Robust Digital Controller Design Research Articles

Robust digital pole-placer for electric drives based on uncertain diophantine equation and interval mathematics

In this paper, a novel robust digital controller design is proposed and implemented for induction motor speed control. The objective is to design a robust output feedback controller that places the closed-loop poles in a specified region in order to achieve the desired dynamic performance for a system with variable load. The design is carried out in the frequency domain by solving the uncertain Diophantine equation using interval mathematics and non-linear optimization method. In order to capture the load variations, the characteristic equation is relaxed and enlarged from a fixed-point to an interval set. A simple model-based design methodology is adopted in this work and implemented experimentally using a Hardware-in-the-Loop environment. The proposed design is simulated and then validated using real induction drive system. The proposed controller is compared with two other controllers: the auto tuned PID and a least-square-based robust controller. Experimental results show that the designed robust controller provides a better dynamic response than conventional controllers used in the industry when the motor’s load is varied. These results validate the proposed design as the plant’s output follows the reference signal with minimal overshoot and settling time.

Pole placement with sensitivity function shaping using 2nd order digital notch filters

This technical note deals with the design of robust digital controllers using pole placement with sensitivity shaping by means of the use of digital notch (band-stop) filters. The use of this type of filters drastically simplifies the effective shaping of the sensitivity functions and the resulting procedure competes with the procedure based on the use of Q-parameterization combined with convex optimization (Automatica 35 (1999) 1111). The feasibility of the technique is illustrated by its application to the control of a very flexible arm.

Tracking Digital Controller for Robot Manipulator

The problem of the robust digital controller design to solve a tracking problem for robotic manipulators is studied. The design method based on the formation of two-time scale motions in the closed loop system is used. It has been shown that if a sufficient time-scale separation between the fast and slow modes in the discussed closed loop system and stability of fast modes are provided then slow modes have the desired form and thus the output transient performance indices are insensitive to parameter variations and external disturbances of the robotic manipulator. Numerical simulations of the two-link robotic manipulator are presented.

Design of the Universal Digital Flight Controller for an Aircraft with Not Exactly Known Parameters

The problem of the robust digital controller design to solve a tracking problem for Euler angles of aircraft motion is studied. The design method based on the formation of two-time scale motions in the closed loop system is used. A resulting output feedback digital controller has a simple form of a combination of three low-order linear dynamical discrete-time systems and a matrix whose entries depend non-linearly on certain known process variables. Assuming a small sampling period, robust decoupled output tracking with desired continuous-time dynamics is accomplished under conditions of incomplete information about varying parameters of the system and unknown external disturbances.

Accuracy Analysis of Digital Control Systems With Two-Time-Scale Motions

The problems of the robust digital controller design and control accuracy analysis are discussed. The design method based on the formation of two-time scale motions in the closed loop system is used. If a sufficient time-scale separation between the fast and slow modes in the discussed closed loop system and stability of fast modes are provided then slow modes have the desired form. Thus the output transient performance indices are insensitive to external disturbances. The relationships for control accuracy analysis and choice of the sampling period are obtained. Finally, an example with simulation results is presented.

Design of Digital Controller for Aircraft Longitudinal Motion

The problem of the robust digital controller design to form the desired transients for aircraft longitudinal motion is discussed. The design method based on the formation of two-time scale motions in the closed loop system is used. Assuming a small sampling period, robust decoupled output tracking with desired continuous-time dynamics is accomplished under conditions of incomplete information about varying parameters of the system and unknown external disturbances. Simulation results are presented.

Combined pole placement/sensitivity function shaping method using convex optimization criteria

This paper deals with the design of robust digital controllers by the combined pole placement/sensitivity function shaping method. The problem of assigning a desired region for the closed-loop poles and simultaneously respecting certain bounds on the sensitivity functions is formulated and solved as a convex optimization problem. Specifications like dominant closed-loop poles or integration controller action may be introduced just as well as other fixed parts for the controller. The method is illustrated by the controller design for a very flexible 360° arm.

Pole Placement Design Using Convex Optimisation Criteria for the Flexible Transmission Benchmark

This paper deals with the design of robust digital controllers by the combined pole placement/sensitivity function shaping method. It shows that the design problem can be formulated and solved as a convex optimisation problem. Specifications like dominant closed-loop poles or integration controller action may be introduced just as well as other fixed parts for the controller. The method is illustrated by the application to a benchmark of robust control of a flexible transmission system. Simulation results and real-time comparisons with previously designed controllers are presented.

Direct Robust Sampled-Data Marine Control Systems Design on Basis of Parametric Transfer Function Method

The problem of robust digital control of a continuous-time plant is addressed. A novel method is proposed for the direct design of robust digital controllers, that provides for stability and high-quality plant stabilization under non-parametric perturbations in the plant and disturbance models. The method is based upon the parametric transfer function concept. A polynomial-based algorithm is presented for designing discrete transfer function of the optimal robust controller.

Robust digital controller design for processes with dead times: New results

The Dahlin controller is studied in the complex-frequency domain in terms of performance and robust stability. Several well known digital control algorithms are compared with the Dahlin controller and found to be equivalent to it. The possibility of extending the Dahlin controller to the control of plants with zeros outside the unit circle and unstable plants is discussed. The essential cause of ringing is investigated and some ambiguous formulation is clarified. A new procedure is developed for digital controller design. Compared with conventional methods, it provides a more effective method of eliminating ringing. Finally, numerical examples are given to illustrate the new approach.

Robust digital control of systems with time delay (the Smith predictor revisited)

The design of robust digital controllers for systems with time delay is investigated. A particular class of digital controller is considered, namely those for which the closed-loop poles include the poles of the system to be controlled. Robust design with respect to time delay variations requires the introduction of additional closed-loop poles and/or reduction of the gain of the feedback path at high frequencies (near 0-5 fs , where fs is sampling frequency). Relationships with other robustification procedures are examined.

Design of robust digital controllers and sampling-time selection for SISO systems

The stability of a digital control system and its performance in terms of the continuous plant output are studied. A two-step controller design is proposed. In the first step, the assumption of no modelling error is made and a controller that combines properties of the algorithm that minimizes the sum of squared errors and a deadbeat-type algorithm is designed so that no intersample rippling appears. In the second step, a filter is designed so that appropriate conditions which guarantee robust stability and performance in the presence of model-plant mismatch are satisfied. The effect of the sampling time on the achievable performance and the robustness properties of the system is examined and the results are incorporated in a complete procedure for sampling-time selection and robust controller design. Finally, the procedure and some theoretical implications are illustrated with examples.

Design of robust digital controllers for gas turbines with explicit actuator and sensor dynamics

Design of robust digital controllers for gas turbines with explicit actuator and sensor dynamics