-type embedded computers are considered. First, it deals with the integrated design of the input filter and the controller parameters, since both are interdependent. Secondly, the method of setting the controllers from step responses by Ziegler and Nichols is modified for the case of digital signal processing (without drawing the tangent), while it recommends the suitability of its modification in terms of the use of both integral and static models. Third, the most suitable anti-windup solution for the given controller structure is proposed. In summary, the paper shows that an appropriate design of the embedded controller can achieve excellent closed-loop performance even in a noisy process environment with limited control signals.

Improving disturbance rejection of PID controllers by means of the magnitude optimum method.

The magnitude optimum (MO) method provides a relatively fast and non-oscillatory closed-loop tracking response for a large class of process models frequently encountered in the process and chemical industries. However, the deficiency of the method is poor disturbance rejection performance of some processes. In this paper, disturbance rejection performance of the PID controller is improved by applying the "disturbance rejection magnitude optimum" (DRMO) optimisation method, while the tracking performance has been improved by a set-point weighting and set-point filtering PID controller structure. The DRMO tuning method requires numerical optimisation for the calculation of PID controller parameters. The method was applied to two different 2-degrees-of-freedom PID controllers and has been tested on several different representatives of process models and one laboratory set-up. A comparison with some other tuning methods has shown that the proposed tuning method, with a set-point filtering PID controller, is quite efficient in improving disturbance rejection performance, while retaining tracking performance comparable with the original MO method.

Comparative study of decay ratios of disturbance-rejection magnitude optimum method for PI controllers.

One of the key time-domain closed-loop performance requirements is the closed-loop response decay ratio. In this paper, the decay ratios of the disturbance-rejection magnitude optimum (DRMO) tuning method [Vrancic D, Strmcnik S, Kocijan J. Improving disturbance rejection of PI controllers by means of the magnitude optimum method. ISA Trans 2004; 43: 73-84; Vrancic D, Strmcnik S. Achieving optimal disturbance rejection by using the magnitude optimum method. In: Pre-prints of the CSCC'99 conference. 1999. p. 3401-6] are analyzed and compared to decay ratios of two other modern tuning methods, i.e. the Kappa-Tau tuning method (based on time-domain step-response characteristics) [Aström KJ, Högglund T. PID controllers: Theory, design, and tuning. 2nd ed. Instrument Society of America; 1995] and the non-convex optimization tuning method (based on frequency response) [Panagopoulos H, Aström KJ, Hägglund T. Design of PI controllers based on non-convex optimization. Automatica 1998; 34: 585-601; Panagopoulos H, Aström KJ, Hägglund T. Design of PID controllers based on constrained optimisation. IEE Proc Control Theory Appl 2002; 149 (1): 32-40]. It is shown that the DRMO method results in such a closed-loop response that the decay ratio is within a relatively narrow interval when compared to the other two methods.

Improving disturbance rejection of PI controllers by means of the magnitude optimum method.

The magnitude optimum (MO) method provides a relatively fast and nonoscillatory closed-loop tracking response for a large class of process models frequently encountered in the process and chemical industries. However, the deficiency of the method is poor disturbance rejection when controlling low-order processes. In this paper, the MO criterion is modified in order to optimize disturbance rejection performance, while the tracking performance has been improved by an integral set-point filtering PI controller structure. The new tuning rules, referred to as the disturbance rejection magnitude optimum (DRMO) method, were applied to several different two-degrees-of-freedom PI controllers. The DRMO method has also been tested on several different representatives of process models. The results of experiments have shown that the proposed tuning method with the integral set-point filtering PI controller is quite efficient in improving disturbance rejection performance, while retaining tracking performance comparable to the original MO method.