Discrete-time Control Design Research Articles

Combined Observer-Based State Feedback and Optimized P/PI Control for a Robust Operation of Quadrotors

This paper deals with a discrete-time observer-based state feedback control design by taking into consideration bounded parameter uncertainty, actuator faults, and stochastic noise in an inner control loop which is extended in a cascaded manner by outer PI- and P-control loops for velocity and position regulation. The aim of the corresponding subdivision of the quadrotor model is the treatment of the control design in a systematic manner. In the inner loop, linear matrix inequality techniques are employed for the placement of poles into a desired area within the complex z-plane. A robustification of the design towards noise is achieved by optimizing both control and observer gains simultaneously guaranteeing stability in a predefined bounded state domain. This procedure helps to reduce the sensitivity of the inner control loop towards changes induced by the outer one. Finally, a model-based optimization process is employed to tune the parameters of the outer P/PI controllers. To allow for the validation of accurate trajectory tracking, a comparison of the novel approach with the use of a standard extended Kalman filter-based linear-quadratic regulator synthesis is presented to demonstrate the superiority of the new design.

Sliding-mode-based impulsive control for a class of time-delay systems with input disturbance

This paper addresses the impulsive stabilization problem for a class of time-delay systems in the presence of input disturbances. A novel impulsive control law is constructed, which is based on the discrete-time equivalent control design technique. The sliding-mode-based impulsive control law allows counteracting the disturbance effect using its previous step value. To adapt in real time to the variation in sampling periods, the sliding function is designed as a function of impulse interval. Piecewise Lyapunov functions based on the partition on the maximum impulse interval are introduced to deal with the time-varying structure of the sliding function. Sufficient conditions for exponential input-to-state stability (EISS) of the impulsively controlled systems are derived, in which the EISS gain characterizes the attenuation ability of the proposed impulsive control law on the disturbance estimation error. The disturbance attenuation performance of the proposed impulsive control strategy is demonstrated through the time-delay Chua’s circuit.

Hybrid output regulation for linear impulsive systems with aperiodic jumps: A discrete-time feedback controller design approach

This paper is concerned with the problem of hybrid output regulation for a class of linear impulsive systems with aperiodic jumps. Firstly, by leveraging time-dependent Lyapunov function technique and impulsive control theory, sufficient conditions for achieving output regulation are obtained in state feedback case. Then, the results are extended to error feedback case by constructing an impulsive observer. In this framework, two novel hybrid controllers are designed. Such controllers only need the discrete-time system state or error signal for feedback. The complete procedures for controller designs are also presented. Finally, two illustrative examples, including a numerical example and an LC circuit, are given to show the validity and applicability of the proposed control laws.

Discrete-time Flatness-based Controller Design using an Implicit Euler-discretization

In this contribution, we present a constructive method to derive flat sampled-data models for continuous-time flat systems through an implicit Euler-discretization. We show how the sampled-data model can be used subsequently for a flatness-based controller design, and illustrate our results with the well-known planar VTOL aircraft example.

Simultaneous design of discrete-time inverse response predictor control systems

Inverse response is exhibited by a wide array of industrial processes. The presence of inverse response imposes certain innate limitations on the achievable control performance of a conventional feedback control system. In order to alleviate these limitations, an additional predictor block is added to the conventional feedback system to compensate for the effects of inverse response and the modified process dynamics is controlled by a PID controller. However, all the previous model-based design methods have been developed in Laplace domain. Hence, this work proposes a data-based method for discrete-time predictive controller design for processes with inverse response using Virtual Reference Feedback Tuning (VRFT) design method. A robust stability criterion is also developed for the proposed predictive control system. Simulation results are presented to illustrate applications of the proposed design method and a comparison with the model-based predictor system and a VRFT-based conventional PID design is made.

Electrical Drives Control via Discrete-Time Variable Structure Systems with Sliding Mode

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.

Discrete-Time Controller Design for Pitch Channel

Discrete-Time Controller Design for Pitch Channel

Discrete-time filter proportional–integral–derivative controller design for linear time-invariant systems

This paper introduces a new discrete-time filter proportional–integral–derivative (FPID) controller framework for linear time-invariant (LTI) systems. The discrete-time FPID controller plays an important role in both determining the dynamic response of the system and further improving the performance of the controller in itself. However, the introduction of the filter parameter brings more challenge for the design of discrete-time FPID controllers than that of discrete-time PID controllers. A novel result on the co-design of such a controller via dominant eigenvalue assignment is first provided, which enables us to tune the controller directly in accordance with the desired system performance indexes. Then, a further result on the discrete-time FPID controller design to improve the dynamic response of the closed-loop system is derived by placing the non-dominant eigenvalues in some assigned region. Compared with the discrete-time PID controller, on the one hand, the discrete-time FPID controller plays a significant role in improving the output of the controller in addition to guaranteeing the desired dynamic performance of the closed-loop system. On the other hand, a discrete-time FPID controller makes it possible to expand the effective parameter region and give a set of parameters which makes the controller achieve the objective of dominant eigenvalue assignment for the closed-loop system when a traditional discrete-time PID controller cannot do. Numerical examples have illustrated the effectiveness of the proposed results.

