Neural Networks for Helicopter Azimuth and ... - Semantic Scholar
Neural Networks for Helicopter Azimuth and Elevation Angles Control Obtained by Cloning Processes Tarik Uzunovic, Jasmin Velagic, Nedim Osmic, Almir Badnjevic, Emir Zunic Department of Automatic Control and Electronics Faculty of Electrical Engineering, University of Sarajevo Sarajevo, Bosnia and Herzegovina Abstract— Neural networks have been applied very successfully in the identification and control of nonlinear dynamic systems. The paper presents a design of neural network based control system for 2DOF nonlinear laboratory helicopter model (Humusoft CE 150). The main objective of this paper is to develop artificial neural networks to control helicopter’s motors, or consequently elevation and azimuth angles. Neural networks are obtained by cloning various type of controllers designed in our previous papers. Those procedures included a cloning linear PID controller, gain scheduling controller and fuzzy controller. Keywords—helicopter model, neural network, cloning process, fuzzy controller, adaptive gain scheduling control
I.
INTRODUCTION
The helicopter was known to be inherently unstable, complicated and nonlinear dynamic system under a significant influence of disturbances and parameter perturbations. The system has to be stabilized using a feedback controller. The stabilizing controller may be designed by the model-based mathematical approach or by heuristic control algorithms. Due to the complexity of the helicopter dynamics, there have been efforts to apply non-model-based approaches such as fuzzylogic control, neural network (NN) control, or a combination of these. The problem of helicopter control has received much attention and especially during the last two decade, its nonlinear version has been intensively developed [1] - [3]. Nonlinear control techniques, such as feedback linearization, rely heavily upon accurate knowledge of the helicopter dynamics. However, some aerodynamic effects are very difficult to model [4], [5]. Accounting for uncertain effects using robust control is, in general, a conservative approach and may sacrifice achievable performance. In contrast, a control system that adapts the nonlinear dynamics of various flight regimes as they occur has the potential to achieve superior performance throughout the full envelope. To date, most adaptive flight control designs have addressed the issue of the uncertain aerodynamic effects within the context of linear control [6]. Many of the results in adaptive control are derived from Lyapunov stability theory, such as parameter and indirect adaptive control schemes [6], [7]. The sensitivity of some adaptive schemes to disturbances and unmodeled dynamics
prompted many researchers to investigate robust adaptive nonlinear control [8], [9]. Because of their well known abilities to approximate uncertain nonlinear mappings to a high degree of accuracy and their ability to learn, NN’s have come to be seen as a potential solution to many outstanding problems in adaptive and/or robust control of nonlinear systems [10], [11]. At present, most of the works on system identification using neural networks are based on multilayer feedforward neural networks with backpropogation learning or more efficient variations of this algorithm. The literature includes numerous applications of NN’s to flight control systems, a selection of which will be discussed here. Baron et al., employed polynomial networks for fault detection and reconfigurable flight control [12]. Linse and Stengel demonstrated that NN’s could be used to identify aerodynamic coefficients [13]. Applications in which NN’s are used to control super maneuverable aircraft are described by [14] and [15]. Survey papers commenting on the role of NN technology in flight control system design have been contributed by Werbos [16] and Steinberg [17, 18]. In this paper we have used controllers designed in our recent papers [19], [20] and [21] to generate the input/output training data for NN design. The main objective is to mimic the behaviors of these controllers and to improve their control performance. For this purpose, the supervised learning capabilities of NNs can be used for identifying controller models from input/output data. All networks used in this paper are feedforward neural networks with the backpropagation (BP) learning algorithm. This paper is organized as follows. Section II presents the control system for azimuth and elevation angles. In section III the mathematical model of 2DOF helicopter is described. Section IV demonstrates the design of NN controllers those mimic the behaviors of previous designed PID, adaptive and fuzzy controllers. Simulation and experimental results are given in section V. II.
