This article proposes a new robust dead‐beat controller for multivariable systems using multirate sampled data. Applying a discrete‐time higher order sliding mode control approach, the proposed dead‐beat controller design uses the state‐space nominal model (model without disturbances) of the system and its controllability indices to compute the state feedback matrix. The obtained control annihilates the system state in a minimal number of sampling periods. For example, a heuristic procedure for selecting a sampling time is considered in order to keep maximal amplitudes of control inputs within the allowable limits. Since the dead‐beat control has poor robustness, a new discrete‐time supertwisting disturbance observer is used to suppressed disturbance effects. Stability analysis of the proposed observer has shown that it is suitable for Lipschitz type of disturbances. The sampling period of the disturbance observer is generally smaller than the control sampling period. Properties of the proposed control system are demonstrated in simulation examples.

Modern control techniques of electrical drives (EDs) use robust control algorithms. One of such algorithms is variable structure control (VSC) with sliding mode (SM). SM control needs more information on the controlled plant than the conventional PI(D) control. Valid mathematical model of the controlled plant is necessary for the SM controller design. Generalized mathematical model of two-phase electrical machine and its adaptation to direct current (DC) and induction motor (IM) are given in this paper, employed in the cascade control structure. Also, the basic SM control theory and discrete-time controller design approach, developed by the authors, are given. Finally, experimentally realized examples of speed and position control of DC and IM are given as an illustration of the efficiency of the promoted EDs controller design via discrete-time VSC.

Abstract The paper proposes a discrete-time sliding mode controller for single input linear dynamical systems, under requirements of the fast response without overshoot and strong robustness to matched disturbances. The system input saturation is imposed during the design due to inevitable limitations of most actuators. The system disturbances are compensated by employing nonlinear estimation by integrating the signum of the sliding variable. Hence, the proposed control structure may be regarded as a super-twisting-like algorithm. The designed system stability is analyzed as well as the sliding manifold convergence conditions are derived using a discrete-time model of the system in the δ-domain. The results obtained theoretically have been verified by computer simulations.

This paper proposes a control method for multi-input linear systems that provides the closed-loop system dynamics of an arbitrary order having a specified feasible spectrum of poles. By appropriate selection of auxiliary outputs, the system is decoupled into a set of subsystems. The number of these subsystems is equal to the number of control inputs. The desired dynamic of the considered system is achieved using higher order sliding mode, where the sliding mode of appropriate order is realized in each subsystem. The proposed control approach is illustrated by a simulation example.

This paper presents a new dead-beat control design for a class of multi-input linear time-invariant continuous-time controllable systems. The system is controlled using multi-rate sampled data. First step in design is to obtain the controllability index vector. Using elements of this vector known as controllability indices, the state feedback matrix is computed applying higher order sliding mode control approach. The number of sliding variables is equal to the number of control inputs. Obtained control annihilates system state in a minimal number of sampling periods which is equal to the maximal value of controllability indices. Since, the dead-beat control has poor robustness, a disturbance compensation is designed. In this paper, the compensation control is equal to the negative value of the disturbance estimate. The estimate is obtained using the equivalent control approach, while the compensation sampling period is not the same as the deadbeat control sampling period. The control is formed as the dead-beat control term and the compensation control which suppressed disturbance effects. The sampling period of compensation control is generally smaller than the control sampling period. Properties of the proposed control system are demonstrated on a simulation example.

This paper introduces a control method for finite time stabilization of continuous-time controllable linear time invariant multiple-input multiple-output systems. The proposed approach uses higher order sliding mode control to reduce the system order to zero and thus providing the system states to reach the origin in finite time. Such control is called finite time order zeroing control, because it annihilates all sliding variables and their associated derivatives in finite time, while system states converge to equilibrium point. Sliding manifold reaching control uses quasi-continuous control functions. Properties of the proposed control system are demonstrated on a simulation example of a real system model.