Optimal design of discrete-time fractional-order PID controller for idle speed control of an IC engine

This paper aims at proposing a discrete-time fractional-order PID (FOPID) controller, which can stabilise the variation of the idle speed of an internal combustion engine due to the occurrence of the external load disturbance. The nonlinear idle speed dynamics is linearised to be approximated by a first order plus dead time (FOPDT) model so that the FOPID controller can be initialised by a Ziegler-Nichols type tuning rule. The initialised FOPID controller can stabilise the linearised model, but it may lose its control capability in nonlinear idle speed dynamics. Therefore, an optimisation problem is solved through genetic algorithm (GA) to minimise a cost function within a small region around the FOPID's initial parameters. The optimal discrete-time FOPID controller are compared to a conventional discrete-time PID controller. The simulation study reveals that the optimal discrete-time FOPID controller secures an excellent control performance to the nonlinear idle speed model.

Optimal design of discrete-time fractional-order PID controller for idle speed control of an IC engine

This paper aims at proposing a discrete-time fractional-order PID (FOPID) controller, which can stabilise the variation of the idle speed of an internal combustion engine due to the occurrence of the external load disturbance. The nonlinear idle speed dynamics is linearised to be approximated by a first order plus dead time (FOPDT) model so that the FOPID controller can be initialised by a Ziegler-Nichols type tuning rule. The initialised FOPID controller can stabilise the linearised model, but it may lose its control capability in nonlinear idle speed dynamics. Therefore, an optimisation problem is solved through genetic algorithm (GA) to minimise a cost function within a small region around the FOPID's initial parameters. The optimal discrete-time FOPID controller are compared to a conventional discrete-time PID controller. The simulation study reveals that the optimal discrete-time FOPID controller secures an excellent control performance to the nonlinear idle speed model.

Discrete-Time Control Design Based on Symplectic Integration: Linear Systems

We propose a novel approach to design discrete-time state feedback controllers for sampled control systems with guaranteed stability under arbitrary sampling times that fulfill the Nyquist-Shannon condition. The key idea is borrowed from symplectic integration and backward error analysis of Hamiltonian systems: The closed-loop target system is the discretized version of a continuous-time system with appropriately shaped Hamiltonian, where a symplectic scheme is used for discretization. We adopt this argumentation for a systematic discrete-time design procedure for controllable linear systems based on the implicit midpoint rule. We motivate the approach on the example of two basic linear systems under zero order hold sampling, we show the construction of target systems with desired eigenvalues based on the discrete-time controller canonical form, and we illustrate the quality of the main result on a random sixth order system.

Robust decentralized controller design based on equivalent subsystems

A method for robust decentralized controller design of continuous and discrete-time controllers for SISO and MIMO systems is proposed. The uncertain MIMO system is given by a set of square transfer matrices of any dimension. The design procedure relies on the Equivalent Subsystems Method (ESM) – an independent design of local controllers for stability and required performance of the overall system. The ESM has been extended by integrating robust stability conditions directly in the independent design of local controllers to obtain a unified robust decentralized controller design method. To demonstrate the design procedure, a discrete-time robust decentralized PID controller for a minimum-phase system was designed.

Online discrete-time LQR controller design with integral action for bulk Bucket Wheel Reclaimer operational processes via Action-Dependent Heuristic Dynamic Programming

In this paper, a novel approach for online design of optimal control systems applied to the bulk resumption process by bucket wheel reclaimer (BWR) is presented. This approach is based on reinforcement learning paradigms, more specifically Action Dependent Heuristic Dynamic Programming (ADHDP), that learn online in real-time the Discrete Linear Quadratic Regulator (DLQR) optimal control solution with integral action. Due to the geometric irregularities of the storage yard stacks and variation in physical and chemical characteristics of the stacked material, the flow control of solid bulks by bucket wheel reclaimer requires methods that are suitable with the high degree of imprecision of process variables and environment uncertainties. The resumption of bulk solids is carried out by dividing the stack into layers, each layer is approximately 4 m high, and the layers are divided into workbenches up to 12 m in length. To take up a workbench several translation steps are required (penetration in the stack), with the translation step varying from 0 to 1 m. In order to maintain the desired ore flow throughout the process, the BWR lance speed must be periodically adjusted. The main advantage of the proposed control method is that besides the decision rule is fully independent of plant model, the gains of the resulting controller are self-adjustable. The control system was designed in such a way that the ADHDP-based DLQR controller with integral action would act in real-time in the plant control, using only the input and output signals and states measured along the system trajectory.

