Improved digital tracking controller design for pilot-scale unmanned helicopter

Abstract

In this paper, methods for improved design of digital tracking controller for a pilot-scale unmanned helicopter are considered. By discretizing the linearized helicopter model, the linear quadratic with integral (LQI) capability is investigated and applied in order to develop an efficient tracking system including a state-feedback plus integral action. The helicopter velocities are used to formulate a prescribed position reference tracking trajectory. When both process and measurement noises are present, a Kalman filter (KF) is combined with the LQI to form a linear quadratic Gaussian with integral (LQGI) tracking system. Simulation studies illuminate both the capability of the controller design and the accuracy of the estimator. Next, H₂, $H_{\infty }$ and mixed $H_2/H_{\infty }$ controls are designed and the results between methods are produced and compared.

Introduction

In recent years, we have witnessed wide variety of techniques and applications of control theory to several systems engineering areas robust control [1], [2], [3], including PID control [4], time-varying systems [5], [6], networked control systems [7], [8], autonomous systems [9], [10], [11], Internet control [12], attitude stabilization of rigid spacecraft [13], [14], [15], to name a few. The primary focus of this work is on a class of autonomous systems [9]. In this regard, unmanned aerial vehicle (UAV) with helicopter-like capabilities such as vertical take-off and landing is becoming popular in systems studies. The interest in helicopter-based unmanned aerial vehicle (HUAV) has central focus for both military and civil applications. It is well-known that helicopter is a non-linear complex system with unstable nature and, in turn, these characteristics render the design in flight control systems a difficult task. Pilot-scale unmanned helicopter constitute by now common platforms for HUAV control development with many great advances been made since the last decade. Compared with traditional full-size helicopters, a pilot-scale helicopter tend to be naturally more maneuverable and responsive [10]. Some related results are reported in [16], [17], [18].

System identification has been used as a modeling technique to derive linear models for control design and to study the vehicle flying qualities. Also, system identification is utilized for the validation and refinement of detailed non-linear first-principle models. There are several reported applications of system identification techniques to modeling of pilot-scale helicopters, including the model identification of YAMAHA R-50 [10], and X-Cell [19] for flight control, and a 6-DOF dynamic modeling of Raptor-50 V2 for simulations [9]. In this paper, the pilot-scale unmanned helicopter dynamics reported in [10] will be used in the sequel as the preliminary vehicle for control system design.

Most HUAVs used classical control system such as single-loop PD systems. The tuning for controller parameters usually performed manually for certain operating point such as hover and cruise mode. This condition giving a wide opportunity for multi-variable controller synthesis method to be implemented. In previous work [20], linear quadratic trajectory tracking system with derivative on the error for HUAV conducted in continuous-time mode, and reports encouraging preliminary results. There are numerous predicted utilizations for HUAV either individually or working as a team, including surveillance, search and rescue, and mobile sensor networks. For this uses, HUAV needs to be able to navigate to the desired destination through desired trajectory, the position control as well as velocity control are performed for this scenario. A controller that can accommodate this scenario is needed, linear quadratic integral (LQI) [21] tracking control is proposed, and for practical needs in the presence of process and measurements noise, linear quadratic Gaussian integral (LQGI) tracking control is proposed with the assumption that the noise is white. This motivates the study of this paper by looking at effective methods for controlling pilot-scale HUAVs.

Looked at in this light, this paper provides improved digital controller design and simulations using the powerful tools of MATLAB and SIMULINK. Computer simulation in discrete-time is conducted with certain sampling time will allow direct implementation on the practical controller. The dynamics of helicopter on cruise is used for the trajectory tracking system [10]. Then a linear quadratic Gaussian with integral (LQGI) control is designed with the assumption that sensor available is only for velocities and corrupted with white noise. The ensuing measurements are used to perform state estimation using Kalman filter (KF). For the controller design based on H₂, $H_{\infty }$ and mixed $H_2/H_{\infty }$ performance, the simulations are performed in continuous-time mode. The results are presented and a comparison among design methods is performed.