Digital Pid Controller Design for Delayed Multivariable Systems

Abstract

A new methodology is proposed to design digital PID controllers for multivariable systems with time delays. Except for a few parameters that are preliminarily selected, most of the PID parameters are systematically tuned using the developed plant state-feedback and controller state-feedforward LQR approach, such that satisfactory performance with guaranteed closed-loop stability is achieved. In order to deal with the modeling error owing to the delay time rational approximation, an IMC structure is utilized, such that robust stability is achieved, without need for an observer, and with improved online tuning convenience. Using the prediction-based digital redesign method, the digital implementation is obtained based on the above-proposed analog controller, such that the resulting mixed-signal system performance will closely match that of the analog controlled system. An illustrative example is given for comparison with alternative techniques.

Inverter synchronization control with Internal Model Principle

“…Among them, the prediction-based digital redesign method in [8,9] is utilized in this paper, which can shift the discrete-time control signal to defined inter-sampling instant to minimize the A/D conversion error by means of "equivalent area" principle.…”

“…In order to reduce the calculation rate, closed-loop global digital redesign techniques are better suited since it takes into account the closed-loop nature of the whole system [8][9][10][11]. Among them, the prediction-based digital redesign method in [8,9] is utilized in this paper, which can shift the discrete-time control signal to defined inter-sampling instant to minimize the A/D conversion error by means of "equivalent area" principle.…”

“…Since the digital controller is working in discrete-time domain, the afore-mentioned continuous-time s-domain controller needs to be converted into the corresponding zdomain function. Other than the direct digital design method in z-domain only, advantages of digital redesign approach are: (i) Continuous-time design theory and tools are well developed, and intuitively more familiar to most engineers; (ii) Digital redesign separates the problems of basic controller design from that of sampling and calculating period selection and adjustment [8][9][10][11].…”

“…Since proposed controller will have three poles on complex axis, Linear Quadratic Regulator (LQR) in [7] is introduced to enhance stability. Based on the continuous-time controller in s-domain, digital redesign in [8,9] is then conducted to obtain the corresponding discrete-time controller in zdomain. Other than the direct digital design method in zdomain only, advantages of digital redesign approach include: (i) Continuous-time design theory and tools are well developed, and intuitively more familiar to most engineers; (ii) Digital redesign separates the problems of basic controller design from that of sampling and calculating period selection and adjustment [10]; (iii) Compared with conventional redesign method like bilinear transform, proposed global digital redesign method can effectively enlarge the sampling period while maintaining the essential performance [11].…”

Design of a Model-following Controller Using a Decoupling Active Disturbance Rejection Control Method

“…There are many reports concerning these problems, and basic important results are already known [9][10][11][12]. To solve the decoupling problems, specific design methods have been investigated, including those based on state feedback [13] and state decouplers [14][15][16]. However, most of these methods depend on the plant parameters, and large variations in the plant parameters make it difficult for the system to decouple.…”