In this paper, an effective method is proposed for robust proportional-integral-derivative (PID) control that is easily implementable on commonly used equipment such as programmable logic controller (PLC) and programmable automation controller (PAC). The method is based on a two-loop model following control (MFC) system containing a nominal model of the controlled plant and two PID controllers. Basic features exhibited by the MFC structure are presented, and a technique to tune both component controllers is given. The proposed structures have been implemented in a programmable logic controller and tested on control plants with perturbed parameters. Also, the proposed control system has been checked for its performance in cases when the operation of PID controllers is based on fuzzy logic. Tuning rules for the fuzzy controllers in the presented MFC system have been proposed. Results of tests lend support to the view that the proposed control structures may find wide application to robust control of plants with time-varying parameters.

During milling of flexible workpieces a regenerative chatter vibration may become a critical factor that limits productivity. It is shown in this paper that a selection of cutting parameters based on a stability lobes diagram may not always be a remedy for low productivity due to increased forced vibration level. Additionally, other factors such as tool wear may limit the selection of stable spindle speeds. This paper presents an active control system that counteracts the development of chatter vibration. The proposed active control system employs Linear Quadratic Gaussian (LQG) algorithm and piezoelectric actuator to suppress vibration during cutting. The Kalman filter is used to estimate the state of the system required by LQG algorithm. The active control introduces damping into the system, thereby raising the critical depth of cut and reducing forced vibration amplitude. It enables stable cutting under a much wider range of cutting parameters than for the uncontrolled system. Cutting tests are performed to demonstrate an effectiveness of the control system. Practical issues limiting applications of the proposed technique are discussed.

The paper deals with robustness to plant parameter perturbations and sensitivity to disturbances of two‐loop control structures containing a model of the controlled plant and two PID controllers. Special attention is paid to high robustness of considered structure to perturbations of the controlled plant in relation to its nominal model and to good reduction of disturbances. On the basis of presented simulation results one can compare properties of the proposed structure with properties of the Smith predictor and classic control system structure with single feedback loop. The proposed model following control structures may find wide application to robust control of parameter‐varying plants.

In the paper a multiple use of the fractional-order differential calculus theory in the model predictive control is proposed. First, the principle of the integer-order linear predictive control and theoretical foundations of the fractional-order differential calculus are reminded. Using the presented theoretical foundations attention is focused further on the possibility of developing the fractional-order model predictive control with an internal process model and a fractional-order cost function. The introduction of the fractional-order differential calculus at the stage of synthesizing the control algorithm offers an additional degree of freedom in tuning a control loop. The discussion is illustrated with results of some laboratory experiments.