CONTROL SYSTEM DESCRIPTION
The main components of the proposed real-time helicopter control system are shown in Fig. 1. The system is composed of three main components: PC based controller, hardware interface and helicopter model. The neural network (NN) based
,(((
1076
Load Ref. Inputs
NN Controller
RT Workshop
xPC Target
MF 624 card
PWM drives
DC motors
Helicopter body
Ψ, φ
Matlab/ Simulink
Interface bit/rad
32-bit words
MF 624 card
Encoders
Helicopter model
Computer
Figure 1. Block diagram of the proposed real-time control system for a laboratory helicopter model.
controllers are designed in the Matlab/Simulink program package. The second component (MF624) represents the multifunctional card for data acquisition and transmission. It connects the PC and helicopter system and provides implementation control algorithm from the PC to the helicopter system. The helicopter system contains the DC motors with permanent stator magnets, power amplifiers (PWMs), encoders as sensors and axel gear (represents load). In the following subsections the mentioned components will be described.
The axes of the main and tail rotors and the vertical and horizontal helicopter axis are perpendicular to each-other. In this paper the helicopter model can be represented as a nonlinear multi-variable system with two inputs (u1 and u2) and two outputs (ψ and φ are measured in radians or degrees):
A. Helicopter Model Physical model as well as simplified laboratory model helicopter which includes a helicopter body is driven by two motors that drive the main and tail propeller.
The inputs u1 and u2 are measured in machine units ranging from [–1,1]. An interface unit (Fig. 2.), which connects the helicopter and the computer, converts the inputs from machine units to appropriate voltage values that drive the motors. Output ψ denotes the elevation angle, i.e. the angle between the vertical axis and the longitudinal axis of the helicopter body, where as φ denotes the azimuth angle, i.e. the angle in the horizontal plane between the longitudinal axis of the helicopter body and its zero position.
The laboratory helicopter set-up (Fig. 2.) comprises a helicopter body carrying two motors, which drive the main and the tail propeller of the helicopter. The helicopter body is connected to a base so that two degrees of freedom (2 DOF) are enabled: • •
rotation around the horizontal axis-elevation angle ψ rotation around the vertical axis-azimuth angle φ.
Figure 2. Simplified model helicopter with two inputs and two outputs.
• • • •
u1 – voltage driving the main motor u2 – voltage driving the tail motor ψ – elevation angle φ – azimuth angle
As can be seen in the Fig. 2. the helicopter is controlled by computer. Within the computer the stresses are given voltages u1, u2 which allow the main and tail motors to spin with lower or higher speed depending on the value of given stress on their inputs. Speed of motors spinning, trough propellers which aren’t connected, produces forces in the vertical and horizontal axes, which leads to pitch and rotation of the helicopter body. Basically, in this way, we control the helicopter. B. Control Interface The MF 624 multifunction I/O card is designed for the need of connecting PC compatible computers to real world signals. The MF 624 contains 8 channel fast 14 bit A/D converter with simultaneous sample/hold circuit, 8 independent 14 bit D/A converters, 8 bit digital input port and 8 bit digital output port, 4 quadrature encoder inputs with single-ended or differential interface and 5 timers/counters. The card is designed for standard data acquisition and control applications and optimized for use with Real Time Toolbox for Simulink®. MF 624 features fully 32 bit architecture for fast throughput.
1077
III.
Iψ = I sinψ
(8)
τ 2 = kω 2 l 2 sin ψω 2 2
(9)
τ f = C ϕ signϕ& − Bϕ ϕ&
(10)
THEORETICAL MODELING
Theoretical bases for modeling systems that are used in the paper are given in [20]. When modeling a system it is important to find a balance between simplicity and complexity of the model, according to its purpose and operating conditions. The model has to be clear, concise and flexible, yet it must consider all the relevant sub-processes in the system. In the following section, modeling procedure will be described.