Accurate two-degree-of-freedom discrete-time current controller design for PMSM using complex vectors

Properties of the current controller are essential for permanent magnet synchronous machine (PMSM) drives, but the conventional continuous-time current controller cannot fully decouple the cross-coupling terms when applied in the digital processor. Its performance is related closely to the rotational speed. To improve the performance of the current loop, the direct design method in the discrete-time domain is adopted using the accurate discrete-time complex vector model. An integrated accurate hold-equivalent discrete model for PMSM is derived considering the difference between the output of the voltage source inverter and the back electro-motive force. Then an accurate two-degree-of-freedom (2DOF) current controller with a third-order closed-loop transfer function is designed. The 2DOF controller has more freedom in pole placement, and two schemes with a different cancelled pole-zero pair are investigated. Analysis is conducted by the robust root locus method via the complex vector root locus and sensitivity functions, showing properties in disturbance rejection and sensitivity to parameter variation of two schemes. Both schemes have their own advantages. Finally, the dynamic performance and flexibility of the proposed current controller is verified on a 2.5-kW PMSM test bench.

Digital stabilizer design for a switched linear system

We consider the problem of designing a digital controller stabilizing a continuoustime switched linear system. Our approach to stabilization includes the construction of a continuous-discrete time closed-loop system, the passage to its discrete-time model, and the subsequent discrete-time controller design based on simultaneous stabilization methods.

Identification of Discrete-Time Output Error Model Using Filtered Input Excitation for Integrating Processes With Time Delay

A discrete-time output error (OE) model identification method is proposed for industrial integrating processes with time delay, to facilitate the discrete-time controller design and implementation in sampled systems. By subtly introducing a differential filter to the input excitation, an open-loop identification test can be performed for such a process while complying with the output limit. Correspondingly, the parameter estimation is equivalently transformed to identify a stable type OE model with time delay. A recursive identification algorithm is developed to simultaneously estimate all the model parameters including the integer delay, and a linear interpolation of the input excitation is given for the recursive computation to guarantee consistent estimation. The convergence of parameter estimation is analyzed with a proof. An illustrative example is used to demonstrate the effectiveness of the proposed method.

Characteristic model-based control of robotic manipulators with dynamic uncertainties

In this paper, we investigate the problem of the discrete-time adaptive control design of robotic manipulators by utilizing the characteristic model theory. Different from the traditional plants manipulated by the characteristic model-based control strategy, the Coriolis matrix in the robotic dynamics makes the bound of the characteristic model coefficients rely on the state information, proposing great challenge for the controller design and stability analysis. To conquer this problem, we develop a projection estimation algorithm depending on the state information, and propose an adaptive control law via introducing a discrete-time sliding vector. A new stability analysis framework is proposed by use of the recursive induction methodology, giving rise to the asymptotic convergence of joint positions. Simulations are performed to test the effectiveness of our methodology. Our design extends the characteristic model theory frame by proposing the control design and stability analysis methods for the the characteristic model with the state-relevance coefficients.

Design of Discrete Time Controllers for the DC-DC Boost Converter

In this paper, a small signal model for the boost converter is obtained. Two digital controllers using pole placement technique and Linear Quadratic Optimal Regulator (LQR) methods are designed and applied to the boost converter. The compensated system’s operations and analysis are discussed and verified through MATLAB/Simulink simulation. Comparison between the two controllers related to the design methodology, implementation issues and transient measured performance is carried out.

Piezoelectric Nanopositioning Control Using Second-Order Discrete-Time Terminal Sliding-Mode Strategy

This paper presents the design of a novel second-order discrete-time terminal sliding-mode control (2-DTSMC) strategy and its application to motion tracking control of a piezoelectric nanopositioning system, which possesses a high-order plant model. The 2-DTSMC strategy is established based on the output feedback only, which eliminates the use of a state observer and facilitates an easy realization. Theoretical analysis proves that the quasi-sliding mode is reached in finite time along with high accuracy of the output tracking. The effectiveness of the proposed control scheme is validated through comparative investigations. Experimental results show that the 2-DTSMC strategy is superior to traditional discrete-time sliding-mode control (DSMC), second-order DSMC, and DTSMC algorithms in terms of motion tracking accuracy, which demonstrates the efficiency of the reported 2-DTSMC scheme with a second-order nonlinear sliding surface.

Fixed-structure LPV discrete-time controller design with induced l2-norm and performance

ABSTRACTA new method for the design of fixed-structure dynamic output-feedback linear parameter-varying (LPV) controllers for discrete-time LPV systems with bounded scheduling parameter variations is presented. Sufficient conditions for the stability, and induced l2-norm performance of a given LPV system are represented through a set of linear matrix inequalities (LMIs). These LMIs are used in an iterative algorithm with monotonic convergence for LPV controller design. Extension to the case of uncertain scheduling parameter value is considered as well. Controller parameters appear directly as decision variables in the optimisation program, which enables preserving a desired controller structure in addition to the low order. Efficiency of the proposed method is illustrated on a simulation example, with an iterative convex optimisation scheme used for the improvement of the control system performance.