2
where: - moment of inertia around vertical axis - stabilizing motor driving torque - friction torque Coulomb and viscous - main rotor reaction torque - constant for the tail rotor - angular velocity of the tail rotor - viscous friction coefficient (around z-axis) - Coulomb friction coefficient (around z-axis)
Iψ
τ2
A. Elevation Dynamics Let us consider the forces the vertical plane acting on the vertical helicopter body, whose dynamics are given by the following nonlinear equation:
I ψ&& = τ 1 + τ ϕ& − τ f1 − τ m + τ G
(1)
τ m = Fm l sinψ = mgl sinψ = τ g sinψ ,
(2)
τ ϕ& = mlϕ& 2 sinψ ⋅ cosψ =
1 mlϕ& 2 sin 2ψ 2
(4)
τ f1 = Cψ signψ& + Bψ ψ&
(5)
τ G = kGϕ&ω1 cosψ ,
za ϕ&
I.
INTRODUCTION
The helicopter was known to be inherently unstable, complicated and nonlinear dynamic system under a significant influence of disturbances and parameter perturbations. The system has to be stabilized using a feedback controller. The stabilizing controller may be designed by the model-based mathematical approach or by heuristic control algorithms. Due to the complexity of the helicopter dynamics, there have been efforts to apply non-model-based approaches such as fuzzylogic control, neural network (NN) control, or a combination of these. The problem of helicopter control has received much attention and especially during the last two decade, its nonlinear version has been intensively developed [1] - [3]. Nonlinear control techniques, such as feedback linearization, rely heavily upon accurate knowledge of the helicopter dynamics. However, some aerodynamic effects are very difficult to model [4], [5]. Accounting for uncertain effects using robust control is, in general, a conservative approach and may sacrifice achievable performance. In contrast, a control system that adapts the nonlinear dynamics of various flight regimes as they occur has the potential to achieve superior performance throughout the full envelope. To date, most adaptive flight control designs have addressed the issue of the uncertain aerodynamic effects within the context of linear control [6]. Many of the results in adaptive control are derived from Lyapunov stability theory, such as parameter and indirect adaptive control schemes [6], [7]. The sensitivity of some adaptive schemes to disturbances and unmodeled dynamics
prompted many researchers to investigate robust adaptive nonlinear control [8], [9]. Because of their well known abilities to approximate uncertain nonlinear mappings to a high degree of accuracy and their ability to learn, NN’s have come to be seen as a potential solution to many outstanding problems in adaptive and/or robust control of nonlinear systems [10], [11]. At present, most of the works on system identification using neural networks are based on multilayer feedforward neural networks with backpropogation learning or more efficient variations of this algorithm. The literature includes numerous applications of NN’s to flight control systems, a selection of which will be discussed here. Baron et al., employed polynomial networks for fault detection and reconfigurable flight control [12]. Linse and Stengel demonstrated that NN’s could be used to identify aerodynamic coefficients [13]. Applications in which NN’s are used to control super maneuverable aircraft are described by [14] and [15]. Survey papers commenting on the role of NN technology in flight control system design have been contributed by Werbos [16] and Steinberg [17, 18]. In this paper we have used controllers designed in our recent papers [19], [20] and [21] to generate the input/output training data for NN design. The main objective is to mimic the behaviors of these controllers and to improve their control performance. For this purpose, the supervised learning capabilities of NNs can be used for identifying controller models from input/output data. All networks used in this paper are feedforward neural networks with the backpropagation (BP) learning algorithm. This paper is organized as follows. Section II presents the control system for azimuth and elevation angles. In section III the mathematical model of 2DOF helicopter is described. Section IV demonstrates the design of NN controllers those mimic the behaviors of previous designed PID, adaptive and fuzzy controllers. Simulation and experimental results are given in section V. II.
CONTROL SYSTEM DESCRIPTION
The main components of the proposed real-time helicopter control system are shown in Fig. 1. The system is composed of three main components: PC based controller, hardware interface and helicopter model. The neural network (NN) based
,(((
1076
Load Ref. Inputs
NN Controller
RT Workshop
xPC Target
MF 624 card
PWM drives
DC motors
Helicopter body
Ψ, φ
Matlab/ Simulink
Interface bit/rad
32-bit words
MF 624 card
Encoders
Helicopter model
Computer
Figure 1. Block diagram of the proposed real-time control system for a laboratory helicopter model.
controllers are designed in the Matlab/Simulink program package. The second component (MF624) represents the multifunctional card for data acquisition and transmission. It connects the PC and helicopter system and provides implementation control algorithm from the PC to the helicopter system. The helicopter system contains the DC motors with permanent stator magnets, power amplifiers (PWMs), encoders as sensors and axel gear (represents load). In the following subsections the mentioned components will be described.
The axes of the main and tail rotors and the vertical and horizontal helicopter axis are perpendicular to each-other. In this paper the helicopter model can be represented as a nonlinear multi-variable system with two inputs (u1 and u2) and two outputs (ψ and φ are measured in radians or degrees):
A. Helicopter Model Physical model as well as simplified laboratory model helicopter which includes a helicopter body is driven by two motors that drive the main and tail propeller.
The inputs u1 and u2 are measured in machine units ranging from [–1,1]. An interface unit (Fig. 2.), which connects the helicopter and the computer, converts the inputs from machine units to appropriate voltage values that drive the motors. Output ψ denotes the elevation angle, i.e. the angle between the vertical axis and the longitudinal axis of the helicopter body, where as φ denotes the azimuth angle, i.e. the angle in the horizontal plane between the longitudinal axis of the helicopter body and its zero position.
The laboratory helicopter set-up (Fig. 2.) comprises a helicopter body carrying two motors, which drive the main and the tail propeller of the helicopter. The helicopter body is connected to a base so that two degrees of freedom (2 DOF) are enabled: • •
rotation around the horizontal axis-elevation angle ψ rotation around the vertical axis-azimuth angle φ.
Figure 2. Simplified model helicopter with two inputs and two outputs.
• • • •
u1 – voltage driving the main motor u2 – voltage driving the tail motor ψ – elevation angle φ – azimuth angle
As can be seen in the Fig. 2. the helicopter is controlled by computer. Within the computer the stresses are given voltages u1, u2 which allow the main and tail motors to spin with lower or higher speed depending on the value of given stress on their inputs. Speed of motors spinning, trough propellers which aren’t connected, produces forces in the vertical and horizontal axes, which leads to pitch and rotation of the helicopter body. Basically, in this way, we control the helicopter. B. Control Interface The MF 624 multifunction I/O card is designed for the need of connecting PC compatible computers to real world signals. The MF 624 contains 8 channel fast 14 bit A/D converter with simultaneous sample/hold circuit, 8 independent 14 bit D/A converters, 8 bit digital input port and 8 bit digital output port, 4 quadrature encoder inputs with single-ended or differential interface and 5 timers/counters. The card is designed for standard data acquisition and control applications and optimized for use with Real Time Toolbox for Simulink®. MF 624 features fully 32 bit architecture for fast throughput.
1077
III.
Iψ = I sinψ
(8)
τ 2 = kω 2 l 2 sin ψω 2 2
(9)
τ f = C ϕ signϕ& − Bϕ ϕ&
(10)
THEORETICAL MODELING
Theoretical bases for modeling systems that are used in the paper are given in [20]. When modeling a system it is important to find a balance between simplicity and complexity of the model, according to its purpose and operating conditions. The model has to be clear, concise and flexible, yet it must consider all the relevant sub-processes in the system. In the following section, modeling procedure will be described.
2
where: - moment of inertia around vertical axis - stabilizing motor driving torque - friction torque Coulomb and viscous - main rotor reaction torque - constant for the tail rotor - angular velocity of the tail rotor - viscous friction coefficient (around z-axis) - Coulomb friction coefficient (around z-axis)
Iψ
τ2
A. Elevation Dynamics Let us consider the forces the vertical plane acting on the vertical helicopter body, whose dynamics are given by the following nonlinear equation:
I ψ&& = τ 1 + τ ϕ& − τ f1 − τ m + τ G
(1)
τ m = Fm l sinψ = mgl sinψ = τ g sinψ ,
(2)
τ ϕ& = mlϕ& 2 sinψ ⋅ cosψ =
1 mlϕ& 2 sin 2ψ 2
(4)
τ f1 = Cψ signψ& + Bψ ψ&
(5)
τ G = kGϕ&ω1 cosψ ,
za ϕ&
